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

Percentage Accurate: 97.7% → 98.8%

Time: 9.5s

Alternatives: 16

Speedup: 1.0×

• 33.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{z \cdot t}{16} + x \cdot y\right) - \frac{b \cdot a}{4}\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;c + t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, c + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (+ (/ (* z t) 16.0) (* x y)) (/ (* b a) 4.0))))
   (if (<= t_1 INFINITY) (+ c t_1) (fma x y (+ c (* 0.0625 (* z t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((z * t) / 16.0) + (x * y)) - ((b * a) / 4.0);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = c + t_1;
	} else {
		tmp = fma(x, y, (c + (0.0625 * (z * t))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(z * t) / 16.0) + Float64(x * y)) - Float64(Float64(b * a) / 4.0))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(c + t_1);
	else
		tmp = fma(x, y, Float64(c + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(c + t$95$1), $MachinePrecision], N[(x * y + N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16)) (/.f64 (*.f64 a b) 4))

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. +-commutative 0.0%

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

      3. associate--l+ 0.0%

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

      4. +-commutative 0.0%

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

      5. associate-+l- 0.0%

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

      6. fma-neg 16.7%

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

      7. neg-sub0 16.7%

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

      8. associate--l- 16.7%

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

      9. associate-+l- 16.7%

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

      10. neg-sub0 16.7%

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

      11. *-commutative 16.7%

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

      12. associate-*r/ 16.7%

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

      13. distribute-rgt-neg-in 16.7%

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

      14. fma-def 50.0%

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

      15. distribute-frac-neg 50.0%

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

      16. neg-mul-1 50.0%

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

      17. associate-/l* 50.0%

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

      18. associate-/r/ 50.0%

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

      19. metadata-eval 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in b around 0 66.7%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\frac{z \cdot t}{16} + x \cdot y\right) - \frac{b \cdot a}{4} \leq \infty:\\ \;\;\;\;c + \left(\left(\frac{z \cdot t}{16} + x \cdot y\right) - \frac{b \cdot a}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, c + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 2: 98.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. associate-+l- 97.6%

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

   2. +-commutative 97.6%

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

   3. associate--l+ 97.6%

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

   4. +-commutative 97.6%

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

   5. associate-+l- 97.6%

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

   6. fma-neg 98.0%

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

   7. neg-sub0 98.0%

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

   8. associate--l- 98.0%

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

   9. associate-+l- 98.0%

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

   10. neg-sub0 98.0%

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

   11. *-commutative 98.0%

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

   12. associate-*r/ 98.0%

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

   13. distribute-rgt-neg-in 98.0%

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

   14. fma-def 98.8%

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

   15. distribute-frac-neg 98.8%

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

   16. neg-mul-1 98.8%

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

   17. associate-/l* 98.8%

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

   18. associate-/r/ 98.8%

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

   19. metadata-eval 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 3: 99.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. associate-+l- 97.6%

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

   2. +-commutative 97.6%

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

   3. associate--l+ 97.6%

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

   4. associate-*l/ 97.6%

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

   5. *-commutative 97.6%

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

   6. fma-def 98.4%

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

   7. fma-neg 98.8%

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

   8. neg-sub0 98.8%

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

   9. associate-+l- 98.8%

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

   10. neg-sub0 98.8%

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

   11. +-commutative 98.8%

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

   12. unsub-neg 98.8%

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

   13. *-commutative 98.8%

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

   14. associate-*r/ 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 4: 98.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. associate-+l- 97.6%

