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

Percentage Accurate: 97.7% → 99.0%

Time: 12.4s

Alternatives: 14

Speedup: 1.0×

• 32.2% 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: 97.7% 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/ 98.4%

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

   5. fma-neg 98.8%

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

   6. sub-neg 98.8%

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

   7. distribute-neg-in 98.8%

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

   8. remove-double-neg 98.8%

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

   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: 97.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(a * N[(b * -0.25), $MachinePrecision] + c), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(t * N[(z * 0.0625), $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/ 98.4%

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

   5. fma-neg 98.8%

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

   6. sub-neg 98.8%

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

   7. distribute-neg-in 98.8%

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

   8. remove-double-neg 98.8%

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

   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. Step-by-step derivation

   1. fma-udef 98.0%

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

   2. fma-udef 97.7%

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

   3. associate-*l/ 97.3%

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

   4. fma-udef 97.3%

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

   5. associate-/r/ 97.3%

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

   6. associate-+r+ 97.3%

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

   7. associate-*l/ 97.6%

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

   8. fma-udef 97.6%

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

   9. +-commutative 97.6%

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

   10. fma-udef 97.6%

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

   11. associate-*l/ 97.3%

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

   12. associate-+r+ 97.3%

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

   13. div-inv 97.3%

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

   14. fma-def 97.3%

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

   15. clear-num 97.3%

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

   16. div-inv 97.3%

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

   17. metadata-eval 97.3%

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

   18. associate-*l/ 97.7%

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

5. Applied egg-rr 97.7%

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

6. Final simplification 97.7%

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

Alternative 3: 65.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + z \cdot \left(t \cdot 0.0625\right)\\ t_2 := c + a \cdot \left(b \cdot -0.25\right)\\ t_3 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -1.85 \cdot 10^{+76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 6.2 \cdot 10^{-289}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 3.1 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 7.2 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 4.2 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* z (* t 0.0625))))
        (t_2 (+ c (* a (* b -0.25))))
        (t_3 (+ c (* x y))))
   (if (<= (* x y) -1.85e+76)
     t_3
     (if (<= (* x y) -1e-82)
       t_1
       (if (<= (* x y) 6.2e-289)
         t_2
         (if (<= (* x y) 3.1e-175)
           t_1
           (if (<= (* x y) 7.2e-101)
             t_2
             (if (<= (* x y) 4.2e+156) 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 + (z * (t * 0.0625));
	double t_2 = c + (a * (b * -0.25));
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -1.85e+76) {
		tmp = t_3;
	} else if ((x * y) <= -1e-82) {
		tmp = t_1;
	} else if ((x * y) <= 6.2e-289) {
		tmp = t_2;
	} else if ((x * y) <= 3.1e-175) {
		tmp = t_1;
	} else if ((x * y) <= 7.2e-101) {
		tmp = t_2;
	} else if ((x * y) <= 4.2e+156) {
		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 + (z * (t * 0.0625d0))
    t_2 = c + (a * (b * (-0.25d0)))
    t_3 = c + (x * y)
    if ((x * y) <= (-1.85d+76)) then
        tmp = t_3
    else if ((x * y) <= (-1d-82)) then
        tmp = t_1
    else if ((x * y) <= 6.2d-289) then
        tmp = t_2
    else if ((x * y) <= 3.1d-175) then
        tmp = t_1
    else if ((x * y) <= 7.2d-101) then
        tmp = t_2
    else if ((x * y) <= 4.2d+156) 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 + (z * (t * 0.0625));
	double t_2 = c + (a * (b * -0.25));
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -1.85e+76) {
		tmp = t_3;
	} else if ((x * y) <= -1e-82) {
		tmp = t_1;
	} else if ((x * y) <= 6.2e-289) {
		tmp = t_2;
	} else if ((x * y) <= 3.1e-175) {
		tmp = t_1;
	} else if ((x * y) <= 7.2e-101) {
		tmp = t_2;
	} else if ((x * y) <= 4.2e+156) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (z * (t * 0.0625))
	t_2 = c + (a * (b * -0.25))
	t_3 = c + (x * y)
	tmp = 0
	if (x * y) <= -1.85e+76:
		tmp = t_3
	elif (x * y) <= -1e-82:
		tmp = t_1
	elif (x * y) <= 6.2e-289:
		tmp = t_2
	elif (x * y) <= 3.1e-175:
		tmp = t_1
	elif (x * y) <= 7.2e-101:
		tmp = t_2
	elif (x * y) <= 4.2e+156:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(z * Float64(t * 0.0625)))
	t_2 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -1.85e+76)
		tmp = t_3;
	elseif (Float64(x * y) <= -1e-82)
		tmp = t_1;
	elseif (Float64(x * y) <= 6.2e-289)
		tmp = t_2;
	elseif (Float64(x * y) <= 3.1e-175)
		tmp = t_1;
	elseif (Float64(x * y) <= 7.2e-101)
		tmp = t_2;
	elseif (Float64(x * y) <= 4.2e+156)
		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 + (z * (t * 0.0625));
	t_2 = c + (a * (b * -0.25));
	t_3 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -1.85e+76)
		tmp = t_3;
	elseif ((x * y) <= -1e-82)
		tmp = t_1;
	elseif ((x * y) <= 6.2e-289)
		tmp = t_2;
	elseif ((x * y) <= 3.1e-175)
		tmp = t_1;
	elseif ((x * y) <= 7.2e-101)
		tmp = t_2;
	elseif ((x * y) <= 4.2e+156)
		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[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.85e+76], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -1e-82], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 6.2e-289], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 3.1e-175], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 7.2e-101], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 4.2e+156], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.85e76 or 4.19999999999999963e156 < (*.f64 x y)

