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

Percentage Accurate: 97.8% → 99.0%

Time: 9.1s

Alternatives: 16

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.8% 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 98.0%

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

   1. associate-+l- 98.0%

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

   2. associate--l+ 98.0%

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

   3. fma-def 98.4%

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

   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 99.2%

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

   6. sub-neg 99.2%

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

   7. distribute-neg-in 99.2%

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

   8. remove-double-neg 99.2%

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

   9. associate-/l* 99.2%

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

   10. distribute-frac-neg 99.2%

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

   11. associate-/r/ 99.2%

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

   12. fma-def 99.2%

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

   13. neg-mul-1 99.2%

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

   14. *-commutative 99.2%

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

   15. associate-/l* 99.2%

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

   16. metadata-eval 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 98.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. associate-+l- 98.0%

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

   2. associate--l+ 98.0%

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

   3. fma-def 98.4%

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

   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 99.2%

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

   6. sub-neg 99.2%

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

   7. distribute-neg-in 99.2%

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

   8. remove-double-neg 99.2%

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

   9. associate-/l* 99.2%

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

   10. distribute-frac-neg 99.2%

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

   11. associate-/r/ 99.2%

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

   12. fma-def 99.2%

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

   13. neg-mul-1 99.2%

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

   14. *-commutative 99.2%

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

   15. associate-/l* 99.2%

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

   16. metadata-eval 99.2%

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

3. Simplified 99.2%

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

   1. fma-udef 98.4%

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

   2. div-inv 98.4%

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

   3. metadata-eval 98.4%

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

   4. div-inv 98.4%

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

   5. metadata-eval 98.4%

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

5. Applied egg-rr 98.4%

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

6. Final simplification 98.4%

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

Alternative 3: 98.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. associate-+l- 98.0%

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

   2. fma-def 98.4%

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

   3. *-commutative 98.4%

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

   4. associate-/l* 98.3%

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

   5. associate-/l* 98.3%

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

3. Simplified 98.3%

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

4. Final simplification 98.3%

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

Alternative 4: 57.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ t_3 := -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \cdot b \leq -3.8 \cdot 10^{+47}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \cdot b \leq -5.5:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -1.25 \cdot 10^{-109}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 4.2 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 1.3 \cdot 10^{-85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 2.7 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 1.32 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 3.6 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* 0.0625 (* z t))) (t_3 (* -0.25 (* a b))))
   (if (<= (* a b) -3.8e+47)
     t_3
     (if (<= (* a b) -5.5)
       t_1
       (if (<= (* a b) -1.25e-109)
         t_2
         (if (<= (* a b) 4.2e-185)
           t_1
           (if (<= (* a b) 1.3e-85)
             t_2
             (if (<= (* a b) 2.7e-43)
               t_1
               (if (<= (* a b) 1.32e-15)
                 t_2
                 (if (<= (* a b) 3.6e+84) t_1 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = 0.0625 * (z * t);
	double t_3 = -0.25 * (a * b);
	double tmp;
	if ((a * b) <= -3.8e+47) {
		tmp = t_3;
	} else if ((a * b) <= -5.5) {
		tmp = t_1;
	} else if ((a * b) <= -1.25e-109) {
		tmp = t_2;
	} else if ((a * b) <= 4.2e-185) {
		tmp = t_1;
	} else if ((a * b) <= 1.3e-85) {
		tmp = t_2;
	} else if ((a * b) <= 2.7e-43) {
		tmp = t_1;
	} else if ((a * b) <= 1.32e-15) {
		tmp = t_2;
	} else if ((a * b) <= 3.6e+84) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = 0.0625d0 * (z * t)
    t_3 = (-0.25d0) * (a * b)
    if ((a * b) <= (-3.8d+47)) then
        tmp = t_3
    else if ((a * b) <= (-5.5d0)) then
        tmp = t_1
    else if ((a * b) <= (-1.25d-109)) then
        tmp = t_2
    else if ((a * b) <= 4.2d-185) then
        tmp = t_1
    else if ((a * b) <= 1.3d-85) then
        tmp = t_2
    else if ((a * b) <= 2.7d-43) then
        tmp = t_1
    else if ((a * b) <= 1.32d-15) then
        tmp = t_2
    else if ((a * b) <= 3.6d+84) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = 0.0625 * (z * t);
	double t_3 = -0.25 * (a * b);
	double tmp;
	if ((a * b) <= -3.8e+47) {
		tmp = t_3;
	} else if ((a * b) <= -5.5) {
		tmp = t_1;
	} else if ((a * b) <= -1.25e-109) {
		tmp = t_2;
	} else if ((a * b) <= 4.2e-185) {
		tmp = t_1;
	} else if ((a * b) <= 1.3e-85) {
		tmp = t_2;
	} else if ((a * b) <= 2.7e-43) {
		tmp = t_1;
	} else if ((a * b) <= 1.32e-15) {
		tmp = t_2;
	} else if ((a * b) <= 3.6e+84) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = 0.0625 * (z * t)
	t_3 = -0.25 * (a * b)
	tmp = 0
	if (a * b) <= -3.8e+47:
		tmp = t_3
	elif (a * b) <= -5.5:
		tmp = t_1
	elif (a * b) <= -1.25e-109:
		tmp = t_2
	elif (a * b) <= 4.2e-185:
		tmp = t_1
	elif (a * b) <= 1.3e-85:
		tmp = t_2
	elif (a * b) <= 2.7e-43:
		tmp = t_1
	elif (a * b) <= 1.32e-15:
		tmp = t_2
	elif (a * b) <= 3.6e+84:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(0.0625 * Float64(z * t))
	t_3 = Float64(-0.25 * Float64(a * b))
	tmp = 0.0
	if (Float64(a * b) <= -3.8e+47)
		tmp = t_3;
	elseif (Float64(a * b) <= -5.5)
		tmp = t_1;
	elseif (Float64(a * b) <= -1.25e-109)
		tmp = t_2;
	elseif (Float64(a * b) <= 4.2e-185)
		tmp = t_1;
	elseif (Float64(a * b) <= 1.3e-85)
		tmp = t_2;
	elseif (Float64(a * b) <= 2.7e-43)
		tmp = t_1;
	elseif (Float64(a * b) <= 1.32e-15)
		tmp = t_2;
	elseif (Float64(a * b) <= 3.6e+84)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = 0.0625 * (z * t);
	t_3 = -0.25 * (a * b);
	tmp = 0.0;
	if ((a * b) <= -3.8e+47)
		tmp = t_3;
	elseif ((a * b) <= -5.5)
		tmp = t_1;
	elseif ((a * b) <= -1.25e-109)
		tmp = t_2;
	elseif ((a * b) <= 4.2e-185)
		tmp = t_1;
	elseif ((a * b) <= 1.3e-85)
		tmp = t_2;
	elseif ((a * b) <= 2.7e-43)
		tmp = t_1;
	elseif ((a * b) <= 1.32e-15)
		tmp = t_2;
	elseif ((a * b) <= 3.6e+84)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -3.8e+47], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], -5.5], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -1.25e-109], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 4.2e-185], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1.3e-85], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 2.7e-43], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1.32e-15], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 3.6e+84], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3.8000000000000003e47 or 3.5999999999999999e84 < (*.f64 a b)