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

   2. sub-neg 97.6%

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

   3. neg-mul-1 97.6%

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

   4. metadata-eval 97.6%

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

   5. metadata-eval 97.6%

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

   6. cancel-sign-sub-inv 97.6%

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

   7. fma-def 98.0%

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

   8. associate-/l* 98.0%

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

   9. metadata-eval 98.0%

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

   10. *-lft-identity 98.0%

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

   11. associate-/l* 97.9%

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

3. Simplified 97.9%

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

4. Final simplification 97.9%

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

Alternative 5: 44.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := -0.25 \cdot \left(b \cdot a\right)\\ \mathbf{if}\;b \cdot a \leq -5.8 \cdot 10^{+148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -1.25 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -1.45 \cdot 10^{-152}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq -4 \cdot 10^{-218}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -1.65 \cdot 10^{-226}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq -6.8 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -1.05 \cdot 10^{-278}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -5 \cdot 10^{-323}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq 2.25 \cdot 10^{-94}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 1.62 \cdot 10^{+112}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (* -0.25 (* b a))))
   (if (<= (* b a) -5.8e+148)
     t_2
     (if (<= (* b a) -1.25e-59)
       t_1
       (if (<= (* b a) -1.45e-152)
         c
         (if (<= (* b a) -4e-218)
           (* x y)
           (if (<= (* b a) -1.65e-226)
             c
             (if (<= (* b a) -6.8e-273)
               t_1
               (if (<= (* b a) -1.05e-278)
                 (* x y)
                 (if (<= (* b a) -5e-323)
                   c
                   (if (<= (* b a) 2.25e-94)
                     (* x y)
                     (if (<= (* b a) 1.62e+112) c t_2))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = -0.25 * (b * a);
	double tmp;
	if ((b * a) <= -5.8e+148) {
		tmp = t_2;
	} else if ((b * a) <= -1.25e-59) {
		tmp = t_1;
	} else if ((b * a) <= -1.45e-152) {
		tmp = c;
	} else if ((b * a) <= -4e-218) {
		tmp = x * y;
	} else if ((b * a) <= -1.65e-226) {
		tmp = c;
	} else if ((b * a) <= -6.8e-273) {
		tmp = t_1;
	} else if ((b * a) <= -1.05e-278) {
		tmp = x * y;
	} else if ((b * a) <= -5e-323) {
		tmp = c;
	} else if ((b * a) <= 2.25e-94) {
		tmp = x * y;
	} else if ((b * a) <= 1.62e+112) {
		tmp = c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    t_2 = (-0.25d0) * (b * a)
    if ((b * a) <= (-5.8d+148)) then
        tmp = t_2
    else if ((b * a) <= (-1.25d-59)) then
        tmp = t_1
    else if ((b * a) <= (-1.45d-152)) then
        tmp = c
    else if ((b * a) <= (-4d-218)) then
        tmp = x * y
    else if ((b * a) <= (-1.65d-226)) then
        tmp = c
    else if ((b * a) <= (-6.8d-273)) then
        tmp = t_1
    else if ((b * a) <= (-1.05d-278)) then
        tmp = x * y
    else if ((b * a) <= (-5d-323)) then
        tmp = c
    else if ((b * a) <= 2.25d-94) then
        tmp = x * y
    else if ((b * a) <= 1.62d+112) then
        tmp = c
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = -0.25 * (b * a);
	double tmp;
	if ((b * a) <= -5.8e+148) {
		tmp = t_2;
	} else if ((b * a) <= -1.25e-59) {
		tmp = t_1;
	} else if ((b * a) <= -1.45e-152) {
		tmp = c;
	} else if ((b * a) <= -4e-218) {
		tmp = x * y;
	} else if ((b * a) <= -1.65e-226) {
		tmp = c;
	} else if ((b * a) <= -6.8e-273) {
		tmp = t_1;
	} else if ((b * a) <= -1.05e-278) {
		tmp = x * y;
	} else if ((b * a) <= -5e-323) {
		tmp = c;
	} else if ((b * a) <= 2.25e-94) {
		tmp = x * y;
	} else if ((b * a) <= 1.62e+112) {
		tmp = c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = -0.25 * (b * a)
	tmp = 0
	if (b * a) <= -5.8e+148:
		tmp = t_2
	elif (b * a) <= -1.25e-59:
		tmp = t_1
	elif (b * a) <= -1.45e-152:
		tmp = c
	elif (b * a) <= -4e-218:
		tmp = x * y
	elif (b * a) <= -1.65e-226:
		tmp = c
	elif (b * a) <= -6.8e-273:
		tmp = t_1
	elif (b * a) <= -1.05e-278:
		tmp = x * y
	elif (b * a) <= -5e-323:
		tmp = c
	elif (b * a) <= 2.25e-94:
		tmp = x * y
	elif (b * a) <= 1.62e+112:
		tmp = c
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(-0.25 * Float64(b * a))
	tmp = 0.0
	if (Float64(b * a) <= -5.8e+148)
		tmp = t_2;
	elseif (Float64(b * a) <= -1.25e-59)
		tmp = t_1;
	elseif (Float64(b * a) <= -1.45e-152)
		tmp = c;
	elseif (Float64(b * a) <= -4e-218)
		tmp = Float64(x * y);
	elseif (Float64(b * a) <= -1.65e-226)
		tmp = c;
	elseif (Float64(b * a) <= -6.8e-273)
		tmp = t_1;
	elseif (Float64(b * a) <= -1.05e-278)
		tmp = Float64(x * y);
	elseif (Float64(b * a) <= -5e-323)
		tmp = c;
	elseif (Float64(b * a) <= 2.25e-94)
		tmp = Float64(x * y);
	elseif (Float64(b * a) <= 1.62e+112)
		tmp = c;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	t_2 = -0.25 * (b * a);
	tmp = 0.0;
	if ((b * a) <= -5.8e+148)
		tmp = t_2;
	elseif ((b * a) <= -1.25e-59)
		tmp = t_1;
	elseif ((b * a) <= -1.45e-152)
		tmp = c;
	elseif ((b * a) <= -4e-218)
		tmp = x * y;
	elseif ((b * a) <= -1.65e-226)
		tmp = c;
	elseif ((b * a) <= -6.8e-273)
		tmp = t_1;
	elseif ((b * a) <= -1.05e-278)
		tmp = x * y;
	elseif ((b * a) <= -5e-323)
		tmp = c;
	elseif ((b * a) <= 2.25e-94)
		tmp = x * y;
	elseif ((b * a) <= 1.62e+112)
		tmp = c;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -5.8e+148], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -1.25e-59], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -1.45e-152], c, If[LessEqual[N[(b * a), $MachinePrecision], -4e-218], N[(x * y), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], -1.65e-226], c, If[LessEqual[N[(b * a), $MachinePrecision], -6.8e-273], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -1.05e-278], N[(x * y), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], -5e-323], c, If[LessEqual[N[(b * a), $MachinePrecision], 2.25e-94], N[(x * y), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 1.62e+112], c, t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -5.7999999999999999e148 or 1.61999999999999994e112 < (*.f64 a b)

   1. Initial program 93.3%

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

   2. Taylor expanded in z around 0 88.9%

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

   3. Taylor expanded in a around inf 75.0%

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

      1. *-commutative 75.0%

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

   5. Simplified 75.0%

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

   if -5.7999999999999999e148 < (*.f64 a b) < -1.25e-59 or -1.65e-226 < (*.f64 a b) < -6.79999999999999982e-273

   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 66.9%

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

   3. Taylor expanded in t around inf 49.9%

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

   if -1.25e-59 < (*.f64 a b) < -1.4500000000000001e-152 or -4.0000000000000001e-218 < (*.f64 a b) < -1.65e-226 or -1.05000000000000007e-278 < (*.f64 a b) < -4.94066e-323 or 2.2500000000000001e-94 < (*.f64 a b) < 1.61999999999999994e112

   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 49.7%

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

   if -1.4500000000000001e-152 < (*.f64 a b) < -4.0000000000000001e-218 or -6.79999999999999982e-273 < (*.f64 a b) < -1.05000000000000007e-278 or -4.94066e-323 < (*.f64 a b) < 2.2500000000000001e-94

   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 0 75.4%

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

   3. Taylor expanded in y around inf 52.9%

      \[\leadsto \color{blue}{y \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5.8 \cdot 10^{+148}:\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \mathbf{elif}\;b \cdot a \leq -1.25 \cdot 10^{-59}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;b \cdot a \leq -1.45 \cdot 10^{-152}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq -4 \cdot 10^{-218}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -1.65 \cdot 10^{-226}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq -6.8 \cdot 10^{-273}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;b \cdot a \leq -1.05 \cdot 10^{-278}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -5 \cdot 10^{-323}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq 2.25 \cdot 10^{-94}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 1.62 \cdot 10^{+112}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \end{array} \]

