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

Percentage Accurate: 97.7% → 98.8%

Time: 8.8s

Alternatives: 16

Speedup: 1.0×

• 32.8% 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

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;\left(\frac{z \cdot t}{16} + x \cdot y\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(x, y, \frac{t}{\frac{16}{z}}\right) + \left(c - \frac{a}{\frac{4}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, \left(a \cdot b\right) \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (- (+ (/ (* z t) 16.0) (* x y)) (/ (* a b) 4.0)) INFINITY)
   (+ (fma x y (/ t (/ 16.0 z))) (- c (/ a (/ 4.0 b))))
   (fma y x (* (* a b) -0.25))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((((z * t) / 16.0) + (x * y)) - ((a * b) / 4.0)) <= ((double) INFINITY)) {
		tmp = fma(x, y, (t / (16.0 / z))) + (c - (a / (4.0 / b)));
	} else {
		tmp = fma(y, x, ((a * b) * -0.25));
	}
	return tmp;
}

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(z * t) / 16.0) + Float64(x * y)) - Float64(Float64(a * b) / 4.0)) <= Inf)
		tmp = Float64(fma(x, y, Float64(t / Float64(16.0 / z))) + Float64(c - Float64(a / Float64(4.0 / b))));
	else
		tmp = fma(y, x, Float64(Float64(a * b) * -0.25));
	end
	return tmp
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(N[(N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision], Infinity], 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], N[(y * x + N[(N[(a * b), $MachinePrecision] * -0.25), $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 99.6%

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

      1. associate-+l- 99.6%

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

      2. fma-def 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-/l* 99.9%

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

      5. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   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. associate--l+ 0.0%

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

      3. fma-def 37.5%

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

      4. associate-*l/ 37.5%

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

      5. fma-neg 50.0%

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

      6. sub-neg 50.0%

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

      7. distribute-neg-in 50.0%

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

      8. remove-double-neg 50.0%

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

      9. associate-/l* 50.0%

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

      10. distribute-frac-neg 50.0%

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

      11. associate-/r/ 50.0%

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

      12. fma-def 50.0%

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

      13. neg-mul-1 50.0%

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

      14. *-commutative 50.0%

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

      15. associate-/l* 50.0%

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

      16. metadata-eval 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in z around 0 62.5%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c + -0.25 \cdot \left(a \cdot b\right)}\right) \]
   5. Step-by-step derivation

      1. metadata-eval 62.5%

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

      2. distribute-lft-neg-in 62.5%

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

      3. +-commutative 62.5%

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

      4. distribute-lft-neg-in 62.5%

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

      5. metadata-eval 62.5%

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

      6. associate-*r* 62.5%

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

      7. *-commutative 62.5%

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

      8. fma-udef 62.5%

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

   6. Simplified 62.5%

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

   7. Taylor expanded in c around 0 37.5%

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

      1. fma-def 62.5%

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

   9. Simplified 62.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\frac{z \cdot t}{16} + x \cdot y\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(x, y, \frac{t}{\frac{16}{z}}\right) + \left(c - \frac{a}{\frac{4}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, \left(a \cdot b\right) \cdot -0.25\right)\\ \end{array} \]

Alternative 2: 98.9% accurate, 0.1× speedup

Math

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

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(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

assert(z < t);
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

z, t = sort([z, t])
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

NOTE: z and t should be sorted in increasing order before calling this function.
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 96.5%

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

   1. associate-+l- 96.5%

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

   2. associate--l+ 96.5%

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

   3. fma-def 97.7%

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

   4. associate-*l/ 98.0%

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

   5. fma-neg 98.4%

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

   6. sub-neg 98.4%

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

   7. distribute-neg-in 98.4%

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

   8. remove-double-neg 98.4%

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

   9. associate-/l* 98.4%

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

   10. distribute-frac-neg 98.4%

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

   11. associate-/r/ 98.4%

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

   12. fma-def 98.4%

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

   13. neg-mul-1 98.4%

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

   14. *-commutative 98.4%

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

   15. associate-/l* 98.4%

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

   16. metadata-eval 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 3: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \left(\frac{z \cdot t}{16} + x \cdot y\right) - \frac{a \cdot b}{4}\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;c + t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, \left(a \cdot b\right) \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (+ (/ (* z t) 16.0) (* x y)) (/ (* a b) 4.0))))
   (if (<= t_1 INFINITY) (+ c t_1) (fma y x (* (* a b) -0.25)))))

C

assert(z < t);
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)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = c + t_1;
	} else {
		tmp = fma(y, x, ((a * b) * -0.25));
	}
	return tmp;
}

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(z * t) / 16.0) + Float64(x * y)) - Float64(Float64(a * b) / 4.0))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(c + t_1);
	else
		tmp = fma(y, x, Float64(Float64(a * b) * -0.25));
	end
	return tmp
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
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[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(c + t$95$1), $MachinePrecision], N[(y * x + N[(N[(a * b), $MachinePrecision] * -0.25), $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 99.6%

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

   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. associate--l+ 0.0%

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

      3. fma-def 37.5%

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

      4. associate-*l/ 37.5%

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

      5. fma-neg 50.0%

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

      6. sub-neg 50.0%

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

      7. distribute-neg-in 50.0%

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

      8. remove-double-neg 50.0%

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

      9. associate-/l* 50.0%

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

      10. distribute-frac-neg 50.0%

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

      11. associate-/r/ 50.0%

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

      12. fma-def 50.0%

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

      13. neg-mul-1 50.0%

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

      14. *-commutative 50.0%

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

      15. associate-/l* 50.0%

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

      16. metadata-eval 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in z around 0 62.5%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c + -0.25 \cdot \left(a \cdot b\right)}\right) \]
   5. Step-by-step derivation