   1. Initial program 96.2%

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

      1. associate-+l- 96.2%

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

      2. associate--l+ 96.2%

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

      3. fma-def 96.2%

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

      4. associate-*l/ 96.2%

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

      5. fma-neg 98.1%

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

      6. sub-neg 98.1%

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

      7. distribute-neg-in 98.1%

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

      8. remove-double-neg 98.1%

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

      9. associate-/l* 98.0%

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

      10. distribute-frac-neg 98.0%

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

      11. associate-/r/ 98.1%

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

      12. fma-def 98.1%

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

      13. neg-mul-1 98.1%

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

      14. *-commutative 98.1%

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

      15. associate-/l* 98.1%

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

      16. metadata-eval 98.1%

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

   3. Simplified 98.1%

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

      1. fma-udef 97.2%

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

      2. div-inv 97.2%

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

      3. metadata-eval 97.2%

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

      4. div-inv 97.2%

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

      5. metadata-eval 97.2%

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

   5. Applied egg-rr 97.2%

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

   6. Taylor expanded in a around inf 62.1%

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

   if -3.8000000000000003e47 < (*.f64 a b) < -5.5 or -1.25000000000000005e-109 < (*.f64 a b) < 4.2e-185 or 1.30000000000000006e-85 < (*.f64 a b) < 2.69999999999999991e-43 or 1.31999999999999995e-15 < (*.f64 a b) < 3.5999999999999999e84

   1. Initial program 99.1%

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

   2. Taylor expanded in x around inf 68.3%

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

   if -5.5 < (*.f64 a b) < -1.25000000000000005e-109 or 4.2e-185 < (*.f64 a b) < 1.30000000000000006e-85 or 2.69999999999999991e-43 < (*.f64 a b) < 1.31999999999999995e-15

   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* 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. div-inv 100.0%