Alternative 6: 66.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + 0.0625 \cdot \left(z \cdot t\right)\\ t_3 := x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{if}\;b \cdot a \leq -7 \cdot 10^{+148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot a \leq -1.72 \cdot 10^{-161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -3.9 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -2.5 \cdot 10^{-303}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq 2.8 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 1.48 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq 4 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y)))
        (t_2 (+ c (* 0.0625 (* z t))))
        (t_3 (- (* x y) (* (* b a) 0.25))))
   (if (<= (* b a) -7e+148)
     t_3
     (if (<= (* b a) -1.72e-161)
       t_2
       (if (<= (* b a) -3.9e-218)
         t_1
         (if (<= (* b a) -2.5e-303)
           t_2
           (if (<= (* b a) 2.8e-94)
             t_1
             (if (<= (* b a) 1.48e-5)
               t_2
               (if (<= (* b a) 4e+109) 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 = c + (0.0625 * (z * t));
	double t_3 = (x * y) - ((b * a) * 0.25);
	double tmp;
	if ((b * a) <= -7e+148) {
		tmp = t_3;
	} else if ((b * a) <= -1.72e-161) {
		tmp = t_2;
	} else if ((b * a) <= -3.9e-218) {
		tmp = t_1;
	} else if ((b * a) <= -2.5e-303) {
		tmp = t_2;
	} else if ((b * a) <= 2.8e-94) {
		tmp = t_1;
	} else if ((b * a) <= 1.48e-5) {
		tmp = t_2;
	} else if ((b * a) <= 4e+109) {
		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 = c + (0.0625d0 * (z * t))
    t_3 = (x * y) - ((b * a) * 0.25d0)
    if ((b * a) <= (-7d+148)) then
        tmp = t_3
    else if ((b * a) <= (-1.72d-161)) then
        tmp = t_2
    else if ((b * a) <= (-3.9d-218)) then
        tmp = t_1
    else if ((b * a) <= (-2.5d-303)) then
        tmp = t_2
    else if ((b * a) <= 2.8d-94) then
        tmp = t_1
    else if ((b * a) <= 1.48d-5) then
        tmp = t_2
    else if ((b * a) <= 4d+109) 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 = c + (0.0625 * (z * t));
	double t_3 = (x * y) - ((b * a) * 0.25);
	double tmp;
	if ((b * a) <= -7e+148) {
		tmp = t_3;
	} else if ((b * a) <= -1.72e-161) {
		tmp = t_2;
	} else if ((b * a) <= -3.9e-218) {
		tmp = t_1;
	} else if ((b * a) <= -2.5e-303) {
		tmp = t_2;
	} else if ((b * a) <= 2.8e-94) {
		tmp = t_1;
	} else if ((b * a) <= 1.48e-5) {
		tmp = t_2;
	} else if ((b * a) <= 4e+109) {
		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 = c + (0.0625 * (z * t))
	t_3 = (x * y) - ((b * a) * 0.25)
	tmp = 0
	if (b * a) <= -7e+148:
		tmp = t_3
	elif (b * a) <= -1.72e-161:
		tmp = t_2
	elif (b * a) <= -3.9e-218:
		tmp = t_1
	elif (b * a) <= -2.5e-303:
		tmp = t_2
	elif (b * a) <= 2.8e-94:
		tmp = t_1
	elif (b * a) <= 1.48e-5:
		tmp = t_2
	elif (b * a) <= 4e+109:
		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(c + Float64(0.0625 * Float64(z * t)))
	t_3 = Float64(Float64(x * y) - Float64(Float64(b * a) * 0.25))
	tmp = 0.0
	if (Float64(b * a) <= -7e+148)
		tmp = t_3;
	elseif (Float64(b * a) <= -1.72e-161)
		tmp = t_2;
	elseif (Float64(b * a) <= -3.9e-218)
		tmp = t_1;
	elseif (Float64(b * a) <= -2.5e-303)
		tmp = t_2;
	elseif (Float64(b * a) <= 2.8e-94)
		tmp = t_1;
	elseif (Float64(b * a) <= 1.48e-5)
		tmp = t_2;
	elseif (Float64(b * a) <= 4e+109)
		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 = c + (0.0625 * (z * t));
	t_3 = (x * y) - ((b * a) * 0.25);
	tmp = 0.0;
	if ((b * a) <= -7e+148)
		tmp = t_3;
	elseif ((b * a) <= -1.72e-161)
		tmp = t_2;
	elseif ((b * a) <= -3.9e-218)
		tmp = t_1;
	elseif ((b * a) <= -2.5e-303)
		tmp = t_2;
	elseif ((b * a) <= 2.8e-94)
		tmp = t_1;
	elseif ((b * a) <= 1.48e-5)
		tmp = t_2;
	elseif ((b * a) <= 4e+109)
		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[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -7e+148], t$95$3, If[LessEqual[N[(b * a), $MachinePrecision], -1.72e-161], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -3.9e-218], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -2.5e-303], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], 2.8e-94], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 1.48e-5], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], 4e+109], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -6.9999999999999998e148 or 3.99999999999999993e109 < (*.f64 a b)

   1. Initial program 93.3%

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

   2. Taylor expanded in z around 0 88.9%

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

   3. Taylor expanded in c around 0 84.9%

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

   if -6.9999999999999998e148 < (*.f64 a b) < -1.71999999999999999e-161 or -3.9e-218 < (*.f64 a b) < -2.4999999999999999e-303 or 2.7999999999999998e-94 < (*.f64 a b) < 1.4800000000000001e-5

   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 77.8%

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

   if -1.71999999999999999e-161 < (*.f64 a b) < -3.9e-218 or -2.4999999999999999e-303 < (*.f64 a b) < 2.7999999999999998e-94 or 1.4800000000000001e-5 < (*.f64 a b) < 3.99999999999999993e109