      1. metadata-eval 62.5%

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

      2. distribute-lft-neg-in 62.5%

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

      3. +-commutative 62.5%

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

      4. distribute-lft-neg-in 62.5%

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

      5. metadata-eval 62.5%

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

      6. associate-*r* 62.5%

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

      7. *-commutative 62.5%

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

      8. fma-udef 62.5%

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

   6. Simplified 62.5%

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

   7. Taylor expanded in c around 0 37.5%

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

      1. fma-def 62.5%

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

   9. Simplified 62.5%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\frac{z \cdot t}{16} + x \cdot y\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\left(\frac{z \cdot t}{16} + x \cdot y\right) - \frac{a \cdot b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, \left(a \cdot b\right) \cdot -0.25\right)\\ \end{array} \]

Alternative 4: 67.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+78}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{-69}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-241}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* (* z t) 0.0625))))
   (if (<= (* a b) -1e+78)
     (- (* x y) (* (* a b) 0.25))
     (if (<= (* a b) -4e-69)
       (+ c (* x y))
       (if (<= (* a b) -2e-141)
         t_1
         (if (<= (* a b) -5e-241)
           (+ c (* t (* z 0.0625)))
           (if (<= (* a b) 1e+47) t_1 (+ c (* b (* a -0.25))))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + ((z * t) * 0.0625);
	double tmp;
	if ((a * b) <= -1e+78) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((a * b) <= -4e-69) {
		tmp = c + (x * y);
	} else if ((a * b) <= -2e-141) {
		tmp = t_1;
	} else if ((a * b) <= -5e-241) {
		tmp = c + (t * (z * 0.0625));
	} else if ((a * b) <= 1e+47) {
		tmp = t_1;
	} else {
		tmp = c + (b * (a * -0.25));
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
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 = (x * y) + ((z * t) * 0.0625d0)
    if ((a * b) <= (-1d+78)) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    else if ((a * b) <= (-4d-69)) then
        tmp = c + (x * y)
    else if ((a * b) <= (-2d-141)) then
        tmp = t_1
    else if ((a * b) <= (-5d-241)) then
        tmp = c + (t * (z * 0.0625d0))
    else if ((a * b) <= 1d+47) then
        tmp = t_1
    else
        tmp = c + (b * (a * (-0.25d0)))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + ((z * t) * 0.0625);
	double tmp;
	if ((a * b) <= -1e+78) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((a * b) <= -4e-69) {
		tmp = c + (x * y);
	} else if ((a * b) <= -2e-141) {
		tmp = t_1;
	} else if ((a * b) <= -5e-241) {
		tmp = c + (t * (z * 0.0625));
	} else if ((a * b) <= 1e+47) {
		tmp = t_1;
	} else {
		tmp = c + (b * (a * -0.25));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	t_1 = (x * y) + ((z * t) * 0.0625)
	tmp = 0
	if (a * b) <= -1e+78:
		tmp = (x * y) - ((a * b) * 0.25)
	elif (a * b) <= -4e-69:
		tmp = c + (x * y)
	elif (a * b) <= -2e-141:
		tmp = t_1
	elif (a * b) <= -5e-241:
		tmp = c + (t * (z * 0.0625))
	elif (a * b) <= 1e+47:
		tmp = t_1
	else:
		tmp = c + (b * (a * -0.25))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625))
	tmp = 0.0
	if (Float64(a * b) <= -1e+78)
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	elseif (Float64(a * b) <= -4e-69)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(a * b) <= -2e-141)
		tmp = t_1;
	elseif (Float64(a * b) <= -5e-241)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (Float64(a * b) <= 1e+47)
		tmp = t_1;
	else
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) + ((z * t) * 0.0625);
	tmp = 0.0;
	if ((a * b) <= -1e+78)
		tmp = (x * y) - ((a * b) * 0.25);
	elseif ((a * b) <= -4e-69)
		tmp = c + (x * y);
	elseif ((a * b) <= -2e-141)
		tmp = t_1;
	elseif ((a * b) <= -5e-241)
		tmp = c + (t * (z * 0.0625));
	elseif ((a * b) <= 1e+47)
		tmp = t_1;
	else
		tmp = c + (b * (a * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1e+78], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -4e-69], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -2e-141], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -5e-241], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+47], t$95$1, N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a b) < -1.00000000000000001e78

   1. Initial program 93.6%

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

   2. Taylor expanded in z around 0 78.4%

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

   3. Taylor expanded in c around 0 71.6%

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

   if -1.00000000000000001e78 < (*.f64 a b) < -3.9999999999999999e-69

   1. Initial program 96.2%

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

   2. Taylor expanded in x around inf 67.5%

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

   if -3.9999999999999999e-69 < (*.f64 a b) < -2.0000000000000001e-141 or -4.9999999999999998e-241 < (*.f64 a b) < 1e47

   1. Initial program 98.2%

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

      1. associate-+l- 98.2%

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

      2. associate--l+ 98.2%

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

      3. fma-def 98.2%

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

      4. associate-*l/ 99.0%

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

      5. fma-neg 99.0%

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

      6. sub-neg 99.0%

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

      7. distribute-neg-in 99.0%

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

      8. remove-double-neg 99.0%

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

      9. associate-/l* 99.0%

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

      10. distribute-frac-neg 99.0%

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

      11. associate-/r/ 99.0%

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

      12. fma-def 99.0%

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

      13. neg-mul-1 99.0%

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

      14. *-commutative 99.0%

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

      15. associate-/l* 99.0%

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

      16. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in a around 0 96.4%

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

   5. Taylor expanded in c around 0 74.1%

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

   if -2.0000000000000001e-141 < (*.f64 a b) < -4.9999999999999998e-241

   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 93.6%

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

      1. *-commutative 93.6%

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

      2. associate-*r* 93.6%

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

      3. *-commutative 93.6%

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

   4. Simplified 93.6%

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

   if 1e47 < (*.f64 a b)