   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 x around inf 79.2%

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

   if -1.85e76 < (*.f64 x y) < -1e-82 or 6.2e-289 < (*.f64 x y) < 3.09999999999999999e-175 or 7.19999999999999999e-101 < (*.f64 x y) < 4.19999999999999963e156

   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 z around inf 71.3%

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

      1. *-commutative 71.3%

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

      2. *-commutative 71.3%

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

      3. associate-*l* 72.1%

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

   4. Simplified 72.1%

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

   if -1e-82 < (*.f64 x y) < 6.2e-289 or 3.09999999999999999e-175 < (*.f64 x y) < 7.19999999999999999e-101

   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 inf 81.7%

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

      1. *-commutative 81.7%

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

      2. associate-*r* 81.7%

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

   4. Simplified 81.7%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.85 \cdot 10^{+76}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-82}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 6.2 \cdot 10^{-289}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 3.1 \cdot 10^{-175}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 7.2 \cdot 10^{-101}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 4.2 \cdot 10^{+156}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 4: 44.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t \cdot 0.0625\right)\\ t_2 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -4.7 \cdot 10^{+86}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.5 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{-287}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 14000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 8 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (* t 0.0625))) (t_2 (* b (* a -0.25))))
   (if (<= (* x y) -4.7e+86)
     (* x y)
     (if (<= (* x y) -5.5e-87)
       t_1
       (if (<= (* x y) 2.2e-287)
         t_2
         (if (<= (* x y) 3e-176)
           t_1
           (if (<= (* x y) 14000000000.0)
             t_2
             (if (<= (* x y) 8e+156) t_1 (* x y)))))))))

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 t_2 = b * (a * -0.25);
	double tmp;
	if ((x * y) <= -4.7e+86) {
		tmp = x * y;
	} else if ((x * y) <= -5.5e-87) {
		tmp = t_1;
	} else if ((x * y) <= 2.2e-287) {
		tmp = t_2;
	} else if ((x * y) <= 3e-176) {
		tmp = t_1;
	} else if ((x * y) <= 14000000000.0) {
		tmp = t_2;
	} else if ((x * y) <= 8e+156) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (t * 0.0625d0)
    t_2 = b * (a * (-0.25d0))
    if ((x * y) <= (-4.7d+86)) then
        tmp = x * y
    else if ((x * y) <= (-5.5d-87)) then
        tmp = t_1
    else if ((x * y) <= 2.2d-287) then
        tmp = t_2
    else if ((x * y) <= 3d-176) then
        tmp = t_1
    else if ((x * y) <= 14000000000.0d0) then
        tmp = t_2
    else if ((x * y) <= 8d+156) then
        tmp = t_1
    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 t_1 = z * (t * 0.0625);
	double t_2 = b * (a * -0.25);
	double tmp;
	if ((x * y) <= -4.7e+86) {
		tmp = x * y;
	} else if ((x * y) <= -5.5e-87) {
		tmp = t_1;
	} else if ((x * y) <= 2.2e-287) {
		tmp = t_2;
	} else if ((x * y) <= 3e-176) {
		tmp = t_1;
	} else if ((x * y) <= 14000000000.0) {
		tmp = t_2;
	} else if ((x * y) <= 8e+156) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = z * (t * 0.0625)
	t_2 = b * (a * -0.25)
	tmp = 0
	if (x * y) <= -4.7e+86:
		tmp = x * y
	elif (x * y) <= -5.5e-87:
		tmp = t_1
	elif (x * y) <= 2.2e-287:
		tmp = t_2
	elif (x * y) <= 3e-176:
		tmp = t_1
	elif (x * y) <= 14000000000.0:
		tmp = t_2
	elif (x * y) <= 8e+156:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(z * Float64(t * 0.0625))
	t_2 = Float64(b * Float64(a * -0.25))
	tmp = 0.0
	if (Float64(x * y) <= -4.7e+86)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -5.5e-87)
		tmp = t_1;
	elseif (Float64(x * y) <= 2.2e-287)
		tmp = t_2;
	elseif (Float64(x * y) <= 3e-176)
		tmp = t_1;
	elseif (Float64(x * y) <= 14000000000.0)
		tmp = t_2;
	elseif (Float64(x * y) <= 8e+156)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = z * (t * 0.0625);
	t_2 = b * (a * -0.25);
	tmp = 0.0;
	if ((x * y) <= -4.7e+86)
		tmp = x * y;
	elseif ((x * y) <= -5.5e-87)
		tmp = t_1;
	elseif ((x * y) <= 2.2e-287)
		tmp = t_2;
	elseif ((x * y) <= 3e-176)
		tmp = t_1;
	elseif ((x * y) <= 14000000000.0)
		tmp = t_2;
	elseif ((x * y) <= 8e+156)
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4.7e+86], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5.5e-87], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2.2e-287], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 3e-176], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 14000000000.0], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 8e+156], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.7000000000000002e86 or 7.9999999999999999e156 < (*.f64 x y)

   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 z around 0 82.8%

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

   3. Taylor expanded in c around 0 78.9%

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

   4. Taylor expanded in x around inf 74.9%

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

   if -4.7000000000000002e86 < (*.f64 x y) < -5.5000000000000004e-87 or 2.2e-287 < (*.f64 x y) < 3e-176 or 1.4e10 < (*.f64 x y) < 7.9999999999999999e156

   1. Initial program 99.0%

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

      1. associate-+l- 99.0%

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

      2. associate--l+ 99.0%

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

      3. fma-def 99.0%

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

      4. associate-*l/ 100.0%

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

      5. fma-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. associate-/l* 100.0%