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

      3. metadata-eval 100.0%

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

      4. div-inv 100.0%

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

      5. metadata-eval 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in z around inf 68.9%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -3.8 \cdot 10^{+47}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \cdot b \leq -5.5:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -1.25 \cdot 10^{-109}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 4.2 \cdot 10^{-185}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.3 \cdot 10^{-85}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 2.7 \cdot 10^{-43}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 1.32 \cdot 10^{-15}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 3.6 \cdot 10^{+84}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 5: 65.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := c + t_1\\ t_3 := c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -3.05 \cdot 10^{+87}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 9.2 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{-69}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq 0.028:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+166}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (+ c t_1)) (t_3 (+ c (* b (* a -0.25)))))
   (if (<= (* x y) -3.05e+87)
     (+ c (* x y))
     (if (<= (* x y) 9.2e-294)
       t_2
       (if (<= (* x y) 2.1e-69)
         t_3
         (if (<= (* x y) 0.028)
           t_2
           (if (<= (* x y) 5e+166) t_3 (+ (* x y) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = c + t_1;
	double t_3 = c + (b * (a * -0.25));
	double tmp;
	if ((x * y) <= -3.05e+87) {
		tmp = c + (x * y);
	} else if ((x * y) <= 9.2e-294) {
		tmp = t_2;
	} else if ((x * y) <= 2.1e-69) {
		tmp = t_3;
	} else if ((x * y) <= 0.028) {
		tmp = t_2;
	} else if ((x * y) <= 5e+166) {
		tmp = t_3;
	} else {
		tmp = (x * y) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    t_2 = c + t_1
    t_3 = c + (b * (a * (-0.25d0)))
    if ((x * y) <= (-3.05d+87)) then
        tmp = c + (x * y)
    else if ((x * y) <= 9.2d-294) then
        tmp = t_2
    else if ((x * y) <= 2.1d-69) then
        tmp = t_3
    else if ((x * y) <= 0.028d0) then
        tmp = t_2
    else if ((x * y) <= 5d+166) then
        tmp = t_3
    else
        tmp = (x * y) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = c + t_1;
	double t_3 = c + (b * (a * -0.25));
	double tmp;
	if ((x * y) <= -3.05e+87) {
		tmp = c + (x * y);
	} else if ((x * y) <= 9.2e-294) {
		tmp = t_2;
	} else if ((x * y) <= 2.1e-69) {
		tmp = t_3;
	} else if ((x * y) <= 0.028) {
		tmp = t_2;
	} else if ((x * y) <= 5e+166) {
		tmp = t_3;
	} else {
		tmp = (x * y) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = c + t_1
	t_3 = c + (b * (a * -0.25))
	tmp = 0
	if (x * y) <= -3.05e+87:
		tmp = c + (x * y)
	elif (x * y) <= 9.2e-294:
		tmp = t_2
	elif (x * y) <= 2.1e-69:
		tmp = t_3
	elif (x * y) <= 0.028:
		tmp = t_2
	elif (x * y) <= 5e+166:
		tmp = t_3
	else:
		tmp = (x * y) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(c + t_1)
	t_3 = Float64(c + Float64(b * Float64(a * -0.25)))
	tmp = 0.0
	if (Float64(x * y) <= -3.05e+87)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(x * y) <= 9.2e-294)
		tmp = t_2;
	elseif (Float64(x * y) <= 2.1e-69)
		tmp = t_3;
	elseif (Float64(x * y) <= 0.028)
		tmp = t_2;
	elseif (Float64(x * y) <= 5e+166)
		tmp = t_3;
	else
		tmp = Float64(Float64(x * y) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	t_2 = c + t_1;
	t_3 = c + (b * (a * -0.25));
	tmp = 0.0;
	if ((x * y) <= -3.05e+87)
		tmp = c + (x * y);
	elseif ((x * y) <= 9.2e-294)
		tmp = t_2;
	elseif ((x * y) <= 2.1e-69)
		tmp = t_3;
	elseif ((x * y) <= 0.028)
		tmp = t_2;
	elseif ((x * y) <= 5e+166)
		tmp = t_3;
	else
		tmp = (x * y) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.05e+87], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 9.2e-294], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 2.1e-69], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 0.028], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5e+166], t$95$3, N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -3.0499999999999999e87

   1. Initial program 95.3%

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

   2. Taylor expanded in x around inf 81.8%

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

   if -3.0499999999999999e87 < (*.f64 x y) < 9.20000000000000064e-294 or 2.1e-69 < (*.f64 x y) < 0.0280000000000000006

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 71.3%

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

   if 9.20000000000000064e-294 < (*.f64 x y) < 2.1e-69 or 0.0280000000000000006 < (*.f64 x y) < 5.0000000000000002e166

   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 70.0%

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

      1. associate-*r* 70.0%

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

      2. *-commutative 70.0%

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

   4. Simplified 70.0%

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

   if 5.0000000000000002e166 < (*.f64 x y)