   1. Initial program 95.7%

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

   2. Taylor expanded in a around inf 82.4%

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

      1. associate-*r* 82.4%

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

      2. *-commutative 82.4%

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

   4. Simplified 82.4%

      \[\leadsto \color{blue}{\left(a \cdot -0.25\right) \cdot b} + c \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+78}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{-69}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-141}:\\ \;\;\;\;x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{-241}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+47}:\\ \;\;\;\;x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 5: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 10^{+47}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+99}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+134}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+198}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* a b) 0.25))))
   (if (<= (* a b) -5e+158)
     t_1
     (if (<= (* a b) 1e+47)
       (+ c (+ (* x y) (* (* z t) 0.0625)))
       (if (<= (* a b) 5e+99)
         (+ c (* b (* a -0.25)))
         (if (<= (* a b) 1e+134)
           (+ c (* x y))
           (if (<= (* a b) 5e+198) t_1 (* (* a b) -0.25))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((a * b) <= -5e+158) {
		tmp = t_1;
	} else if ((a * b) <= 1e+47) {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	} else if ((a * b) <= 5e+99) {
		tmp = c + (b * (a * -0.25));
	} else if ((a * b) <= 1e+134) {
		tmp = c + (x * y);
	} else if ((a * b) <= 5e+198) {
		tmp = t_1;
	} else {
		tmp = (a * b) * -0.25;
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
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 = (x * y) - ((a * b) * 0.25d0)
    if ((a * b) <= (-5d+158)) then
        tmp = t_1
    else if ((a * b) <= 1d+47) then
        tmp = c + ((x * y) + ((z * t) * 0.0625d0))
    else if ((a * b) <= 5d+99) then
        tmp = c + (b * (a * (-0.25d0)))
    else if ((a * b) <= 1d+134) then
        tmp = c + (x * y)
    else if ((a * b) <= 5d+198) then
        tmp = t_1
    else
        tmp = (a * b) * (-0.25d0)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((a * b) <= -5e+158) {
		tmp = t_1;
	} else if ((a * b) <= 1e+47) {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	} else if ((a * b) <= 5e+99) {
		tmp = c + (b * (a * -0.25));
	} else if ((a * b) <= 1e+134) {
		tmp = c + (x * y);
	} else if ((a * b) <= 5e+198) {
		tmp = t_1;
	} else {
		tmp = (a * b) * -0.25;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	t_1 = (x * y) - ((a * b) * 0.25)
	tmp = 0
	if (a * b) <= -5e+158:
		tmp = t_1
	elif (a * b) <= 1e+47:
		tmp = c + ((x * y) + ((z * t) * 0.0625))
	elif (a * b) <= 5e+99:
		tmp = c + (b * (a * -0.25))
	elif (a * b) <= 1e+134:
		tmp = c + (x * y)
	elif (a * b) <= 5e+198:
		tmp = t_1
	else:
		tmp = (a * b) * -0.25
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25))
	tmp = 0.0
	if (Float64(a * b) <= -5e+158)
		tmp = t_1;
	elseif (Float64(a * b) <= 1e+47)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625)));
	elseif (Float64(a * b) <= 5e+99)
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	elseif (Float64(a * b) <= 1e+134)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(a * b) <= 5e+198)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * b) * -0.25);
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) - ((a * b) * 0.25);
	tmp = 0.0;
	if ((a * b) <= -5e+158)
		tmp = t_1;
	elseif ((a * b) <= 1e+47)
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	elseif ((a * b) <= 5e+99)
		tmp = c + (b * (a * -0.25));
	elseif ((a * b) <= 1e+134)
		tmp = c + (x * y);
	elseif ((a * b) <= 5e+198)
		tmp = t_1;
	else
		tmp = (a * b) * -0.25;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+158], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1e+47], N[(c + N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+99], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+134], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+198], t$95$1, N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a b) < -4.9999999999999996e158 or 9.99999999999999921e133 < (*.f64 a b) < 5.00000000000000049e198

   1. Initial program 92.4%

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

   2. Taylor expanded in z around 0 81.5%

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

   3. Taylor expanded in c around 0 77.1%

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

   if -4.9999999999999996e158 < (*.f64 a b) < 1e47

   1. Initial program 98.2%

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

   2. Taylor expanded in a around 0 90.7%

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

   if 1e47 < (*.f64 a b) < 5.00000000000000008e99

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 90.7%

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

      1. associate-*r* 90.7%

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

      2. *-commutative 90.7%

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

   4. Simplified 90.7%

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

   if 5.00000000000000008e99 < (*.f64 a b) < 9.99999999999999921e133

   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 91.3%

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

   if 5.00000000000000049e198 < (*.f64 a b)

   1. Initial program 90.0%

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

      1. associate-+l- 90.0%

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

      2. associate--l+ 90.0%

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

      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. Taylor expanded in z around 0 95.0%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c + -0.25 \cdot \left(a \cdot b\right)}\right) \]
   5. Step-by-step derivation

      1. metadata-eval 95.0%

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

      2. distribute-lft-neg-in 95.0%

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

      3. +-commutative 95.0%

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

      4. distribute-lft-neg-in 95.0%

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

      5. metadata-eval 95.0%

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

      6. associate-*r* 95.0%

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

      7. *-commutative 95.0%

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

      8. fma-udef 95.0%

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

   6. Simplified 95.0%

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

   7. Taylor expanded in a around inf 95.0%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+158}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 10^{+47}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+99}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+134}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+198}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]