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

      10. distribute-frac-neg 100.0%

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

      11. associate-/r/ 100.0%

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

      12. fma-def 100.0%

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

      13. neg-mul-1 100.0%

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

      14. *-commutative 100.0%

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

      15. associate-/l* 100.0%

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

      16. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-udef 100.0%

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

      3. associate-*l/ 99.0%

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

      4. fma-udef 99.0%

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

      5. associate-/r/ 99.0%

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

      6. associate-+r+ 99.0%

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

      7. associate-*l/ 100.0%

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

      8. fma-udef 100.0%

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

      9. +-commutative 100.0%

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

      10. fma-udef 100.0%

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

      11. associate-*l/ 99.0%

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

      12. associate-+r+ 99.0%

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

      13. div-inv 99.0%

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

      14. fma-def 99.0%

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

      15. clear-num 99.0%

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

      16. div-inv 99.0%

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

      17. metadata-eval 99.0%

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

      18. associate-*l/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in t around inf 43.9%

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

      1. associate-*r* 44.9%

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

      2. *-commutative 44.9%

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

      3. *-commutative 44.9%

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

      4. *-commutative 44.9%

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

   8. Simplified 44.9%

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

   if -5.5000000000000004e-87 < (*.f64 x y) < 2.2e-287 or 3e-176 < (*.f64 x y) < 1.4e10

   1. Initial program 98.9%

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

      1. associate-+l- 98.9%

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

      2. associate--l+ 98.9%

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

      3. fma-def 98.9%

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

      4. associate-*l/ 98.9%

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

      5. fma-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. associate-/l* 99.8%

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

      10. distribute-frac-neg 99.8%

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

      11. associate-/r/ 100.0%

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

      12. fma-def 100.0%

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

      13. neg-mul-1 100.0%

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

      14. *-commutative 100.0%

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

      15. associate-/l* 100.0%

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

      16. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-udef 98.9%

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

      3. associate-*l/ 98.9%

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

      4. fma-udef 98.9%

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

      5. associate-/r/ 98.8%

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

      6. associate-+r+ 98.8%

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

      7. associate-*l/ 98.8%

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

      8. fma-udef 98.8%

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

      9. +-commutative 98.8%

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

      10. fma-udef 98.8%

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

      11. associate-*l/ 98.8%

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

      12. associate-+r+ 98.8%

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

      13. div-inv 98.9%

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

      14. fma-def 98.9%

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

      15. clear-num 98.9%

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

      16. div-inv 98.9%

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

      17. metadata-eval 98.9%

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

      18. associate-*l/ 98.9%

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

   5. Applied egg-rr 98.9%

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

   6. Taylor expanded in x around 0 94.0%

      \[\leadsto \color{blue}{\left(c + -0.25 \cdot \left(a \cdot b\right)\right)} + t \cdot \left(z \cdot 0.0625\right) \]
   7. Step-by-step derivation

      1. +-commutative 94.0%

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

      2. *-commutative 94.0%

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

      3. associate-*r* 94.0%

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

      4. fma-udef 94.0%

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

      5. *-commutative 94.0%

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

   8. Simplified 94.0%

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

   9. Taylor expanded in a around inf 48.6%

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

       1. associate-*r* 48.6%

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

   11. Simplified 48.6%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.7 \cdot 10^{+86}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -5.5 \cdot 10^{-87}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 2.2 \cdot 10^{-287}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{-176}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 14000000000:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 8 \cdot 10^{+156}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 5: 65.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + z \cdot \left(t \cdot 0.0625\right)\\ t_2 := x \cdot y + t \cdot \left(z \cdot 0.0625\right)\\ t_3 := c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -4.1 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -1.3 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{-288}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq 4.6 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 1.35 \cdot 10^{-80}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* z (* t 0.0625))))
        (t_2 (+ (* x y) (* t (* z 0.0625))))
        (t_3 (+ c (* a (* b -0.25)))))
   (if (<= (* x y) -4.1e+88)
     t_2
     (if (<= (* x y) -1.3e-80)
       t_1
       (if (<= (* x y) 3.2e-288)
         t_3
         (if (<= (* x y) 4.6e-175) t_1 (if (<= (* x y) 1.35e-80) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (z * (t * 0.0625));
	double t_2 = (x * y) + (t * (z * 0.0625));
	double t_3 = c + (a * (b * -0.25));
	double tmp;
	if ((x * y) <= -4.1e+88) {
		tmp = t_2;
	} else if ((x * y) <= -1.3e-80) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e-288) {
		tmp = t_3;
	} else if ((x * y) <= 4.6e-175) {
		tmp = t_1;
	} else if ((x * y) <= 1.35e-80) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = c + (z * (t * 0.0625d0))
    t_2 = (x * y) + (t * (z * 0.0625d0))
    t_3 = c + (a * (b * (-0.25d0)))
    if ((x * y) <= (-4.1d+88)) then
        tmp = t_2
    else if ((x * y) <= (-1.3d-80)) then
        tmp = t_1
    else if ((x * y) <= 3.2d-288) then
        tmp = t_3
    else if ((x * y) <= 4.6d-175) then
        tmp = t_1
    else if ((x * y) <= 1.35d-80) then
        tmp = t_3
    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 + (z * (t * 0.0625));
	double t_2 = (x * y) + (t * (z * 0.0625));
	double t_3 = c + (a * (b * -0.25));
	double tmp;
	if ((x * y) <= -4.1e+88) {
		tmp = t_2;
	} else if ((x * y) <= -1.3e-80) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e-288) {
		tmp = t_3;
	} else if ((x * y) <= 4.6e-175) {
		tmp = t_1;
	} else if ((x * y) <= 1.35e-80) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (z * (t * 0.0625))
	t_2 = (x * y) + (t * (z * 0.0625))
	t_3 = c + (a * (b * -0.25))
	tmp = 0
	if (x * y) <= -4.1e+88:
		tmp = t_2
	elif (x * y) <= -1.3e-80:
		tmp = t_1
	elif (x * y) <= 3.2e-288:
		tmp = t_3
	elif (x * y) <= 4.6e-175:
		tmp = t_1
	elif (x * y) <= 1.35e-80:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(z * Float64(t * 0.0625)))
	t_2 = Float64(Float64(x * y) + Float64(t * Float64(z * 0.0625)))
	t_3 = Float64(c + Float64(a * Float64(b * -0.25)))
	tmp = 0.0
	if (Float64(x * y) <= -4.1e+88)
		tmp = t_2;
	elseif (Float64(x * y) <= -1.3e-80)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.2e-288)
		tmp = t_3;
	elseif (Float64(x * y) <= 4.6e-175)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.35e-80)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (z * (t * 0.0625));
	t_2 = (x * y) + (t * (z * 0.0625));
	t_3 = c + (a * (b * -0.25));
	tmp = 0.0;
	if ((x * y) <= -4.1e+88)
		tmp = t_2;
	elseif ((x * y) <= -1.3e-80)
		tmp = t_1;
	elseif ((x * y) <= 3.2e-288)
		tmp = t_3;
	elseif ((x * y) <= 4.6e-175)
		tmp = t_1;
	elseif ((x * y) <= 1.35e-80)
		tmp = t_3;
	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[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4.1e+88], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -1.3e-80], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.2e-288], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 4.6e-175], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.35e-80], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.10000000000000028e88 or 1.3500000000000001e-80 < (*.f64 x y)