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 73.2%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -7 \cdot 10^{+148}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq -1.72 \cdot 10^{-161}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;b \cdot a \leq -3.9 \cdot 10^{-218}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -2.5 \cdot 10^{-303}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;b \cdot a \leq 2.8 \cdot 10^{-94}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 1.48 \cdot 10^{-5}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;b \cdot a \leq 4 \cdot 10^{+109}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 7: 66.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot 0.25\\ t_2 := c + x \cdot y\\ t_3 := 0.0625 \cdot \left(z \cdot t\right)\\ t_4 := c + t_3\\ \mathbf{if}\;b \cdot a \leq -2.8 \cdot 10^{+119}:\\ \;\;\;\;t_3 - t_1\\ \mathbf{elif}\;b \cdot a \leq -9.2 \cdot 10^{-141}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \cdot a \leq -3.9 \cdot 10^{-218}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -7 \cdot 10^{-303}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \cdot a \leq 2.9 \cdot 10^{-94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq 3.3 \cdot 10^{-6}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \cdot a \leq 3.3 \cdot 10^{+112}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) 0.25))
        (t_2 (+ c (* x y)))
        (t_3 (* 0.0625 (* z t)))
        (t_4 (+ c t_3)))
   (if (<= (* b a) -2.8e+119)
     (- t_3 t_1)
     (if (<= (* b a) -9.2e-141)
       t_4
       (if (<= (* b a) -3.9e-218)
         t_2
         (if (<= (* b a) -7e-303)
           t_4
           (if (<= (* b a) 2.9e-94)
             t_2
             (if (<= (* b a) 3.3e-6)
               t_4
               (if (<= (* b a) 3.3e+112) 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 = (b * a) * 0.25;
	double t_2 = c + (x * y);
	double t_3 = 0.0625 * (z * t);
	double t_4 = c + t_3;
	double tmp;
	if ((b * a) <= -2.8e+119) {
		tmp = t_3 - t_1;
	} else if ((b * a) <= -9.2e-141) {
		tmp = t_4;
	} else if ((b * a) <= -3.9e-218) {
		tmp = t_2;
	} else if ((b * a) <= -7e-303) {
		tmp = t_4;
	} else if ((b * a) <= 2.9e-94) {
		tmp = t_2;
	} else if ((b * a) <= 3.3e-6) {
		tmp = t_4;
	} else if ((b * a) <= 3.3e+112) {
		tmp = 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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (b * a) * 0.25d0
    t_2 = c + (x * y)
    t_3 = 0.0625d0 * (z * t)
    t_4 = c + t_3
    if ((b * a) <= (-2.8d+119)) then
        tmp = t_3 - t_1
    else if ((b * a) <= (-9.2d-141)) then
        tmp = t_4
    else if ((b * a) <= (-3.9d-218)) then
        tmp = t_2
    else if ((b * a) <= (-7d-303)) then
        tmp = t_4
    else if ((b * a) <= 2.9d-94) then
        tmp = t_2
    else if ((b * a) <= 3.3d-6) then
        tmp = t_4
    else if ((b * a) <= 3.3d+112) then
        tmp = 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 = (b * a) * 0.25;
	double t_2 = c + (x * y);
	double t_3 = 0.0625 * (z * t);
	double t_4 = c + t_3;
	double tmp;
	if ((b * a) <= -2.8e+119) {
		tmp = t_3 - t_1;
	} else if ((b * a) <= -9.2e-141) {
		tmp = t_4;
	} else if ((b * a) <= -3.9e-218) {
		tmp = t_2;
	} else if ((b * a) <= -7e-303) {
		tmp = t_4;
	} else if ((b * a) <= 2.9e-94) {
		tmp = t_2;
	} else if ((b * a) <= 3.3e-6) {
		tmp = t_4;
	} else if ((b * a) <= 3.3e+112) {
		tmp = t_2;
	} else {
		tmp = (x * y) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * 0.25
	t_2 = c + (x * y)
	t_3 = 0.0625 * (z * t)
	t_4 = c + t_3
	tmp = 0
	if (b * a) <= -2.8e+119:
		tmp = t_3 - t_1
	elif (b * a) <= -9.2e-141:
		tmp = t_4
	elif (b * a) <= -3.9e-218:
		tmp = t_2
	elif (b * a) <= -7e-303:
		tmp = t_4
	elif (b * a) <= 2.9e-94:
		tmp = t_2
	elif (b * a) <= 3.3e-6:
		tmp = t_4
	elif (b * a) <= 3.3e+112:
		tmp = t_2
	else:
		tmp = (x * y) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b * a) * 0.25)
	t_2 = Float64(c + Float64(x * y))
	t_3 = Float64(0.0625 * Float64(z * t))
	t_4 = Float64(c + t_3)
	tmp = 0.0
	if (Float64(b * a) <= -2.8e+119)
		tmp = Float64(t_3 - t_1);
	elseif (Float64(b * a) <= -9.2e-141)
		tmp = t_4;
	elseif (Float64(b * a) <= -3.9e-218)
		tmp = t_2;
	elseif (Float64(b * a) <= -7e-303)
		tmp = t_4;
	elseif (Float64(b * a) <= 2.9e-94)
		tmp = t_2;
	elseif (Float64(b * a) <= 3.3e-6)
		tmp = t_4;
	elseif (Float64(b * a) <= 3.3e+112)
		tmp = 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 = (b * a) * 0.25;
	t_2 = c + (x * y);
	t_3 = 0.0625 * (z * t);
	t_4 = c + t_3;
	tmp = 0.0;
	if ((b * a) <= -2.8e+119)
		tmp = t_3 - t_1;
	elseif ((b * a) <= -9.2e-141)
		tmp = t_4;
	elseif ((b * a) <= -3.9e-218)
		tmp = t_2;
	elseif ((b * a) <= -7e-303)
		tmp = t_4;
	elseif ((b * a) <= 2.9e-94)
		tmp = t_2;
	elseif ((b * a) <= 3.3e-6)
		tmp = t_4;
	elseif ((b * a) <= 3.3e+112)
		tmp = 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[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(c + t$95$3), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -2.8e+119], N[(t$95$3 - t$95$1), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], -9.2e-141], t$95$4, If[LessEqual[N[(b * a), $MachinePrecision], -3.9e-218], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -7e-303], t$95$4, If[LessEqual[N[(b * a), $MachinePrecision], 2.9e-94], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], 3.3e-6], t$95$4, If[LessEqual[N[(b * a), $MachinePrecision], 3.3e+112], t$95$2, N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -2.80000000000000013e119