Alternative 6: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+158}:\\ \;\;\;\;x \cdot y - t_1\\ \mathbf{elif}\;a \cdot b \leq 10^{+47}:\\ \;\;\;\;c + \left(x \cdot y + t_2\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+99}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+134}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_2 - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)) (t_2 (* (* z t) 0.0625)))
   (if (<= (* a b) -5e+158)
     (- (* x y) t_1)
     (if (<= (* a b) 1e+47)
       (+ c (+ (* x y) t_2))
       (if (<= (* a b) 5e+99)
         (+ c (* b (* a -0.25)))
         (if (<= (* a b) 1e+134) (+ c (* x y)) (- t_2 t_1)))))))

C

assert(z < t);
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 = (z * t) * 0.0625;
	double tmp;
	if ((a * b) <= -5e+158) {
		tmp = (x * y) - t_1;
	} else if ((a * b) <= 1e+47) {
		tmp = c + ((x * y) + t_2);
	} else if ((a * b) <= 5e+99) {
		tmp = c + (b * (a * -0.25));
	} else if ((a * b) <= 1e+134) {
		tmp = c + (x * y);
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
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 = (z * t) * 0.0625d0
    if ((a * b) <= (-5d+158)) then
        tmp = (x * y) - t_1
    else if ((a * b) <= 1d+47) then
        tmp = c + ((x * y) + t_2)
    else if ((a * b) <= 5d+99) then
        tmp = c + (b * (a * (-0.25d0)))
    else if ((a * b) <= 1d+134) then
        tmp = c + (x * y)
    else
        tmp = t_2 - t_1
    end if
    code = tmp
end function

Java

assert z < t;
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 = (z * t) * 0.0625;
	double tmp;
	if ((a * b) <= -5e+158) {
		tmp = (x * y) - t_1;
	} else if ((a * b) <= 1e+47) {
		tmp = c + ((x * y) + t_2);
	} else if ((a * b) <= 5e+99) {
		tmp = c + (b * (a * -0.25));
	} else if ((a * b) <= 1e+134) {
		tmp = c + (x * y);
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	t_2 = (z * t) * 0.0625
	tmp = 0
	if (a * b) <= -5e+158:
		tmp = (x * y) - t_1
	elif (a * b) <= 1e+47:
		tmp = c + ((x * y) + t_2)
	elif (a * b) <= 5e+99:
		tmp = c + (b * (a * -0.25))
	elif (a * b) <= 1e+134:
		tmp = c + (x * y)
	else:
		tmp = t_2 - t_1
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	t_2 = Float64(Float64(z * t) * 0.0625)
	tmp = 0.0
	if (Float64(a * b) <= -5e+158)
		tmp = Float64(Float64(x * y) - t_1);
	elseif (Float64(a * b) <= 1e+47)
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	elseif (Float64(a * b) <= 5e+99)
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	elseif (Float64(a * b) <= 1e+134)
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(t_2 - t_1);
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	t_2 = (z * t) * 0.0625;
	tmp = 0.0;
	if ((a * b) <= -5e+158)
		tmp = (x * y) - t_1;
	elseif ((a * b) <= 1e+47)
		tmp = c + ((x * y) + t_2);
	elseif ((a * b) <= 5e+99)
		tmp = c + (b * (a * -0.25));
	elseif ((a * b) <= 1e+134)
		tmp = c + (x * y);
	else
		tmp = t_2 - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
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[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+158], N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+47], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+99], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+134], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(t$95$2 - t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a b) < -4.9999999999999996e158

   1. Initial program 91.1%

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

   2. Taylor expanded in z around 0 80.4%

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

   3. Taylor expanded in c around 0 75.3%

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

   if -4.9999999999999996e158 < (*.f64 a b) < 1e47

   1. Initial program 98.2%

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

   2. Taylor expanded in a around 0 90.7%

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

   if 1e47 < (*.f64 a b) < 5.00000000000000008e99

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 90.7%

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

      1. associate-*r* 90.7%

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

      2. *-commutative 90.7%

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

   4. Simplified 90.7%

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

   if 5.00000000000000008e99 < (*.f64 a b) < 9.99999999999999921e133

   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 91.3%

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

   if 9.99999999999999921e133 < (*.f64 a b)