   1. Initial program 93.5%

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

   2. Taylor expanded in a around 0 90.8%

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

   3. Taylor expanded in c around 0 84.6%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.05 \cdot 10^{+87}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 9.2 \cdot 10^{-294}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{-69}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 0.028:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+166}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 6: 88.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := \left(a \cdot b\right) \cdot 0.25\\ t_3 := \left(c + t_1\right) - t_2\\ t_4 := c + \left(x \cdot y + t_1\right)\\ \mathbf{if}\;x \cdot y \leq -2.65 \cdot 10^{+91}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \cdot y \leq 6.5 \cdot 10^{+35}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq 1.7 \cdot 10^{+122}:\\ \;\;\;\;\left(c + x \cdot y\right) - t_2\\ \mathbf{elif}\;x \cdot y \leq 1.85 \cdot 10^{+160}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t)))
        (t_2 (* (* a b) 0.25))
        (t_3 (- (+ c t_1) t_2))
        (t_4 (+ c (+ (* x y) t_1))))
   (if (<= (* x y) -2.65e+91)
     t_4
     (if (<= (* x y) 6.5e+35)
       t_3
       (if (<= (* x y) 1.7e+122)
         (- (+ c (* x y)) t_2)
         (if (<= (* x y) 1.85e+160) t_3 t_4))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = (a * b) * 0.25;
	double t_3 = (c + t_1) - t_2;
	double t_4 = c + ((x * y) + t_1);
	double tmp;
	if ((x * y) <= -2.65e+91) {
		tmp = t_4;
	} else if ((x * y) <= 6.5e+35) {
		tmp = t_3;
	} else if ((x * y) <= 1.7e+122) {
		tmp = (c + (x * y)) - t_2;
	} else if ((x * y) <= 1.85e+160) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	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) :: t_4
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    t_2 = (a * b) * 0.25d0
    t_3 = (c + t_1) - t_2
    t_4 = c + ((x * y) + t_1)
    if ((x * y) <= (-2.65d+91)) then
        tmp = t_4
    else if ((x * y) <= 6.5d+35) then
        tmp = t_3
    else if ((x * y) <= 1.7d+122) then
        tmp = (c + (x * y)) - t_2
    else if ((x * y) <= 1.85d+160) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = (a * b) * 0.25;
	double t_3 = (c + t_1) - t_2;
	double t_4 = c + ((x * y) + t_1);
	double tmp;
	if ((x * y) <= -2.65e+91) {
		tmp = t_4;
	} else if ((x * y) <= 6.5e+35) {
		tmp = t_3;
	} else if ((x * y) <= 1.7e+122) {
		tmp = (c + (x * y)) - t_2;
	} else if ((x * y) <= 1.85e+160) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = (a * b) * 0.25
	t_3 = (c + t_1) - t_2
	t_4 = c + ((x * y) + t_1)
	tmp = 0
	if (x * y) <= -2.65e+91:
		tmp = t_4
	elif (x * y) <= 6.5e+35:
		tmp = t_3
	elif (x * y) <= 1.7e+122:
		tmp = (c + (x * y)) - t_2
	elif (x * y) <= 1.85e+160:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(Float64(a * b) * 0.25)
	t_3 = Float64(Float64(c + t_1) - t_2)
	t_4 = Float64(c + Float64(Float64(x * y) + t_1))
	tmp = 0.0
	if (Float64(x * y) <= -2.65e+91)
		tmp = t_4;
	elseif (Float64(x * y) <= 6.5e+35)
		tmp = t_3;
	elseif (Float64(x * y) <= 1.7e+122)
		tmp = Float64(Float64(c + Float64(x * y)) - t_2);
	elseif (Float64(x * y) <= 1.85e+160)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	t_2 = (a * b) * 0.25;
	t_3 = (c + t_1) - t_2;
	t_4 = c + ((x * y) + t_1);
	tmp = 0.0;
	if ((x * y) <= -2.65e+91)
		tmp = t_4;
	elseif ((x * y) <= 6.5e+35)
		tmp = t_3;
	elseif ((x * y) <= 1.7e+122)
		tmp = (c + (x * y)) - t_2;
	elseif ((x * y) <= 1.85e+160)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.65e+91], t$95$4, If[LessEqual[N[(x * y), $MachinePrecision], 6.5e+35], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 1.7e+122], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.85e+160], t$95$3, t$95$4]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.64999999999999998e91 or 1.85000000000000008e160 < (*.f64 x y)

   1. Initial program 94.6%

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

   2. Taylor expanded in a around 0 92.1%

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

   if -2.64999999999999998e91 < (*.f64 x y) < 6.5000000000000003e35 or 1.7e122 < (*.f64 x y) < 1.85000000000000008e160

   1. Initial program 99.4%

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

   2. Taylor expanded in x around 0 96.7%

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

   if 6.5000000000000003e35 < (*.f64 x y) < 1.7e122

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 94.0%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.65 \cdot 10^{+91}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 6.5 \cdot 10^{+35}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 1.7 \cdot 10^{+122}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 1.85 \cdot 10^{+160}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 7: 65.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := c + b \cdot \left(a \cdot -0.25\right)\\ t_3 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -6.2 \cdot 10^{+87}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq 1.85 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 0.048:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 4.2 \cdot 10^{+170}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* 0.0625 (* z t))))
        (t_2 (+ c (* b (* a -0.25))))
        (t_3 (+ c (* x y))))
   (if (<= (* x y) -6.2e+87)
     t_3
     (if (<= (* x y) 1.85e-293)
       t_1
       (if (<= (* x y) 4e-64)
         t_2
         (if (<= (* x y) 0.048) t_1 (if (<= (* x y) 4.2e+170) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (0.0625 * (z * t));
	double t_2 = c + (b * (a * -0.25));
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -6.2e+87) {
		tmp = t_3;
	} else if ((x * y) <= 1.85e-293) {
		tmp = t_1;
	} else if ((x * y) <= 4e-64) {
		tmp = t_2;
	} else if ((x * y) <= 0.048) {
		tmp = t_1;
	} else if ((x * y) <= 4.2e+170) {
		tmp = t_2;
	} 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 + (0.0625d0 * (z * t))
    t_2 = c + (b * (a * (-0.25d0)))
    t_3 = c + (x * y)
    if ((x * y) <= (-6.2d+87)) then
        tmp = t_3
    else if ((x * y) <= 1.85d-293) then
        tmp = t_1
    else if ((x * y) <= 4d-64) then
        tmp = t_2
    else if ((x * y) <= 0.048d0) then
        tmp = t_1
    else if ((x * y) <= 4.2d+170) then
        tmp = t_2
    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 + (0.0625 * (z * t));
	double t_2 = c + (b * (a * -0.25));
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -6.2e+87) {
		tmp = t_3;
	} else if ((x * y) <= 1.85e-293) {
		tmp = t_1;
	} else if ((x * y) <= 4e-64) {
		tmp = t_2;
	} else if ((x * y) <= 0.048) {
		tmp = t_1;
	} else if ((x * y) <= 4.2e+170) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (0.0625 * (z * t))
	t_2 = c + (b * (a * -0.25))
	t_3 = c + (x * y)
	tmp = 0
	if (x * y) <= -6.2e+87:
		tmp = t_3
	elif (x * y) <= 1.85e-293:
		tmp = t_1
	elif (x * y) <= 4e-64:
		tmp = t_2
	elif (x * y) <= 0.048:
		tmp = t_1
	elif (x * y) <= 4.2e+170:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(0.0625 * Float64(z * t)))
	t_2 = Float64(c + Float64(b * Float64(a * -0.25)))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -6.2e+87)
		tmp = t_3;
	elseif (Float64(x * y) <= 1.85e-293)
		tmp = t_1;
	elseif (Float64(x * y) <= 4e-64)
		tmp = t_2;
	elseif (Float64(x * y) <= 0.048)
		tmp = t_1;
	elseif (Float64(x * y) <= 4.2e+170)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (0.0625 * (z * t));
	t_2 = c + (b * (a * -0.25));
	t_3 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -6.2e+87)
		tmp = t_3;
	elseif ((x * y) <= 1.85e-293)
		tmp = t_1;
	elseif ((x * y) <= 4e-64)
		tmp = t_2;
	elseif ((x * y) <= 0.048)
		tmp = t_1;
	elseif ((x * y) <= 4.2e+170)
		tmp = t_2;
	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[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -6.2e+87], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 1.85e-293], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4e-64], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 0.048], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4.2e+170], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -6.1999999999999999e87 or 4.19999999999999996e170 < (*.f64 x y)