   1. Initial program 90.4%

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

   2. Taylor expanded in x around 0 83.7%

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

   3. Taylor expanded in c around 0 79.6%

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

   if -2.80000000000000013e119 < (*.f64 a b) < -9.1999999999999998e-141 or -3.9e-218 < (*.f64 a b) < -7e-303 or 2.89999999999999995e-94 < (*.f64 a b) < 3.30000000000000017e-6

   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 78.9%

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

   if -9.1999999999999998e-141 < (*.f64 a b) < -3.9e-218 or -7e-303 < (*.f64 a b) < 2.89999999999999995e-94 or 3.30000000000000017e-6 < (*.f64 a b) < 3.2999999999999999e112

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 73.2%

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

   if 3.2999999999999999e112 < (*.f64 a b)

   1. Initial program 97.6%

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

   2. Taylor expanded in z around 0 95.3%

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

   3. Taylor expanded in c around 0 91.9%

      \[\leadsto \color{blue}{y \cdot x - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2.8 \cdot 10^{+119}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq -9.2 \cdot 10^{-141}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;b \cdot a \leq -3.9 \cdot 10^{-218}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -7 \cdot 10^{-303}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;b \cdot a \leq 2.9 \cdot 10^{-94}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 3.3 \cdot 10^{-6}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;b \cdot a \leq 3.3 \cdot 10^{+112}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 8: 63.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := c + x \cdot y\\ t_3 := -0.25 \cdot \left(b \cdot a\right)\\ \mathbf{if}\;b \cdot a \leq -6.5 \cdot 10^{+148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot a \leq -2.15 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -3.7 \cdot 10^{-218}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -7.5 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 5.5 \cdot 10^{-94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq 1.9 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 2.1 \cdot 10^{+192}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* 0.0625 (* z t))))
        (t_2 (+ c (* x y)))
        (t_3 (* -0.25 (* b a))))
   (if (<= (* b a) -6.5e+148)
     t_3
     (if (<= (* b a) -2.15e-151)
       t_1
       (if (<= (* b a) -3.7e-218)
         t_2
         (if (<= (* b a) -7.5e-304)
           t_1
           (if (<= (* b a) 5.5e-94)
             t_2
             (if (<= (* b a) 1.9e-5)
               t_1
               (if (<= (* b a) 2.1e+192) 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 + (x * y);
	double t_3 = -0.25 * (b * a);
	double tmp;
	if ((b * a) <= -6.5e+148) {
		tmp = t_3;
	} else if ((b * a) <= -2.15e-151) {
		tmp = t_1;
	} else if ((b * a) <= -3.7e-218) {
		tmp = t_2;
	} else if ((b * a) <= -7.5e-304) {
		tmp = t_1;
	} else if ((b * a) <= 5.5e-94) {
		tmp = t_2;
	} else if ((b * a) <= 1.9e-5) {
		tmp = t_1;
	} else if ((b * a) <= 2.1e+192) {
		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 + (x * y)
    t_3 = (-0.25d0) * (b * a)
    if ((b * a) <= (-6.5d+148)) then
        tmp = t_3
    else if ((b * a) <= (-2.15d-151)) then
        tmp = t_1
    else if ((b * a) <= (-3.7d-218)) then
        tmp = t_2
    else if ((b * a) <= (-7.5d-304)) then
        tmp = t_1
    else if ((b * a) <= 5.5d-94) then
        tmp = t_2
    else if ((b * a) <= 1.9d-5) then
        tmp = t_1
    else if ((b * a) <= 2.1d+192) 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 + (x * y);
	double t_3 = -0.25 * (b * a);
	double tmp;
	if ((b * a) <= -6.5e+148) {
		tmp = t_3;
	} else if ((b * a) <= -2.15e-151) {
		tmp = t_1;
	} else if ((b * a) <= -3.7e-218) {
		tmp = t_2;
	} else if ((b * a) <= -7.5e-304) {
		tmp = t_1;
	} else if ((b * a) <= 5.5e-94) {
		tmp = t_2;
	} else if ((b * a) <= 1.9e-5) {
		tmp = t_1;
	} else if ((b * a) <= 2.1e+192) {
		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 + (x * y)
	t_3 = -0.25 * (b * a)
	tmp = 0
	if (b * a) <= -6.5e+148:
		tmp = t_3
	elif (b * a) <= -2.15e-151:
		tmp = t_1
	elif (b * a) <= -3.7e-218:
		tmp = t_2
	elif (b * a) <= -7.5e-304:
		tmp = t_1
	elif (b * a) <= 5.5e-94:
		tmp = t_2
	elif (b * a) <= 1.9e-5:
		tmp = t_1
	elif (b * a) <= 2.1e+192:
		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(x * y))
	t_3 = Float64(-0.25 * Float64(b * a))
	tmp = 0.0
	if (Float64(b * a) <= -6.5e+148)
		tmp = t_3;
	elseif (Float64(b * a) <= -2.15e-151)
		tmp = t_1;
	elseif (Float64(b * a) <= -3.7e-218)
		tmp = t_2;
	elseif (Float64(b * a) <= -7.5e-304)
		tmp = t_1;
	elseif (Float64(b * a) <= 5.5e-94)
		tmp = t_2;
	elseif (Float64(b * a) <= 1.9e-5)
		tmp = t_1;
	elseif (Float64(b * a) <= 2.1e+192)
		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 + (x * y);
	t_3 = -0.25 * (b * a);
	tmp = 0.0;
	if ((b * a) <= -6.5e+148)
		tmp = t_3;
	elseif ((b * a) <= -2.15e-151)
		tmp = t_1;
	elseif ((b * a) <= -3.7e-218)
		tmp = t_2;
	elseif ((b * a) <= -7.5e-304)
		tmp = t_1;
	elseif ((b * a) <= 5.5e-94)
		tmp = t_2;
	elseif ((b * a) <= 1.9e-5)
		tmp = t_1;
	elseif ((b * a) <= 2.1e+192)
		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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -6.5e+148], t$95$3, If[LessEqual[N[(b * a), $MachinePrecision], -2.15e-151], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -3.7e-218], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -7.5e-304], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 5.5e-94], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], 1.9e-5], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 2.1e+192], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -6.49999999999999947e148 or 2.09999999999999995e192 < (*.f64 a b)