   1. Initial program 92.9%

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

   2. Taylor expanded in x around 0 93.2%

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

   3. Taylor expanded in c around 0 93.0%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+158}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 10^{+47}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+99}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+134}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625 - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 7: 43.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -5.6 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -2.3 \cdot 10^{-70}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-129}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;a \cdot b \leq -2.9 \cdot 10^{-243}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 2.35 \cdot 10^{+55}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) -0.25)))
   (if (<= (* a b) -5.6e+77)
     t_1
     (if (<= (* a b) -2.3e-70)
       c
       (if (<= (* a b) -1e-129)
         (* (* z t) 0.0625)
         (if (<= (* a b) -2.9e-243)
           c
           (if (<= (* a b) 2.35e+55) (* x y) t_1)))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -5.6e+77) {
		tmp = t_1;
	} else if ((a * b) <= -2.3e-70) {
		tmp = c;
	} else if ((a * b) <= -1e-129) {
		tmp = (z * t) * 0.0625;
	} else if ((a * b) <= -2.9e-243) {
		tmp = c;
	} else if ((a * b) <= 2.35e+55) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) * (-0.25d0)
    if ((a * b) <= (-5.6d+77)) then
        tmp = t_1
    else if ((a * b) <= (-2.3d-70)) then
        tmp = c
    else if ((a * b) <= (-1d-129)) then
        tmp = (z * t) * 0.0625d0
    else if ((a * b) <= (-2.9d-243)) then
        tmp = c
    else if ((a * b) <= 2.35d+55) then
        tmp = x * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -5.6e+77) {
		tmp = t_1;
	} else if ((a * b) <= -2.3e-70) {
		tmp = c;
	} else if ((a * b) <= -1e-129) {
		tmp = (z * t) * 0.0625;
	} else if ((a * b) <= -2.9e-243) {
		tmp = c;
	} else if ((a * b) <= 2.35e+55) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * -0.25
	tmp = 0
	if (a * b) <= -5.6e+77:
		tmp = t_1
	elif (a * b) <= -2.3e-70:
		tmp = c
	elif (a * b) <= -1e-129:
		tmp = (z * t) * 0.0625
	elif (a * b) <= -2.9e-243:
		tmp = c
	elif (a * b) <= 2.35e+55:
		tmp = x * y
	else:
		tmp = t_1
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * -0.25)
	tmp = 0.0
	if (Float64(a * b) <= -5.6e+77)
		tmp = t_1;
	elseif (Float64(a * b) <= -2.3e-70)
		tmp = c;
	elseif (Float64(a * b) <= -1e-129)
		tmp = Float64(Float64(z * t) * 0.0625);
	elseif (Float64(a * b) <= -2.9e-243)
		tmp = c;
	elseif (Float64(a * b) <= 2.35e+55)
		tmp = Float64(x * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * -0.25;
	tmp = 0.0;
	if ((a * b) <= -5.6e+77)
		tmp = t_1;
	elseif ((a * b) <= -2.3e-70)
		tmp = c;
	elseif ((a * b) <= -1e-129)
		tmp = (z * t) * 0.0625;
	elseif ((a * b) <= -2.9e-243)
		tmp = c;
	elseif ((a * b) <= 2.35e+55)
		tmp = x * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5.6e+77], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -2.3e-70], c, If[LessEqual[N[(a * b), $MachinePrecision], -1e-129], N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -2.9e-243], c, If[LessEqual[N[(a * b), $MachinePrecision], 2.35e+55], N[(x * y), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -5.60000000000000001e77 or 2.35e55 < (*.f64 a b)

   1. Initial program 94.5%

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

      1. associate-+l- 94.5%

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

      2. associate--l+ 94.5%

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

      3. fma-def 97.2%

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

      4. associate-*l/ 97.2%

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

      5. fma-neg 98.2%

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

      6. sub-neg 98.2%

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

      7. distribute-neg-in 98.2%

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

      8. remove-double-neg 98.2%

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

      9. associate-/l* 98.1%

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

      10. distribute-frac-neg 98.1%

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

      11. associate-/r/ 98.2%

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

      12. fma-def 98.2%

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

      13. neg-mul-1 98.2%

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

      14. *-commutative 98.2%

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

      15. associate-/l* 98.2%

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

      16. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around 0 85.7%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c + -0.25 \cdot \left(a \cdot b\right)}\right) \]
   5. Step-by-step derivation

      1. metadata-eval 85.7%

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

      2. distribute-lft-neg-in 85.7%

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

      3. +-commutative 85.7%

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

      4. distribute-lft-neg-in 85.7%

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

      5. metadata-eval 85.7%

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

      6. associate-*r* 85.7%

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

      7. *-commutative 85.7%

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

      8. fma-udef 85.7%

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

   6. Simplified 85.7%

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

   7. Taylor expanded in a around inf 57.8%

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

   if -5.60000000000000001e77 < (*.f64 a b) < -2.30000000000000001e-70 or -9.9999999999999993e-130 < (*.f64 a b) < -2.89999999999999977e-243

   1. Initial program 97.7%

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

   2. Taylor expanded in c around inf 48.8%

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

   if -2.30000000000000001e-70 < (*.f64 a b) < -9.9999999999999993e-130

   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 x around 0 72.3%

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

   3. Taylor expanded in t around inf 57.6%

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

   if -2.89999999999999977e-243 < (*.f64 a b) < 2.35e55

   1. Initial program 97.9%

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

      1. associate-+l- 97.9%

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

      2. associate--l+ 97.9%

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

      3. fma-def 97.9%

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

      4. associate-*l/ 98.9%

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

      5. fma-neg 98.9%

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

      6. sub-neg 98.9%

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

      7. distribute-neg-in 98.9%

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

      8. remove-double-neg 98.9%

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

      9. associate-/l* 98.9%

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

      10. distribute-frac-neg 98.9%

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

      11. associate-/r/ 98.9%

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

      12. fma-def 98.9%

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

      13. neg-mul-1 98.9%

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

      14. *-commutative 98.9%

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

      15. associate-/l* 98.9%

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

      16. metadata-eval 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around 0 70.3%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c + -0.25 \cdot \left(a \cdot b\right)}\right) \]
   5. Step-by-step derivation

      1. metadata-eval 70.3%

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

      2. distribute-lft-neg-in 70.3%

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

      3. +-commutative 70.3%

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

      4. distribute-lft-neg-in 70.3%

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

      5. metadata-eval 70.3%

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

      6. associate-*r* 70.3%

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

      7. *-commutative 70.3%

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

      8. fma-udef 70.3%

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

   6. Simplified 70.3%

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

   7. Taylor expanded in x around inf 43.9%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.6 \cdot 10^{+77}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq -2.3 \cdot 10^{-70}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-129}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;a \cdot b \leq -2.9 \cdot 10^{-243}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 2.35 \cdot 10^{+55}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]