   1. Initial program 95.9%

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

      1. associate-+l- 95.9%

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

      2. associate--l+ 95.9%

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

      3. fma-def 97.6%

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

      4. associate-*l/ 97.6%

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

      5. fma-neg 97.6%

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

      6. sub-neg 97.6%

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

      7. distribute-neg-in 97.6%

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

      8. remove-double-neg 97.6%

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

      9. associate-/l* 97.5%

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

      10. distribute-frac-neg 97.5%

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

      11. associate-/r/ 97.6%

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

      12. fma-def 97.6%

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

      13. neg-mul-1 97.6%

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

      14. *-commutative 97.6%

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

      15. associate-/l* 97.6%

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

      16. metadata-eval 97.6%

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

   3. Simplified 97.6%

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

      1. fma-udef 95.9%

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

      2. fma-udef 95.9%

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

      3. associate-*l/ 95.9%

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

      4. fma-udef 95.9%

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

      5. associate-/r/ 95.9%

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

      6. associate-+r+ 95.9%

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

      7. associate-*l/ 95.9%

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

      8. fma-udef 95.9%

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

      9. +-commutative 95.9%

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

      10. fma-udef 95.9%

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

      11. associate-*l/ 95.9%

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

      12. associate-+r+ 95.9%

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

      13. div-inv 95.9%

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

      14. fma-def 95.9%

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

      15. clear-num 95.9%

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

      16. div-inv 95.9%

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

      17. metadata-eval 95.9%

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

      18. associate-*l/ 95.9%

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

   5. Applied egg-rr 95.9%

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

   6. Taylor expanded in x around inf 76.5%

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

   if -4.10000000000000028e88 < (*.f64 x y) < -1.3e-80 or 3.2e-288 < (*.f64 x y) < 4.6e-175

   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 z around inf 80.4%

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

      1. *-commutative 80.4%

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

      2. *-commutative 80.4%

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

      3. associate-*l* 81.8%

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

   4. Simplified 81.8%

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

   if -1.3e-80 < (*.f64 x y) < 3.2e-288 or 4.6e-175 < (*.f64 x y) < 1.3500000000000001e-80

   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 a around inf 81.1%

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

      1. *-commutative 81.1%

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

      2. associate-*r* 81.1%

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

   4. Simplified 81.1%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.1 \cdot 10^{+88}:\\ \;\;\;\;x \cdot y + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq -1.3 \cdot 10^{-80}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{-288}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 4.6 \cdot 10^{-175}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 1.35 \cdot 10^{-80}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]

Alternative 6: 42.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+83}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{-279}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 5.6 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 1.12 \cdot 10^{-85}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 4.5 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (* t 0.0625))))
   (if (<= (* x y) -2.8e+83)
     (* x y)
     (if (<= (* x y) 1.9e-279)
       c
       (if (<= (* x y) 5.6e-226)
         t_1
         (if (<= (* x y) 1.12e-85)
           c
           (if (<= (* x y) 4.5e+156) t_1 (* x y))))))))