   1. Initial program 92.6%

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

   2. Taylor expanded in z around 0 88.9%

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

   3. Taylor expanded in a around inf 78.6%

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

      1. *-commutative 78.6%

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

   5. Simplified 78.6%

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

   if -6.49999999999999947e148 < (*.f64 a b) < -2.15000000000000009e-151 or -3.7000000000000002e-218 < (*.f64 a b) < -7.50000000000000069e-304 or 5.49999999999999989e-94 < (*.f64 a b) < 1.9000000000000001e-5

   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 77.8%

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

   if -2.15000000000000009e-151 < (*.f64 a b) < -3.7000000000000002e-218 or -7.50000000000000069e-304 < (*.f64 a b) < 5.49999999999999989e-94 or 1.9000000000000001e-5 < (*.f64 a b) < 2.09999999999999995e192

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 71.4%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -6.5 \cdot 10^{+148}:\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \mathbf{elif}\;b \cdot a \leq -2.15 \cdot 10^{-151}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;b \cdot a \leq -3.7 \cdot 10^{-218}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -7.5 \cdot 10^{-304}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;b \cdot a \leq 5.5 \cdot 10^{-94}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 1.9 \cdot 10^{-5}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;b \cdot a \leq 2.1 \cdot 10^{+192}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \end{array} \]

Alternative 9: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := c + x \cdot y\\ t_3 := -0.25 \cdot \left(b \cdot a\right)\\ \mathbf{if}\;b \cdot a \leq -6.5 \cdot 10^{+148}:\\ \;\;\;\;c + t_3\\ \mathbf{elif}\;b \cdot a \leq -6 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -3.7 \cdot 10^{-218}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -4.4 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 2.6 \cdot 10^{-94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq 3 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 1.05 \cdot 10^{+193}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* 0.0625 (* z t))))
        (t_2 (+ c (* x y)))
        (t_3 (* -0.25 (* b a))))
   (if (<= (* b a) -6.5e+148)
     (+ c t_3)
     (if (<= (* b a) -6e-165)
       t_1
       (if (<= (* b a) -3.7e-218)
         t_2
         (if (<= (* b a) -4.4e-304)
           t_1
           (if (<= (* b a) 2.6e-94)
             t_2
             (if (<= (* b a) 3e-6)
               t_1
               (if (<= (* b a) 1.05e+193) 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 + (x * y);
	double t_3 = -0.25 * (b * a);
	double tmp;
	if ((b * a) <= -6.5e+148) {
		tmp = c + t_3;
	} else if ((b * a) <= -6e-165) {
		tmp = t_1;
	} else if ((b * a) <= -3.7e-218) {
		tmp = t_2;
	} else if ((b * a) <= -4.4e-304) {
		tmp = t_1;
	} else if ((b * a) <= 2.6e-94) {
		tmp = t_2;
	} else if ((b * a) <= 3e-6) {
		tmp = t_1;
	} else if ((b * a) <= 1.05e+193) {
		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 + (x * y)
    t_3 = (-0.25d0) * (b * a)
    if ((b * a) <= (-6.5d+148)) then
        tmp = c + t_3
    else if ((b * a) <= (-6d-165)) then
        tmp = t_1
    else if ((b * a) <= (-3.7d-218)) then
        tmp = t_2
    else if ((b * a) <= (-4.4d-304)) then
        tmp = t_1
    else if ((b * a) <= 2.6d-94) then
        tmp = t_2
    else if ((b * a) <= 3d-6) then
        tmp = t_1
    else if ((b * a) <= 1.05d+193) 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 + (x * y);
	double t_3 = -0.25 * (b * a);
	double tmp;
	if ((b * a) <= -6.5e+148) {
		tmp = c + t_3;
	} else if ((b * a) <= -6e-165) {
		tmp = t_1;
	} else if ((b * a) <= -3.7e-218) {
		tmp = t_2;
	} else if ((b * a) <= -4.4e-304) {
		tmp = t_1;
	} else if ((b * a) <= 2.6e-94) {
		tmp = t_2;
	} else if ((b * a) <= 3e-6) {
		tmp = t_1;
	} else if ((b * a) <= 1.05e+193) {
		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 + (x * y)
	t_3 = -0.25 * (b * a)
	tmp = 0
	if (b * a) <= -6.5e+148:
		tmp = c + t_3
	elif (b * a) <= -6e-165:
		tmp = t_1
	elif (b * a) <= -3.7e-218:
		tmp = t_2
	elif (b * a) <= -4.4e-304:
		tmp = t_1
	elif (b * a) <= 2.6e-94:
		tmp = t_2
	elif (b * a) <= 3e-6:
		tmp = t_1
	elif (b * a) <= 1.05e+193:
		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(x * y))
	t_3 = Float64(-0.25 * Float64(b * a))
	tmp = 0.0
	if (Float64(b * a) <= -6.5e+148)
		tmp = Float64(c + t_3);
	elseif (Float64(b * a) <= -6e-165)
		tmp = t_1;
	elseif (Float64(b * a) <= -3.7e-218)
		tmp = t_2;
	elseif (Float64(b * a) <= -4.4e-304)
		tmp = t_1;
	elseif (Float64(b * a) <= 2.6e-94)
		tmp = t_2;
	elseif (Float64(b * a) <= 3e-6)
		tmp = t_1;
	elseif (Float64(b * a) <= 1.05e+193)
		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 + (x * y);
	t_3 = -0.25 * (b * a);
	tmp = 0.0;
	if ((b * a) <= -6.5e+148)
		tmp = c + t_3;
	elseif ((b * a) <= -6e-165)
		tmp = t_1;
	elseif ((b * a) <= -3.7e-218)
		tmp = t_2;
	elseif ((b * a) <= -4.4e-304)
		tmp = t_1;
	elseif ((b * a) <= 2.6e-94)
		tmp = t_2;
	elseif ((b * a) <= 3e-6)
		tmp = t_1;
	elseif ((b * a) <= 1.05e+193)
		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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -6.5e+148], N[(c + t$95$3), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], -6e-165], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -3.7e-218], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -4.4e-304], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 2.6e-94], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], 3e-6], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 1.05e+193], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -6.49999999999999947e148