Alternative 8: 60.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{if}\;t \leq -0.145:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-123}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+250}:\\ \;\;\;\;x \cdot y + t_2\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* (* z t) 0.0625)))
   (if (<= t -0.145)
     t_2
     (if (<= t -8e-287)
       t_1
       (if (<= t 2.9e-123)
         (+ c (* b (* a -0.25)))
         (if (<= t 1.35e+90)
           t_1
           (if (<= t 5.2e+250) (+ (* x y) t_2) (+ c (* t (* z 0.0625))))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = (z * t) * 0.0625;
	double tmp;
	if (t <= -0.145) {
		tmp = t_2;
	} else if (t <= -8e-287) {
		tmp = t_1;
	} else if (t <= 2.9e-123) {
		tmp = c + (b * (a * -0.25));
	} else if (t <= 1.35e+90) {
		tmp = t_1;
	} else if (t <= 5.2e+250) {
		tmp = (x * y) + t_2;
	} else {
		tmp = c + (t * (z * 0.0625));
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = (z * t) * 0.0625d0
    if (t <= (-0.145d0)) then
        tmp = t_2
    else if (t <= (-8d-287)) then
        tmp = t_1
    else if (t <= 2.9d-123) then
        tmp = c + (b * (a * (-0.25d0)))
    else if (t <= 1.35d+90) then
        tmp = t_1
    else if (t <= 5.2d+250) then
        tmp = (x * y) + t_2
    else
        tmp = c + (t * (z * 0.0625d0))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = (z * t) * 0.0625;
	double tmp;
	if (t <= -0.145) {
		tmp = t_2;
	} else if (t <= -8e-287) {
		tmp = t_1;
	} else if (t <= 2.9e-123) {
		tmp = c + (b * (a * -0.25));
	} else if (t <= 1.35e+90) {
		tmp = t_1;
	} else if (t <= 5.2e+250) {
		tmp = (x * y) + t_2;
	} else {
		tmp = c + (t * (z * 0.0625));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = (z * t) * 0.0625
	tmp = 0
	if t <= -0.145:
		tmp = t_2
	elif t <= -8e-287:
		tmp = t_1
	elif t <= 2.9e-123:
		tmp = c + (b * (a * -0.25))
	elif t <= 1.35e+90:
		tmp = t_1
	elif t <= 5.2e+250:
		tmp = (x * y) + t_2
	else:
		tmp = c + (t * (z * 0.0625))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(Float64(z * t) * 0.0625)
	tmp = 0.0
	if (t <= -0.145)
		tmp = t_2;
	elseif (t <= -8e-287)
		tmp = t_1;
	elseif (t <= 2.9e-123)
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	elseif (t <= 1.35e+90)
		tmp = t_1;
	elseif (t <= 5.2e+250)
		tmp = Float64(Float64(x * y) + t_2);
	else
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = (z * t) * 0.0625;
	tmp = 0.0;
	if (t <= -0.145)
		tmp = t_2;
	elseif (t <= -8e-287)
		tmp = t_1;
	elseif (t <= 2.9e-123)
		tmp = c + (b * (a * -0.25));
	elseif (t <= 1.35e+90)
		tmp = t_1;
	elseif (t <= 5.2e+250)
		tmp = (x * y) + t_2;
	else
		tmp = c + (t * (z * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]}, If[LessEqual[t, -0.145], t$95$2, If[LessEqual[t, -8e-287], t$95$1, If[LessEqual[t, 2.9e-123], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+90], t$95$1, If[LessEqual[t, 5.2e+250], N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -0.14499999999999999

   1. Initial program 96.7%

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

   2. Taylor expanded in x around 0 80.9%

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

   3. Taylor expanded in t around inf 55.3%

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

   if -0.14499999999999999 < t < -8.00000000000000017e-287 or 2.90000000000000004e-123 < t < 1.35e90

   1. Initial program 99.0%

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

   2. Taylor expanded in x around inf 60.1%

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

   if -8.00000000000000017e-287 < t < 2.90000000000000004e-123

   1. Initial program 98.2%

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

   2. Taylor expanded in a around inf 68.3%

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

      1. associate-*r* 68.3%

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

      2. *-commutative 68.3%

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

   4. Simplified 68.3%

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

   if 1.35e90 < t < 5.20000000000000023e250

   1. Initial program 87.7%

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

      1. associate-+l- 87.7%

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

      2. associate--l+ 87.7%

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

      3. fma-def 87.7%

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

      4. associate-*l/ 91.3%

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

      5. fma-neg 95.7%

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

      6. sub-neg 95.7%

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

      7. distribute-neg-in 95.7%

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

      8. remove-double-neg 95.7%

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

      9. associate-/l* 95.7%

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

      10. distribute-frac-neg 95.7%

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

      11. associate-/r/ 95.7%

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

      12. fma-def 95.7%

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

      13. neg-mul-1 95.7%

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

      14. *-commutative 95.7%

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

      15. associate-/l* 95.7%

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

      16. metadata-eval 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in a around 0 75.5%

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

   5. Taylor expanded in c around 0 71.0%

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

   if 5.20000000000000023e250 < t

   1. Initial program 80.0%

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

   2. Taylor expanded in z around inf 80.0%

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

      1. *-commutative 80.0%

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

      2. associate-*r* 80.0%

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

      3. *-commutative 80.0%

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

   4. Simplified 80.0%

      \[\leadsto \color{blue}{t \cdot \left(0.0625 \cdot z\right)} + c \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.145:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-287}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-123}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+90}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+250}:\\ \;\;\;\;x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]

Alternative 9: 87.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{-40} \lor \neg \left(a \cdot b \leq 100000000\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -1e-40) (not (<= (* a b) 100000000.0)))
   (- (+ c (* x y)) (* (* a b) 0.25))
   (+ c (+ (* x y) (* (* z t) 0.0625)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -1e-40) || !((a * b) <= 100000000.0)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((a * b) <= (-1d-40)) .or. (.not. ((a * b) <= 100000000.0d0))) then
        tmp = (c + (x * y)) - ((a * b) * 0.25d0)
    else
        tmp = c + ((x * y) + ((z * t) * 0.0625d0))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -1e-40) || !((a * b) <= 100000000.0)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -1e-40) or not ((a * b) <= 100000000.0):
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + ((z * t) * 0.0625))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -1e-40) || !(Float64(a * b) <= 100000000.0))
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -1e-40) || ~(((a * b) <= 100000000.0)))
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1e-40], N[Not[LessEqual[N[(a * b), $MachinePrecision], 100000000.0]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -9.9999999999999993e-41 or 1e8 < (*.f64 a b)