   1. Initial program 94.5%

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

   2. Taylor expanded in x around inf 77.9%

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

   if -6.1999999999999999e87 < (*.f64 x y) < 1.85000000000000004e-293 or 3.99999999999999986e-64 < (*.f64 x y) < 0.048000000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 71.3%

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

   if 1.85000000000000004e-293 < (*.f64 x y) < 3.99999999999999986e-64 or 0.048000000000000001 < (*.f64 x y) < 4.19999999999999996e170

   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 70.4%

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

      1. associate-*r* 70.4%

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

      2. *-commutative 70.4%

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

   4. Simplified 70.4%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6.2 \cdot 10^{+87}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.85 \cdot 10^{-293}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-64}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 0.048:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 4.2 \cdot 10^{+170}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 8: 43.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \cdot y \leq -5.5 \cdot 10^{+91}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.1 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-315}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.75 \cdot 10^{+178}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -0.25 (* a b))))
   (if (<= (* x y) -5.5e+91)
     (* x y)
     (if (<= (* x y) -1.1e-107)
       t_1
       (if (<= (* x y) -1e-315) c (if (<= (* x y) 1.75e+178) t_1 (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -0.25 * (a * b);
	double tmp;
	if ((x * y) <= -5.5e+91) {
		tmp = x * y;
	} else if ((x * y) <= -1.1e-107) {
		tmp = t_1;
	} else if ((x * y) <= -1e-315) {
		tmp = c;
	} else if ((x * y) <= 1.75e+178) {
		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 = (-0.25d0) * (a * b)
    if ((x * y) <= (-5.5d+91)) then
        tmp = x * y
    else if ((x * y) <= (-1.1d-107)) then
        tmp = t_1
    else if ((x * y) <= (-1d-315)) then
        tmp = c
    else if ((x * y) <= 1.75d+178) 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 = -0.25 * (a * b);
	double tmp;
	if ((x * y) <= -5.5e+91) {
		tmp = x * y;
	} else if ((x * y) <= -1.1e-107) {
		tmp = t_1;
	} else if ((x * y) <= -1e-315) {
		tmp = c;
	} else if ((x * y) <= 1.75e+178) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -0.25 * (a * b)
	tmp = 0
	if (x * y) <= -5.5e+91:
		tmp = x * y
	elif (x * y) <= -1.1e-107:
		tmp = t_1
	elif (x * y) <= -1e-315:
		tmp = c
	elif (x * y) <= 1.75e+178:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-0.25 * Float64(a * b))
	tmp = 0.0
	if (Float64(x * y) <= -5.5e+91)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.1e-107)
		tmp = t_1;
	elseif (Float64(x * y) <= -1e-315)
		tmp = c;
	elseif (Float64(x * y) <= 1.75e+178)
		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 = -0.25 * (a * b);
	tmp = 0.0;
	if ((x * y) <= -5.5e+91)
		tmp = x * y;
	elseif ((x * y) <= -1.1e-107)
		tmp = t_1;
	elseif ((x * y) <= -1e-315)
		tmp = c;
	elseif ((x * y) <= 1.75e+178)
		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[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5.5e+91], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.1e-107], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1e-315], c, If[LessEqual[N[(x * y), $MachinePrecision], 1.75e+178], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.4999999999999998e91 or 1.75e178 < (*.f64 x y)

   1. Initial program 94.3%

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

      1. associate-+l- 94.3%

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

      2. associate--l+ 94.3%

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

      3. fma-def 95.7%

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

      4. associate-*l/ 95.7%

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

      5. fma-neg 97.1%

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

      6. sub-neg 97.1%

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

      7. distribute-neg-in 97.1%

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

      8. remove-double-neg 97.1%

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

      9. associate-/l* 97.1%

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

      10. distribute-frac-neg 97.1%

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

      11. associate-/r/ 97.1%

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

      12. fma-def 97.1%

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

      13. neg-mul-1 97.1%

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

      14. *-commutative 97.1%

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

      15. associate-/l* 97.1%

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

      16. metadata-eval 97.1%

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

   3. Simplified 97.1%

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

      1. fma-udef 94.3%

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

      2. div-inv 94.3%

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

      3. metadata-eval 94.3%

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

      4. div-inv 94.3%

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

      5. metadata-eval 94.3%

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

   5. Applied egg-rr 94.3%

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

   6. Taylor expanded in x around inf 69.0%

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

   if -5.4999999999999998e91 < (*.f64 x y) < -1.10000000000000006e-107 or -9.999999985e-316 < (*.f64 x y) < 1.75e178