   1. Initial program 89.4%

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

   2. Taylor expanded in a around inf 75.7%

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

      1. *-commutative 75.7%

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

   4. Simplified 75.7%

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

   if -6.49999999999999947e148 < (*.f64 a b) < -5.99999999999999958e-165 or -3.7000000000000002e-218 < (*.f64 a b) < -4.4e-304 or 2.59999999999999994e-94 < (*.f64 a b) < 3.0000000000000001e-6

   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 77.8%

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

   if -5.99999999999999958e-165 < (*.f64 a b) < -3.7000000000000002e-218 or -4.4e-304 < (*.f64 a b) < 2.59999999999999994e-94 or 3.0000000000000001e-6 < (*.f64 a b) < 1.05e193

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 71.4%

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

   if 1.05e193 < (*.f64 a b)

   1. Initial program 97.1%

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

   2. Taylor expanded in z around 0 97.0%

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

   3. Taylor expanded in a around inf 88.8%

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

      1. *-commutative 88.8%

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

   5. Simplified 88.8%

      \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -6.5 \cdot 10^{+148}:\\ \;\;\;\;c + -0.25 \cdot \left(b \cdot a\right)\\ \mathbf{elif}\;b \cdot a \leq -6 \cdot 10^{-165}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;b \cdot a \leq -3.7 \cdot 10^{-218}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -4.4 \cdot 10^{-304}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;b \cdot a \leq 2.6 \cdot 10^{-94}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 3 \cdot 10^{-6}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;b \cdot a \leq 1.05 \cdot 10^{+193}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \end{array} \]

Alternative 10: 74.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-36} \lor \neg \left(t \leq 1.45 \cdot 10^{+57} \lor \neg \left(t \leq 7.5 \cdot 10^{+97}\right) \land t \leq 5.1 \cdot 10^{+241}\right):\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -1.05e-36)
         (not (or (<= t 1.45e+57) (and (not (<= t 7.5e+97)) (<= t 5.1e+241)))))
   (+ c (* 0.0625 (* z t)))
   (- (+ c (* x y)) (* (* b a) 0.25))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.05e-36) || !((t <= 1.45e+57) || (!(t <= 7.5e+97) && (t <= 5.1e+241)))) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-1.05d-36)) .or. (.not. (t <= 1.45d+57) .or. (.not. (t <= 7.5d+97)) .and. (t <= 5.1d+241))) then
        tmp = c + (0.0625d0 * (z * t))
    else
        tmp = (c + (x * y)) - ((b * a) * 0.25d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.05e-36) || !((t <= 1.45e+57) || (!(t <= 7.5e+97) && (t <= 5.1e+241)))) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -1.05e-36) or not ((t <= 1.45e+57) or (not (t <= 7.5e+97) and (t <= 5.1e+241))):
		tmp = c + (0.0625 * (z * t))
	else:
		tmp = (c + (x * y)) - ((b * a) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -1.05e-36) || !((t <= 1.45e+57) || (!(t <= 7.5e+97) && (t <= 5.1e+241))))
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	else
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(b * a) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -1.05e-36) || ~(((t <= 1.45e+57) || (~((t <= 7.5e+97)) && (t <= 5.1e+241)))))
		tmp = c + (0.0625 * (z * t));
	else
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -1.05e-36], N[Not[Or[LessEqual[t, 1.45e+57], And[N[Not[LessEqual[t, 7.5e+97]], $MachinePrecision], LessEqual[t, 5.1e+241]]]], $MachinePrecision]], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.04999999999999995e-36 or 1.4500000000000001e57 < t < 7.5000000000000004e97 or 5.1000000000000002e241 < t

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 69.0%

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

   if -1.04999999999999995e-36 < t < 1.4500000000000001e57 or 7.5000000000000004e97 < t < 5.1000000000000002e241

   1. Initial program 97.6%

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

   2. Taylor expanded in z around 0 89.5%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-36} \lor \neg \left(t \leq 1.45 \cdot 10^{+57} \lor \neg \left(t \leq 7.5 \cdot 10^{+97}\right) \land t \leq 5.1 \cdot 10^{+241}\right):\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 11: 83.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot 0.25\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+37} \lor \neg \left(z \leq 7.5\right):\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) 0.25)))
   (if (or (<= z -9.5e+37) (not (<= z 7.5)))
     (- (+ c (* 0.0625 (* z t))) t_1)
     (- (+ 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 = (b * a) * 0.25;
	double tmp;
	if ((z <= -9.5e+37) || !(z <= 7.5)) {
		tmp = (c + (0.0625 * (z * t))) - t_1;
	} else {
		tmp = (c + (x * y)) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * a) * 0.25d0
    if ((z <= (-9.5d+37)) .or. (.not. (z <= 7.5d0))) then
        tmp = (c + (0.0625d0 * (z * t))) - t_1
    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 = (b * a) * 0.25;
	double tmp;
	if ((z <= -9.5e+37) || !(z <= 7.5)) {
		tmp = (c + (0.0625 * (z * t))) - t_1;
	} else {
		tmp = (c + (x * y)) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * 0.25
	tmp = 0
	if (z <= -9.5e+37) or not (z <= 7.5):
		tmp = (c + (0.0625 * (z * t))) - t_1
	else:
		tmp = (c + (x * y)) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b * a) * 0.25)
	tmp = 0.0
	if ((z <= -9.5e+37) || !(z <= 7.5))
		tmp = Float64(Float64(c + Float64(0.0625 * Float64(z * t))) - t_1);
	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 = (b * a) * 0.25;
	tmp = 0.0;
	if ((z <= -9.5e+37) || ~((z <= 7.5)))
		tmp = (c + (0.0625 * (z * t))) - t_1;
	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[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]}, If[Or[LessEqual[z, -9.5e+37], N[Not[LessEqual[z, 7.5]], $MachinePrecision]], N[(N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999995e37 or 7.5 < z