   1. Initial program 94.8%

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

   2. Taylor expanded in z around 0 84.7%

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

   if -9.9999999999999993e-41 < (*.f64 a b) < 1e8

   1. Initial program 98.4%

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

   2. Taylor expanded in a around 0 97.6%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{-40} \lor \neg \left(a \cdot b \leq 100000000\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \]

Alternative 10: 43.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -9.5 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -8.2 \cdot 10^{-253}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 5.2 \cdot 10^{+53}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) -0.25)))
   (if (<= (* a b) -9.5e+74)
     t_1
     (if (<= (* a b) -8.2e-253) c (if (<= (* a b) 5.2e+53) (* x y) t_1)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -9.5e+74) {
		tmp = t_1;
	} else if ((a * b) <= -8.2e-253) {
		tmp = c;
	} else if ((a * b) <= 5.2e+53) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) * (-0.25d0)
    if ((a * b) <= (-9.5d+74)) then
        tmp = t_1
    else if ((a * b) <= (-8.2d-253)) then
        tmp = c
    else if ((a * b) <= 5.2d+53) then
        tmp = x * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -9.5e+74) {
		tmp = t_1;
	} else if ((a * b) <= -8.2e-253) {
		tmp = c;
	} else if ((a * b) <= 5.2e+53) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * -0.25
	tmp = 0
	if (a * b) <= -9.5e+74:
		tmp = t_1
	elif (a * b) <= -8.2e-253:
		tmp = c
	elif (a * b) <= 5.2e+53:
		tmp = x * y
	else:
		tmp = t_1
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * -0.25)
	tmp = 0.0
	if (Float64(a * b) <= -9.5e+74)
		tmp = t_1;
	elseif (Float64(a * b) <= -8.2e-253)
		tmp = c;
	elseif (Float64(a * b) <= 5.2e+53)
		tmp = Float64(x * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * -0.25;
	tmp = 0.0;
	if ((a * b) <= -9.5e+74)
		tmp = t_1;
	elseif ((a * b) <= -8.2e-253)
		tmp = c;
	elseif ((a * b) <= 5.2e+53)
		tmp = x * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -9.5e+74], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -8.2e-253], c, If[LessEqual[N[(a * b), $MachinePrecision], 5.2e+53], N[(x * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -9.5000000000000006e74 or 5.19999999999999996e53 < (*.f64 a b)

   1. Initial program 94.5%

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

      1. associate-+l- 94.5%

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

      2. associate--l+ 94.5%

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

      3. fma-def 97.2%

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

      4. associate-*l/ 97.2%

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

      5. fma-neg 98.2%

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

      6. sub-neg 98.2%

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

      7. distribute-neg-in 98.2%

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

      8. remove-double-neg 98.2%

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

      9. associate-/l* 98.1%

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

      10. distribute-frac-neg 98.1%

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

      11. associate-/r/ 98.2%

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

      12. fma-def 98.2%

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

      13. neg-mul-1 98.2%

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

      14. *-commutative 98.2%

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

      15. associate-/l* 98.2%

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

      16. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around 0 85.7%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c + -0.25 \cdot \left(a \cdot b\right)}\right) \]
   5. Step-by-step derivation

      1. metadata-eval 85.7%

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

      2. distribute-lft-neg-in 85.7%

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

      3. +-commutative 85.7%

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

      4. distribute-lft-neg-in 85.7%

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

      5. metadata-eval 85.7%

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

      6. associate-*r* 85.7%

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

      7. *-commutative 85.7%

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

      8. fma-udef 85.7%

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

   6. Simplified 85.7%

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

   7. Taylor expanded in a around inf 57.8%

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

   if -9.5000000000000006e74 < (*.f64 a b) < -8.20000000000000004e-253

   1. Initial program 98.2%

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

   2. Taylor expanded in c around inf 41.0%

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

   if -8.20000000000000004e-253 < (*.f64 a b) < 5.19999999999999996e53

   1. Initial program 97.9%

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

      1. associate-+l- 97.9%

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

      2. associate--l+ 97.9%

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

      3. fma-def 97.9%

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

      4. associate-*l/ 98.9%

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

      5. fma-neg 98.9%

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

      6. sub-neg 98.9%

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

      7. distribute-neg-in 98.9%

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

      8. remove-double-neg 98.9%

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

      9. associate-/l* 98.9%

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

      10. distribute-frac-neg 98.9%

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

      11. associate-/r/ 98.9%

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

      12. fma-def 98.9%

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

      13. neg-mul-1 98.9%

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

      14. *-commutative 98.9%

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

      15. associate-/l* 98.9%

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

      16. metadata-eval 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around 0 70.3%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c + -0.25 \cdot \left(a \cdot b\right)}\right) \]
   5. Step-by-step derivation

      1. metadata-eval 70.3%

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

      2. distribute-lft-neg-in 70.3%

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

      3. +-commutative 70.3%

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

      4. distribute-lft-neg-in 70.3%

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

      5. metadata-eval 70.3%

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

      6. associate-*r* 70.3%

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

      7. *-commutative 70.3%

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

      8. fma-udef 70.3%

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

   6. Simplified 70.3%

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

   7. Taylor expanded in x around inf 43.9%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -9.5 \cdot 10^{+74}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq -8.2 \cdot 10^{-253}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 5.2 \cdot 10^{+53}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]