   1. Initial program 99.4%

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

      1. associate-+l- 99.4%

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

      2. associate--l+ 99.4%

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

      3. fma-def 99.4%

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

      4. associate-*l/ 99.4%

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

      5. fma-neg 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. div-inv 100.0%

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

      3. metadata-eval 100.0%

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

      4. div-inv 100.0%

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

      5. metadata-eval 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in a around inf 40.8%

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

   if -1.10000000000000006e-107 < (*.f64 x y) < -9.999999985e-316

   1. Initial program 100.0%

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

   2. Taylor expanded in c around inf 31.6%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.5 \cdot 10^{+91}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.1 \cdot 10^{-107}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-315}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 1.75 \cdot 10^{+178}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 9: 44.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \cdot b \leq -1.1 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq -1.3 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -1.25 \cdot 10^{-307}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 2.3 \cdot 10^{+159}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (* -0.25 (* a b))))
   (if (<= (* a b) -1.1e+62)
     t_2
     (if (<= (* a b) -1.3e-109)
       t_1
       (if (<= (* a b) -1.25e-307) c (if (<= (* a b) 2.3e+159) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = -0.25 * (a * b);
	double tmp;
	if ((a * b) <= -1.1e+62) {
		tmp = t_2;
	} else if ((a * b) <= -1.3e-109) {
		tmp = t_1;
	} else if ((a * b) <= -1.25e-307) {
		tmp = c;
	} else if ((a * b) <= 2.3e+159) {
		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 = 0.0625d0 * (z * t)
    t_2 = (-0.25d0) * (a * b)
    if ((a * b) <= (-1.1d+62)) then
        tmp = t_2
    else if ((a * b) <= (-1.3d-109)) then
        tmp = t_1
    else if ((a * b) <= (-1.25d-307)) then
        tmp = c
    else if ((a * b) <= 2.3d+159) 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 = 0.0625 * (z * t);
	double t_2 = -0.25 * (a * b);
	double tmp;
	if ((a * b) <= -1.1e+62) {
		tmp = t_2;
	} else if ((a * b) <= -1.3e-109) {
		tmp = t_1;
	} else if ((a * b) <= -1.25e-307) {
		tmp = c;
	} else if ((a * b) <= 2.3e+159) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = -0.25 * (a * b)
	tmp = 0
	if (a * b) <= -1.1e+62:
		tmp = t_2
	elif (a * b) <= -1.3e-109:
		tmp = t_1
	elif (a * b) <= -1.25e-307:
		tmp = c
	elif (a * b) <= 2.3e+159:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(-0.25 * Float64(a * b))
	tmp = 0.0
	if (Float64(a * b) <= -1.1e+62)
		tmp = t_2;
	elseif (Float64(a * b) <= -1.3e-109)
		tmp = t_1;
	elseif (Float64(a * b) <= -1.25e-307)
		tmp = c;
	elseif (Float64(a * b) <= 2.3e+159)
		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 = 0.0625 * (z * t);
	t_2 = -0.25 * (a * b);
	tmp = 0.0;
	if ((a * b) <= -1.1e+62)
		tmp = t_2;
	elseif ((a * b) <= -1.3e-109)
		tmp = t_1;
	elseif ((a * b) <= -1.25e-307)
		tmp = c;
	elseif ((a * b) <= 2.3e+159)
		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[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.1e+62], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -1.3e-109], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -1.25e-307], c, If[LessEqual[N[(a * b), $MachinePrecision], 2.3e+159], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.10000000000000007e62 or 2.29999999999999995e159 < (*.f64 a b)

   1. Initial program 95.8%

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

      1. associate-+l- 95.8%

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

      2. associate--l+ 95.8%

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

      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 97.9%

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

      6. sub-neg 97.9%

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

      7. distribute-neg-in 97.9%

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

      8. remove-double-neg 97.9%

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

      9. associate-/l* 97.8%

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

      10. distribute-frac-neg 97.8%

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

      11. associate-/r/ 97.9%

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

      12. fma-def 97.9%

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

      13. neg-mul-1 97.9%

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

      14. *-commutative 97.9%

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

      15. associate-/l* 97.9%

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

      16. metadata-eval 97.9%

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

   3. Simplified 97.9%

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

      1. fma-udef 96.8%

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

      2. div-inv 96.8%

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

      3. metadata-eval 96.8%

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

      4. div-inv 96.8%

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

      5. metadata-eval 96.8%

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

   5. Applied egg-rr 96.8%

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

   6. Taylor expanded in a around inf 66.0%

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

   if -1.10000000000000007e62 < (*.f64 a b) < -1.2999999999999999e-109 or -1.25000000000000003e-307 < (*.f64 a b) < 2.29999999999999995e159

   1. Initial program 99.3%

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

      1. associate-+l- 99.3%

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

      2. associate--l+ 99.3%

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

      3. fma-def 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* 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 99.3%