   1. Initial program 94.7%

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

   2. Taylor expanded in x around 0 79.4%

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

   if -9.4999999999999995e37 < z < 7.5

   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 0 88.5%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+37} \lor \neg \left(z \leq 7.5\right):\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 12: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

2. Final simplification 97.6%

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

Alternative 13: 38.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-85}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq -1.44 \cdot 10^{-257}:\\ \;\;\;\;c\\ \mathbf{elif}\;z \leq 95:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= z -5.5e+38)
     t_1
     (if (<= z -4.4e-85)
       (* x y)
       (if (<= z -1.44e-257) c (if (<= z 95.0) (* 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 tmp;
	if (z <= -5.5e+38) {
		tmp = t_1;
	} else if (z <= -4.4e-85) {
		tmp = x * y;
	} else if (z <= -1.44e-257) {
		tmp = c;
	} else if (z <= 95.0) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if (z <= (-5.5d+38)) then
        tmp = t_1
    else if (z <= (-4.4d-85)) then
        tmp = x * y
    else if (z <= (-1.44d-257)) then
        tmp = c
    else if (z <= 95.0d0) then
        tmp = x * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if (z <= -5.5e+38) {
		tmp = t_1;
	} else if (z <= -4.4e-85) {
		tmp = x * y;
	} else if (z <= -1.44e-257) {
		tmp = c;
	} else if (z <= 95.0) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if z <= -5.5e+38:
		tmp = t_1
	elif z <= -4.4e-85:
		tmp = x * y
	elif z <= -1.44e-257:
		tmp = c
	elif z <= 95.0:
		tmp = x * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (z <= -5.5e+38)
		tmp = t_1;
	elseif (z <= -4.4e-85)
		tmp = Float64(x * y);
	elseif (z <= -1.44e-257)
		tmp = c;
	elseif (z <= 95.0)
		tmp = Float64(x * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if (z <= -5.5e+38)
		tmp = t_1;
	elseif (z <= -4.4e-85)
		tmp = x * y;
	elseif (z <= -1.44e-257)
		tmp = c;
	elseif (z <= 95.0)
		tmp = x * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+38], t$95$1, If[LessEqual[z, -4.4e-85], N[(x * y), $MachinePrecision], If[LessEqual[z, -1.44e-257], c, If[LessEqual[z, 95.0], N[(x * y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5000000000000003e38 or 95 < z

   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 z around inf 58.6%

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

   3. Taylor expanded in t around inf 42.0%

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

   if -5.5000000000000003e38 < z < -4.4e-85 or -1.43999999999999992e-257 < z < 95

   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 0 89.4%

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

   3. Taylor expanded in y around inf 32.7%

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

   if -4.4e-85 < z < -1.43999999999999992e-257

   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 39.8%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+38}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-85}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq -1.44 \cdot 10^{-257}:\\ \;\;\;\;c\\ \mathbf{elif}\;z \leq 95:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]

Alternative 14: 64.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1.55 \cdot 10^{+119} \lor \neg \left(b \cdot a \leq 7 \cdot 10^{+189}\right):\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -1.55e+119) (not (<= (* b a) 7e+189)))
   (* -0.25 (* b a))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -1.55e+119) || !((b * a) <= 7e+189)) {
		tmp = -0.25 * (b * a);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((b * a) <= (-1.55d+119)) .or. (.not. ((b * a) <= 7d+189))) then
        tmp = (-0.25d0) * (b * a)
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -1.55e+119) || !((b * a) <= 7e+189)) {
		tmp = -0.25 * (b * a);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((b * a) <= -1.55e+119) or not ((b * a) <= 7e+189):
		tmp = -0.25 * (b * a)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(b * a) <= -1.55e+119) || !(Float64(b * a) <= 7e+189))
		tmp = Float64(-0.25 * Float64(b * a));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((b * a) <= -1.55e+119) || ~(((b * a) <= 7e+189)))
		tmp = -0.25 * (b * a);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -1.55e+119], N[Not[LessEqual[N[(b * a), $MachinePrecision], 7e+189]], $MachinePrecision]], N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.54999999999999998e119 or 6.99999999999999991e189 < (*.f64 a b)

   1. Initial program 93.0%

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

   2. Taylor expanded in z around 0 86.2%

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

   3. Taylor expanded in a around inf 76.4%

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

      1. *-commutative 76.4%

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

   5. Simplified 76.4%

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

   if -1.54999999999999998e119 < (*.f64 a b) < 6.99999999999999991e189

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 64.9%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1.55 \cdot 10^{+119} \lor \neg \left(b \cdot a \leq 7 \cdot 10^{+189}\right):\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 15: 37.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8.2 \cdot 10^{+109}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{+25}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -8.2e+109) c (if (<= c 2.4e+25) (* x y) c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -8.2e+109) {
		tmp = c;
	} else if (c <= 2.4e+25) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= (-8.2d+109)) then
        tmp = c
    else if (c <= 2.4d+25) then
        tmp = x * y
    else
        tmp = c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -8.2e+109) {
		tmp = c;
	} else if (c <= 2.4e+25) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -8.2e+109:
		tmp = c
	elif c <= 2.4e+25:
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -8.2e+109)
		tmp = c;
	elseif (c <= 2.4e+25)
		tmp = Float64(x * y);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -8.2e+109)
		tmp = c;
	elseif (c <= 2.4e+25)
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -8.2e+109], c, If[LessEqual[c, 2.4e+25], N[(x * y), $MachinePrecision], c]]

Derivation

1. Split input into 2 regimes

2. if c < -8.19999999999999939e109 or 2.39999999999999996e25 < c

   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 c around inf 44.4%

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

   if -8.19999999999999939e109 < c < 2.39999999999999996e25

   1. Initial program 96.4%

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

   2. Taylor expanded in z around 0 70.8%

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

   3. Taylor expanded in y around inf 34.8%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.2 \cdot 10^{+109}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{+25}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 16: 21.7% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

2. Taylor expanded in c around inf 24.1%

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

3. Final simplification 24.1%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023230 
(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))