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 ((x * y) <= -2.8e+83) {
		tmp = x * y;
	} else if ((x * y) <= 1.9e-279) {
		tmp = c;
	} else if ((x * y) <= 5.6e-226) {
		tmp = t_1;
	} else if ((x * y) <= 1.12e-85) {
		tmp = c;
	} else if ((x * y) <= 4.5e+156) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z * (t * 0.0625d0)
    if ((x * y) <= (-2.8d+83)) then
        tmp = x * y
    else if ((x * y) <= 1.9d-279) then
        tmp = c
    else if ((x * y) <= 5.6d-226) then
        tmp = t_1
    else if ((x * y) <= 1.12d-85) then
        tmp = c
    else if ((x * y) <= 4.5d+156) then
        tmp = t_1
    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 t_1 = z * (t * 0.0625);
	double tmp;
	if ((x * y) <= -2.8e+83) {
		tmp = x * y;
	} else if ((x * y) <= 1.9e-279) {
		tmp = c;
	} else if ((x * y) <= 5.6e-226) {
		tmp = t_1;
	} else if ((x * y) <= 1.12e-85) {
		tmp = c;
	} else if ((x * y) <= 4.5e+156) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = z * (t * 0.0625)
	tmp = 0
	if (x * y) <= -2.8e+83:
		tmp = x * y
	elif (x * y) <= 1.9e-279:
		tmp = c
	elif (x * y) <= 5.6e-226:
		tmp = t_1
	elif (x * y) <= 1.12e-85:
		tmp = c
	elif (x * y) <= 4.5e+156:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(z * Float64(t * 0.0625))
	tmp = 0.0
	if (Float64(x * y) <= -2.8e+83)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 1.9e-279)
		tmp = c;
	elseif (Float64(x * y) <= 5.6e-226)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.12e-85)
		tmp = c;
	elseif (Float64(x * y) <= 4.5e+156)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	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 ((x * y) <= -2.8e+83)
		tmp = x * y;
	elseif ((x * y) <= 1.9e-279)
		tmp = c;
	elseif ((x * y) <= 5.6e-226)
		tmp = t_1;
	elseif ((x * y) <= 1.12e-85)
		tmp = c;
	elseif ((x * y) <= 4.5e+156)
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.8e+83], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.9e-279], c, If[LessEqual[N[(x * y), $MachinePrecision], 5.6e-226], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.12e-85], c, If[LessEqual[N[(x * y), $MachinePrecision], 4.5e+156], t$95$1, N[(x * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.8e83 or 4.50000000000000031e156 < (*.f64 x y)

   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 z around 0 82.8%

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

   3. Taylor expanded in c around 0 78.9%

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

   4. Taylor expanded in x around inf 74.9%

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

   if -2.8e83 < (*.f64 x y) < 1.90000000000000016e-279 or 5.60000000000000016e-226 < (*.f64 x y) < 1.12000000000000004e-85

   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 c around inf 36.7%

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

   if 1.90000000000000016e-279 < (*.f64 x y) < 5.60000000000000016e-226 or 1.12000000000000004e-85 < (*.f64 x y) < 4.50000000000000031e156

   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%

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

      2. associate--l+ 100.0%

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

      3. fma-def 100.0%

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

      4. associate-*l/ 100.0%

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

      5. fma-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. associate-/l* 99.9%

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

      10. distribute-frac-neg 99.9%

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

      11. associate-/r/ 100.0%

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

      12. fma-def 100.0%

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

      13. neg-mul-1 100.0%

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

      14. *-commutative 100.0%

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

      15. associate-/l* 100.0%

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

      16. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-udef 100.0%

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

      3. associate-*l/ 100.0%

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

      4. fma-udef 100.0%

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

      5. associate-/r/ 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-*l/ 99.9%

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

      8. fma-udef 99.9%

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

      9. +-commutative 99.9%

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

      10. fma-udef 99.9%

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

      11. associate-*l/ 99.9%

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

      12. associate-+r+ 99.9%

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

      13. div-inv 100.0%

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

      14. fma-def 100.0%

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

      15. clear-num 100.0%

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

      16. div-inv 100.0%

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

      17. metadata-eval 100.0%

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

      18. associate-*l/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in t around inf 43.7%

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

      1. associate-*r* 43.7%

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

      2. *-commutative 43.7%

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

      3. *-commutative 43.7%

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

      4. *-commutative 43.7%

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

   8. Simplified 43.7%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.8 \cdot 10^{+83}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{-279}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 5.6 \cdot 10^{-226}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 1.12 \cdot 10^{-85}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 4.5 \cdot 10^{+156}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 7: 89.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -2.3 \cdot 10^{+74} \lor \neg \left(x \cdot y \leq 5.6 \cdot 10^{+56}\right):\\ \;\;\;\;c + \left(x \cdot y + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + t_1\right) - 0.25 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (or (<= (* x y) -2.3e+74) (not (<= (* x y) 5.6e+56)))
     (+ c (+ (* x y) t_1))
     (- (+ c t_1) (* 0.25 (* a b))))))

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 tmp;
	if (((x * y) <= -2.3e+74) || !((x * y) <= 5.6e+56)) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + t_1) - (0.25 * (a * b));
	}
	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 = 0.0625d0 * (z * t)
    if (((x * y) <= (-2.3d+74)) .or. (.not. ((x * y) <= 5.6d+56))) then
        tmp = c + ((x * y) + t_1)
    else
        tmp = (c + t_1) - (0.25d0 * (a * b))
    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 tmp;
	if (((x * y) <= -2.3e+74) || !((x * y) <= 5.6e+56)) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + t_1) - (0.25 * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if ((x * y) <= -2.3e+74) or not ((x * y) <= 5.6e+56):
		tmp = c + ((x * y) + t_1)
	else:
		tmp = (c + t_1) - (0.25 * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if ((Float64(x * y) <= -2.3e+74) || !(Float64(x * y) <= 5.6e+56))
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	else
		tmp = Float64(Float64(c + t_1) - Float64(0.25 * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if (((x * y) <= -2.3e+74) || ~(((x * y) <= 5.6e+56)))
		tmp = c + ((x * y) + t_1);
	else
		tmp = (c + t_1) - (0.25 * (a * b));
	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]}, If[Or[LessEqual[N[(x * y), $MachinePrecision], -2.3e+74], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5.6e+56]], $MachinePrecision]], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(c + t$95$1), $MachinePrecision] - N[(0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.2999999999999999e74 or 5.60000000000000017e56 < (*.f64 x y)