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

      2. div-inv 99.3%

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

      3. metadata-eval 99.3%

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

      4. div-inv 99.3%

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

      5. metadata-eval 99.3%

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

   5. Applied egg-rr 99.3%

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

   6. Taylor expanded in z around inf 44.7%

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

   if -1.2999999999999999e-109 < (*.f64 a b) < -1.25000000000000003e-307

   1. Initial program 100.0%

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

   2. Taylor expanded in c around inf 54.4%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.1 \cdot 10^{+62}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \cdot b \leq -1.3 \cdot 10^{-109}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq -1.25 \cdot 10^{-307}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 2.3 \cdot 10^{+159}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 10: 87.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+203} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+106}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -2e+203) (not (<= (* a b) 2e+106)))
   (- (* x y) (* (* a b) 0.25))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -2e+203) || !((a * b) <= 2e+106)) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((a * b) <= (-2d+203)) .or. (.not. ((a * b) <= 2d+106))) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -2e+203) || !((a * b) <= 2e+106)) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -2e+203) or not ((a * b) <= 2e+106):
		tmp = (x * y) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -2e+203) || !(Float64(a * b) <= 2e+106))
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -2e+203) || ~(((a * b) <= 2e+106)))
		tmp = (x * y) - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -2e+203], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e+106]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2e203 or 2.00000000000000018e106 < (*.f64 a b)

   1. Initial program 95.8%

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

   2. Taylor expanded in z around 0 86.7%

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

   3. Taylor expanded in c around 0 84.1%

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

   if -2e203 < (*.f64 a b) < 2.00000000000000018e106

   1. Initial program 98.9%

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

   2. Taylor expanded in a around 0 87.3%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+203} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+106}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 11: 86.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+50}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+106}:\\ \;\;\;\;c + \left(x \cdot y + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)) (t_2 (* 0.0625 (* z t))))
   (if (<= (* a b) -2e+50)
     (- t_2 t_1)
     (if (<= (* a b) 2e+106) (+ c (+ (* x y) t_2)) (- (* x y) 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 t_2 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -2e+50) {
		tmp = t_2 - t_1;
	} else if ((a * b) <= 2e+106) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (x * y) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    t_2 = 0.0625d0 * (z * t)
    if ((a * b) <= (-2d+50)) then
        tmp = t_2 - t_1
    else if ((a * b) <= 2d+106) then
        tmp = c + ((x * y) + t_2)
    else
        tmp = (x * y) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -2e+50) {
		tmp = t_2 - t_1;
	} else if ((a * b) <= 2e+106) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (x * y) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	t_2 = 0.0625 * (z * t)
	tmp = 0
	if (a * b) <= -2e+50:
		tmp = t_2 - t_1
	elif (a * b) <= 2e+106:
		tmp = c + ((x * y) + t_2)
	else:
		tmp = (x * y) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	t_2 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -2e+50)
		tmp = Float64(t_2 - t_1);
	elseif (Float64(a * b) <= 2e+106)
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	else
		tmp = Float64(Float64(x * y) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	t_2 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((a * b) <= -2e+50)
		tmp = t_2 - t_1;
	elseif ((a * b) <= 2e+106)
		tmp = c + ((x * y) + t_2);
	else
		tmp = (x * y) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+50], N[(t$95$2 - t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+106], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.0000000000000002e50

   1. Initial program 96.9%

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

   2. Taylor expanded in x around 0 90.8%

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

   3. Taylor expanded in c around 0 81.1%

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

   if -2.0000000000000002e50 < (*.f64 a b) < 2.00000000000000018e106

   1. Initial program 99.3%

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

   2. Taylor expanded in a around 0 93.0%

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

   if 2.00000000000000018e106 < (*.f64 a b)

   1. Initial program 94.7%

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

   2. Taylor expanded in z around 0 87.5%

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

   3. Taylor expanded in c around 0 82.5%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+50}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+106}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 12: 87.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+50}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+106}:\\ \;\;\;\;c + \left(x \cdot y + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)) (t_2 (* 0.0625 (* z t))))
   (if (<= (* a b) -2e+50)
     (- t_2 t_1)
     (if (<= (* a b) 2e+106) (+ c (+ (* x y) t_2)) (- (+ c (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -2e+50) {
		tmp = t_2 - t_1;
	} else if ((a * b) <= 2e+106) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (c + (x * y)) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    t_2 = 0.0625d0 * (z * t)
    if ((a * b) <= (-2d+50)) then
        tmp = t_2 - t_1
    else if ((a * b) <= 2d+106) then
        tmp = c + ((x * y) + t_2)
    else
        tmp = (c + (x * y)) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -2e+50) {
		tmp = t_2 - t_1;
	} else if ((a * b) <= 2e+106) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (c + (x * y)) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	t_2 = 0.0625 * (z * t)
	tmp = 0
	if (a * b) <= -2e+50:
		tmp = t_2 - t_1
	elif (a * b) <= 2e+106:
		tmp = c + ((x * y) + t_2)
	else:
		tmp = (c + (x * y)) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	t_2 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -2e+50)
		tmp = Float64(t_2 - t_1);
	elseif (Float64(a * b) <= 2e+106)
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	else
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	t_2 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((a * b) <= -2e+50)
		tmp = t_2 - t_1;
	elseif ((a * b) <= 2e+106)
		tmp = c + ((x * y) + t_2);
	else
		tmp = (c + (x * y)) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+50], N[(t$95$2 - t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+106], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.0000000000000002e50