   1. Initial program 94.9%

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

   2. Taylor expanded in a around 0 89.6%

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

   if -2.2999999999999999e74 < (*.f64 x y) < 5.60000000000000017e56

   1. Initial program 98.8%

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

   2. Taylor expanded in x around 0 94.4%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.3 \cdot 10^{+74} \lor \neg \left(x \cdot y \leq 5.6 \cdot 10^{+56}\right):\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - 0.25 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 8: 87.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right) + t_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+162}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))))
   (if (<= (* a b) -1e+137)
     (+ (* t (* z 0.0625)) t_1)
     (if (<= (* a b) 5e+162) (+ c (+ (* x y) (* 0.0625 (* z t)))) (+ c t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double tmp;
	if ((a * b) <= -1e+137) {
		tmp = (t * (z * 0.0625)) + t_1;
	} else if ((a * b) <= 5e+162) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + 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 = a * (b * (-0.25d0))
    if ((a * b) <= (-1d+137)) then
        tmp = (t * (z * 0.0625d0)) + t_1
    else if ((a * b) <= 5d+162) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = c + 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 = a * (b * -0.25);
	double tmp;
	if ((a * b) <= -1e+137) {
		tmp = (t * (z * 0.0625)) + t_1;
	} else if ((a * b) <= 5e+162) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	tmp = 0
	if (a * b) <= -1e+137:
		tmp = (t * (z * 0.0625)) + t_1
	elif (a * b) <= 5e+162:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = c + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	tmp = 0.0
	if (Float64(a * b) <= -1e+137)
		tmp = Float64(Float64(t * Float64(z * 0.0625)) + t_1);
	elseif (Float64(a * b) <= 5e+162)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(c + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (b * -0.25);
	tmp = 0.0;
	if ((a * b) <= -1e+137)
		tmp = (t * (z * 0.0625)) + t_1;
	elseif ((a * b) <= 5e+162)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = c + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1e+137], N[(N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+162], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1e137

   1. Initial program 93.7%

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

      1. associate-+l- 93.7%

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

      2. associate--l+ 93.7%

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

      3. fma-def 95.8%

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

      4. associate-*l/ 95.8%

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

      5. fma-neg 95.8%

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

      6. sub-neg 95.8%

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

      7. distribute-neg-in 95.8%

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

      8. remove-double-neg 95.8%

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

      9. associate-/l* 95.7%

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

      10. distribute-frac-neg 95.7%

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

      11. associate-/r/ 95.8%

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

      12. fma-def 95.8%

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

      13. neg-mul-1 95.8%

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

      14. *-commutative 95.8%

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

      15. associate-/l* 95.8%

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

      16. metadata-eval 95.8%

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

   3. Simplified 95.8%

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

      1. fma-udef 93.8%

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

      2. fma-udef 93.8%

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

      3. associate-*l/ 93.8%

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

      4. fma-udef 93.7%

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

      5. associate-/r/ 93.7%

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

      6. associate-+r+ 93.7%

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

      7. associate-*l/ 93.7%

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

      8. fma-udef 93.7%

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

      9. +-commutative 93.7%

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

      10. fma-udef 93.7%

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

      11. associate-*l/ 93.7%

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

      12. associate-+r+ 93.7%

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

      13. div-inv 93.7%

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

      14. fma-def 93.7%

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

      15. clear-num 93.8%

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

      16. div-inv 93.8%

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

      17. metadata-eval 93.8%

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

      18. associate-*l/ 93.8%

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

   5. Applied egg-rr 93.8%

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

   6. Taylor expanded in a around inf 82.8%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + t \cdot \left(z \cdot 0.0625\right) \]
   7. Step-by-step derivation

      1. *-commutative 82.8%

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

      2. associate-*r* 82.8%

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

      3. *-commutative 82.8%

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

   8. Simplified 82.8%

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

   if -1e137 < (*.f64 a b) < 4.9999999999999997e162

   1. Initial program 99.6%

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

   2. Taylor expanded in a around 0 91.1%

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

   if 4.9999999999999997e162 < (*.f64 a b)

   1. Initial program 89.3%

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

   2. Taylor expanded in a around inf 79.2%

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

      1. *-commutative 79.2%

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

      2. associate-*r* 79.2%

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

   4. Simplified 79.2%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right) + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+162}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]

Alternative 9: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ c + \left(t \cdot \left(z \cdot 0.0625\right) + \left(x \cdot y - \frac{a}{\frac{4}{b}}\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ c (+ (* t (* z 0.0625)) (- (* x y) (/ a (/ 4.0 b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + ((t * (z * 0.0625)) + ((x * y) - (a / (4.0 / b))));
}

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 + ((t * (z * 0.0625d0)) + ((x * y) - (a / (4.0d0 / b))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + ((t * (z * 0.0625)) + ((x * y) - (a / (4.0 / b))));
}

Python

def code(x, y, z, t, a, b, c):
	return c + ((t * (z * 0.0625)) + ((x * y) - (a / (4.0 / b))))

Julia

function code(x, y, z, t, a, b, c)
	return Float64(c + Float64(Float64(t * Float64(z * 0.0625)) + Float64(Float64(x * y) - Float64(a / Float64(4.0 / b)))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = c + ((t * (z * 0.0625)) + ((x * y) - (a / (4.0 / b))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(c + N[(N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] - N[(a / N[(4.0 / b), $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. +-commutative 97.3%