   1. Initial program 96.9%

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

   2. Taylor expanded in x around 0 90.8%

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

   3. Taylor expanded in c around 0 81.1%

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

   if -2.0000000000000002e50 < (*.f64 a b) < 2.00000000000000018e106

   1. Initial program 99.3%

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

   2. Taylor expanded in a around 0 93.0%

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

   if 2.00000000000000018e106 < (*.f64 a b)

   1. Initial program 94.7%

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

   2. Taylor expanded in z around 0 87.5%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+50}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+106}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 13: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

2. Final simplification 98.0%

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

Alternative 14: 54.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-223}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-81}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))))
   (if (<= x -6.5e+175)
     t_1
     (if (<= x 5.8e-223)
       (+ c (* 0.0625 (* z t)))
       (if (<= x 3.1e-81) (* -0.25 (* a b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double tmp;
	if (x <= -6.5e+175) {
		tmp = t_1;
	} else if (x <= 5.8e-223) {
		tmp = c + (0.0625 * (z * t));
	} else if (x <= 3.1e-81) {
		tmp = -0.25 * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c + (x * y)
    if (x <= (-6.5d+175)) then
        tmp = t_1
    else if (x <= 5.8d-223) then
        tmp = c + (0.0625d0 * (z * t))
    else if (x <= 3.1d-81) then
        tmp = (-0.25d0) * (a * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double tmp;
	if (x <= -6.5e+175) {
		tmp = t_1;
	} else if (x <= 5.8e-223) {
		tmp = c + (0.0625 * (z * t));
	} else if (x <= 3.1e-81) {
		tmp = -0.25 * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	tmp = 0
	if x <= -6.5e+175:
		tmp = t_1
	elif x <= 5.8e-223:
		tmp = c + (0.0625 * (z * t))
	elif x <= 3.1e-81:
		tmp = -0.25 * (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (x <= -6.5e+175)
		tmp = t_1;
	elseif (x <= 5.8e-223)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (x <= 3.1e-81)
		tmp = Float64(-0.25 * Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	tmp = 0.0;
	if (x <= -6.5e+175)
		tmp = t_1;
	elseif (x <= 5.8e-223)
		tmp = c + (0.0625 * (z * t));
	elseif (x <= 3.1e-81)
		tmp = -0.25 * (a * b);
	else
		tmp = t_1;
	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]}, If[LessEqual[x, -6.5e+175], t$95$1, If[LessEqual[x, 5.8e-223], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e-81], N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.49999999999999977e175 or 3.09999999999999988e-81 < x

   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 x around inf 55.3%

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

   if -6.49999999999999977e175 < x < 5.8000000000000001e-223

   1. Initial program 99.1%

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

   2. Taylor expanded in z around inf 61.0%

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

   if 5.8000000000000001e-223 < x < 3.09999999999999988e-81

   1. Initial program 96.2%

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

      1. associate-+l- 96.2%

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

      2. associate--l+ 96.2%

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

      3. fma-def 96.2%

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

      4. associate-*l/ 96.2%

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

      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. div-inv 100.0%

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

      3. metadata-eval 100.0%

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

      4. div-inv 100.0%

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

      5. metadata-eval 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in a around inf 42.4%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+175}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-223}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-81}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 15: 38.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.5 \cdot 10^{+241}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.42 \cdot 10^{+178}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -3.5e+241) (* x y) (if (<= (* x y) 1.42e+178) c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -3.5e+241) {
		tmp = x * y;
	} else if ((x * y) <= 1.42e+178) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((x * y) <= (-3.5d+241)) then
        tmp = x * y
    else if ((x * y) <= 1.42d+178) then
        tmp = c
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -3.5e+241) {
		tmp = x * y;
	} else if ((x * y) <= 1.42e+178) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -3.5e+241:
		tmp = x * y
	elif (x * y) <= 1.42e+178:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -3.5e+241)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 1.42e+178)
		tmp = c;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x * y) <= -3.5e+241)
		tmp = x * y;
	elseif ((x * y) <= 1.42e+178)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -3.5e+241], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.42e+178], c, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.5e241 or 1.41999999999999999e178 < (*.f64 x y)

   1. Initial program 92.6%

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

      1. associate-+l- 92.6%

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

      2. associate--l+ 92.6%

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

      3. fma-def 94.4%

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

      4. associate-*l/ 94.4%

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

      5. fma-neg 96.3%

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

      6. sub-neg 96.3%

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

      7. distribute-neg-in 96.3%

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

      8. remove-double-neg 96.3%

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

      9. associate-/l* 96.2%

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

      10. distribute-frac-neg 96.2%

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

      11. associate-/r/ 96.3%

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

      12. fma-def 96.3%

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

      13. neg-mul-1 96.3%

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

      14. *-commutative 96.3%

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

      15. associate-/l* 96.3%

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

      16. metadata-eval 96.3%

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

   3. Simplified 96.3%

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

      1. fma-udef 92.6%

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

      2. div-inv 92.6%

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

      3. metadata-eval 92.6%

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

      4. div-inv 92.6%

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

      5. metadata-eval 92.6%

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

   5. Applied egg-rr 92.6%

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

   6. Taylor expanded in x around inf 77.4%

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

   if -3.5e241 < (*.f64 x y) < 1.41999999999999999e178

   1. Initial program 99.5%

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

   2. Taylor expanded in c around inf 25.7%

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

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.5 \cdot 10^{+241}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.42 \cdot 10^{+178}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 16: 22.3% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

2. Taylor expanded in c around inf 21.1%

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

3. Final simplification 21.1%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023293 
(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))