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

   2. associate--l+ 97.3%

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

   3. associate-*l/ 97.6%

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

   4. *-commutative 97.6%

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

   5. div-inv 97.6%

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

   6. metadata-eval 97.6%

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

   7. associate-/l* 97.6%

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

3. Applied egg-rr 97.6%

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

4. Final simplification 97.6%

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

Alternative 10: 65.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.5 \cdot 10^{+76} \lor \neg \left(x \cdot y \leq 1.02 \cdot 10^{+58}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.5e+76) (not (<= (* x y) 1.02e+58)))
   (+ c (* x y))
   (+ c (* a (* b -0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.5e+76) || !((x * y) <= 1.02e+58)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (a * (b * -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 (((x * y) <= (-1.5d+76)) .or. (.not. ((x * y) <= 1.02d+58))) then
        tmp = c + (x * y)
    else
        tmp = c + (a * (b * (-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 (((x * y) <= -1.5e+76) || !((x * y) <= 1.02e+58)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.5e+76) or not ((x * y) <= 1.02e+58):
		tmp = c + (x * y)
	else:
		tmp = c + (a * (b * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1.5e+76) || !(Float64(x * y) <= 1.02e+58))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1.5e+76) || ~(((x * y) <= 1.02e+58)))
		tmp = c + (x * y);
	else
		tmp = c + (a * (b * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.5e+76], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.02e+58]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.4999999999999999e76 or 1.02000000000000005e58 < (*.f64 x y)

   1. Initial program 94.9%

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

   2. Taylor expanded in x around inf 73.8%

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

   if -1.4999999999999999e76 < (*.f64 x y) < 1.02000000000000005e58

   1. Initial program 98.8%

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

   2. Taylor expanded in a around inf 65.6%

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

      1. *-commutative 65.6%

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

      2. associate-*r* 65.6%

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

   4. Simplified 65.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.5 \cdot 10^{+76} \lor \neg \left(x \cdot y \leq 1.02 \cdot 10^{+58}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]

Alternative 11: 83.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+57} \lor \neg \left(z \leq 2.5 \cdot 10^{-84}\right):\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -3.8e+57) (not (<= z 2.5e-84)))
   (+ c (+ (* x y) (* 0.0625 (* z t))))
   (- (+ c (* x y)) (* 0.25 (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.8e+57) || !(z <= 2.5e-84)) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (c + (x * y)) - (0.25 * (a * b));
	}
	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 ((z <= (-3.8d+57)) .or. (.not. (z <= 2.5d-84))) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = (c + (x * y)) - (0.25d0 * (a * b))
    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 ((z <= -3.8e+57) || !(z <= 2.5e-84)) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (c + (x * y)) - (0.25 * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -3.8e+57) or not (z <= 2.5e-84):
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = (c + (x * y)) - (0.25 * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -3.8e+57) || !(z <= 2.5e-84))
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(0.25 * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -3.8e+57) || ~((z <= 2.5e-84)))
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = (c + (x * y)) - (0.25 * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -3.8e+57], N[Not[LessEqual[z, 2.5e-84]], $MachinePrecision]], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7999999999999999e57 or 2.5000000000000001e-84 < z

   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 a around 0 76.4%

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

   if -3.7999999999999999e57 < z < 2.5000000000000001e-84

   1. Initial program 97.8%

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

   2. Taylor expanded in z around 0 92.2%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+57} \lor \neg \left(z \leq 2.5 \cdot 10^{-84}\right):\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 12: 52.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{if}\;t \leq -8200000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 0.03:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+67}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+189}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* z (* t 0.0625))))
   (if (<= t -8200000000.0)
     t_2
     (if (<= t 0.03)
       t_1
       (if (<= t 3.2e+67) (* b (* a -0.25)) (if (<= t 1.4e+189) 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 = z * (t * 0.0625);
	double tmp;
	if (t <= -8200000000.0) {
		tmp = t_2;
	} else if (t <= 0.03) {
		tmp = t_1;
	} else if (t <= 3.2e+67) {
		tmp = b * (a * -0.25);
	} else if (t <= 1.4e+189) {
		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 = z * (t * 0.0625d0)
    if (t <= (-8200000000.0d0)) then
        tmp = t_2
    else if (t <= 0.03d0) then
        tmp = t_1
    else if (t <= 3.2d+67) then
        tmp = b * (a * (-0.25d0))
    else if (t <= 1.4d+189) 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 = z * (t * 0.0625);
	double tmp;
	if (t <= -8200000000.0) {
		tmp = t_2;
	} else if (t <= 0.03) {
		tmp = t_1;
	} else if (t <= 3.2e+67) {
		tmp = b * (a * -0.25);
	} else if (t <= 1.4e+189) {
		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 = z * (t * 0.0625)
	tmp = 0
	if t <= -8200000000.0:
		tmp = t_2
	elif t <= 0.03:
		tmp = t_1
	elif t <= 3.2e+67:
		tmp = b * (a * -0.25)
	elif t <= 1.4e+189:
		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(z * Float64(t * 0.0625))
	tmp = 0.0
	if (t <= -8200000000.0)
		tmp = t_2;
	elseif (t <= 0.03)
		tmp = t_1;
	elseif (t <= 3.2e+67)
		tmp = Float64(b * Float64(a * -0.25));
	elseif (t <= 1.4e+189)
		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 = z * (t * 0.0625);
	tmp = 0.0;
	if (t <= -8200000000.0)
		tmp = t_2;
	elseif (t <= 0.03)
		tmp = t_1;
	elseif (t <= 3.2e+67)
		tmp = b * (a * -0.25);
	elseif (t <= 1.4e+189)
		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[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8200000000.0], t$95$2, If[LessEqual[t, 0.03], t$95$1, If[LessEqual[t, 3.2e+67], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+189], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.2e9 or 1.40000000000000003e189 < t

   1. Initial program 95.5%

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

      1. associate-+l- 95.5%

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

      2. associate--l+ 95.5%

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

      3. fma-def 95.5%

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

      4. associate-*l/ 96.4%

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

      5. fma-neg 97.6%

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

      6. sub-neg 97.6%

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

      7. distribute-neg-in 97.6%

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

      8. remove-double-neg 97.6%

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

      9. associate-/l* 97.6%

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

      10. distribute-frac-neg 97.6%

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

      11. associate-/r/ 97.6%

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

      12. fma-def 97.6%

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

      13. neg-mul-1 97.6%

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

      14. *-commutative 97.6%

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

      15. associate-/l* 97.6%

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

      16. metadata-eval 97.6%

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

   3. Simplified 97.6%

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

      1. fma-udef 97.6%

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

      2. fma-udef 96.4%

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

      3. associate-*l/ 95.5%

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

      4. fma-udef 95.5%

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

      5. associate-/r/ 95.4%

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

      6. associate-+r+ 95.4%

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

      7. associate-*l/ 96.4%

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

      8. fma-udef 96.4%

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

      9. +-commutative 96.4%

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

      10. fma-udef 96.4%

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

      11. associate-*l/ 95.4%

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

      12. associate-+r+ 95.4%

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

      13. div-inv 95.4%

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

      14. fma-def 95.4%

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

      15. clear-num 95.5%

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

      16. div-inv 95.5%

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

      17. metadata-eval 95.5%

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

      18. associate-*l/ 96.4%

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

   5. Applied egg-rr 96.4%

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

   6. Taylor expanded in t around inf 51.4%

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

      1. associate-*r* 52.3%

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

      2. *-commutative 52.3%

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

      3. *-commutative 52.3%

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

      4. *-commutative 52.3%

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

   8. Simplified 52.3%

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

   if -8.2e9 < t < 0.029999999999999999 or 3.19999999999999983e67 < t < 1.40000000000000003e189

   1. Initial program 98.1%

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

   2. Taylor expanded in x around inf 58.9%

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

   if 0.029999999999999999 < t < 3.19999999999999983e67

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l+ 99.9%

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

      3. fma-def 99.9%

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

      4. associate-*l/ 99.9%

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

      5. fma-neg 99.9%

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

      6. sub-neg 99.9%

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

      7. distribute-neg-in 99.9%

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

      8. remove-double-neg 99.9%

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

      9. associate-/l* 99.8%

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

      10. distribute-frac-neg 99.8%

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

      11. associate-/r/ 99.9%

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

      12. fma-def 100.0%

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

      13. neg-mul-1 100.0%

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

      14. *-commutative 100.0%

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

      15. associate-/l* 100.0%

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

      16. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. fma-udef 100.0%

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

      3. associate-*l/ 100.0%

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

      4. fma-udef 99.9%

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

      5. associate-/r/ 99.8%

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

      6. associate-+r+ 99.8%

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

      7. associate-*l/ 99.8%

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

      8. fma-udef 99.8%

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

      9. +-commutative 99.8%

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

      10. fma-udef 99.8%

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

      11. associate-*l/ 99.8%

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

      12. associate-+r+ 99.8%

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

      13. div-inv 99.9%

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

      14. fma-def 99.9%

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

      15. clear-num 100.0%

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

      16. div-inv 100.0%

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

      17. metadata-eval 100.0%

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

      18. associate-*l/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 86.7%

      \[\leadsto \color{blue}{\left(c + -0.25 \cdot \left(a \cdot b\right)\right)} + t \cdot \left(z \cdot 0.0625\right) \]
   7. Step-by-step derivation

      1. +-commutative 86.7%

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

      2. *-commutative 86.7%

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

      3. associate-*r* 86.7%

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

      4. fma-udef 86.8%

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

      5. *-commutative 86.8%

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

   8. Simplified 86.8%

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

   9. Taylor expanded in a around inf 46.3%

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

       1. associate-*r* 46.3%

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

   11. Simplified 46.3%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8200000000:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;t \leq 0.03:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+67}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+189}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \]

Alternative 13: 41.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.3 \cdot 10^{+85} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+149}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.3e+85) (not (<= (* x y) 2e+149))) (* x y) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.3e+85) || !((x * y) <= 2e+149)) {
		tmp = x * y;
	} 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 (((x * y) <= (-1.3d+85)) .or. (.not. ((x * y) <= 2d+149))) then
        tmp = x * y
    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 (((x * y) <= -1.3e+85) || !((x * y) <= 2e+149)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.3e+85) or not ((x * y) <= 2e+149):
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1.3e+85) || !(Float64(x * y) <= 2e+149))
		tmp = Float64(x * y);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1.3e+85) || ~(((x * y) <= 2e+149)))
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.3e+85], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+149]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.30000000000000005e85 or 2.0000000000000001e149 < (*.f64 x y)

   1. Initial program 94.0%

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

   2. Taylor expanded in z around 0 82.3%

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

   3. Taylor expanded in c around 0 78.5%

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

   4. Taylor expanded in x around inf 73.4%

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

   if -1.30000000000000005e85 < (*.f64 x y) < 2.0000000000000001e149

   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 c around inf 31.5%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.3 \cdot 10^{+85} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+149}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 14: 22.4% 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. Taylor expanded in c around inf 23.3%

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

3. Final simplification 23.3%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023334 
(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))