Alternative 11: 83.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;x \leq -4.3 \cdot 10^{+48} \lor \neg \left(x \leq 2.45 \cdot 10^{-95}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(c + \left(z \cdot t\right) \cdot 0.0625\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)))
   (if (or (<= x -4.3e+48) (not (<= x 2.45e-95)))
     (- (+ c (* x y)) t_1)
     (- (+ c (* (* z t) 0.0625)) t_1))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double tmp;
	if ((x <= -4.3e+48) || !(x <= 2.45e-95)) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = (c + ((z * t) * 0.0625)) - t_1;
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    if ((x <= (-4.3d+48)) .or. (.not. (x <= 2.45d-95))) then
        tmp = (c + (x * y)) - t_1
    else
        tmp = (c + ((z * t) * 0.0625d0)) - t_1
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double tmp;
	if ((x <= -4.3e+48) || !(x <= 2.45e-95)) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = (c + ((z * t) * 0.0625)) - t_1;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	tmp = 0
	if (x <= -4.3e+48) or not (x <= 2.45e-95):
		tmp = (c + (x * y)) - t_1
	else:
		tmp = (c + ((z * t) * 0.0625)) - t_1
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	tmp = 0.0
	if ((x <= -4.3e+48) || !(x <= 2.45e-95))
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	else
		tmp = Float64(Float64(c + Float64(Float64(z * t) * 0.0625)) - t_1);
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	tmp = 0.0;
	if ((x <= -4.3e+48) || ~((x <= 2.45e-95)))
		tmp = (c + (x * y)) - t_1;
	else
		tmp = (c + ((z * t) * 0.0625)) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, If[Or[LessEqual[x, -4.3e+48], N[Not[LessEqual[x, 2.45e-95]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(c + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.29999999999999978e48 or 2.45e-95 < x

   1. Initial program 94.9%

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

   2. Taylor expanded in z around 0 83.6%

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

   if -4.29999999999999978e48 < x < 2.45e-95

   1. Initial program 98.4%

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

   2. Taylor expanded in x around 0 93.7%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+48} \lor \neg \left(x \leq 2.45 \cdot 10^{-95}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(c + \left(z \cdot t\right) \cdot 0.0625\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 12: 97.7% accurate, 1.0× speedup

Math

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

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (+ c (- (+ (/ (* z t) 16.0) (* x y)) (/ (* a b) 4.0))))

C

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

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
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)) - ((a * b) / 4.0d0))
end function

Java

assert z < t;
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)) - ((a * b) / 4.0));
}

Python

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

Julia

z, t = sort([z, t])
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(a * b) / 4.0)))
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = c + ((((z * t) / 16.0) + (x * y)) - ((a * b) / 4.0));
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
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[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.5%

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

2. Final simplification 96.5%

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

Alternative 13: 60.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := c + x \cdot y\\ \mathbf{if}\;t \leq -0.14:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-122}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))))
   (if (<= t -0.14)
     (* (* z t) 0.0625)
     (if (<= t -9.5e-287)
       t_1
       (if (<= t 1.08e-122)
         (+ c (* b (* a -0.25)))
         (if (<= t 6e+83) t_1 (+ c (* t (* z 0.0625)))))))))

C

assert(z < t);
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 (t <= -0.14) {
		tmp = (z * t) * 0.0625;
	} else if (t <= -9.5e-287) {
		tmp = t_1;
	} else if (t <= 1.08e-122) {
		tmp = c + (b * (a * -0.25));
	} else if (t <= 6e+83) {
		tmp = t_1;
	} else {
		tmp = c + (t * (z * 0.0625));
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
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 (t <= (-0.14d0)) then
        tmp = (z * t) * 0.0625d0
    else if (t <= (-9.5d-287)) then
        tmp = t_1
    else if (t <= 1.08d-122) then
        tmp = c + (b * (a * (-0.25d0)))
    else if (t <= 6d+83) then
        tmp = t_1
    else
        tmp = c + (t * (z * 0.0625d0))
    end if
    code = tmp
end function

Java

assert z < t;
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 (t <= -0.14) {
		tmp = (z * t) * 0.0625;
	} else if (t <= -9.5e-287) {
		tmp = t_1;
	} else if (t <= 1.08e-122) {
		tmp = c + (b * (a * -0.25));
	} else if (t <= 6e+83) {
		tmp = t_1;
	} else {
		tmp = c + (t * (z * 0.0625));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	tmp = 0
	if t <= -0.14:
		tmp = (z * t) * 0.0625
	elif t <= -9.5e-287:
		tmp = t_1
	elif t <= 1.08e-122:
		tmp = c + (b * (a * -0.25))
	elif t <= 6e+83:
		tmp = t_1
	else:
		tmp = c + (t * (z * 0.0625))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (t <= -0.14)
		tmp = Float64(Float64(z * t) * 0.0625);
	elseif (t <= -9.5e-287)
		tmp = t_1;
	elseif (t <= 1.08e-122)
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	elseif (t <= 6e+83)
		tmp = t_1;
	else
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	tmp = 0.0;
	if (t <= -0.14)
		tmp = (z * t) * 0.0625;
	elseif (t <= -9.5e-287)
		tmp = t_1;
	elseif (t <= 1.08e-122)
		tmp = c + (b * (a * -0.25));
	elseif (t <= 6e+83)
		tmp = t_1;
	else
		tmp = c + (t * (z * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.14], N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision], If[LessEqual[t, -9.5e-287], t$95$1, If[LessEqual[t, 1.08e-122], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+83], t$95$1, N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -0.14000000000000001

   1. Initial program 96.7%

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

   2. Taylor expanded in x around 0 80.9%

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

   3. Taylor expanded in t around inf 55.3%

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

   if -0.14000000000000001 < t < -9.5000000000000004e-287 or 1.08e-122 < t < 5.9999999999999999e83

   1. Initial program 99.0%

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

   2. Taylor expanded in x around inf 59.7%

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

   if -9.5000000000000004e-287 < t < 1.08e-122

   1. Initial program 98.2%

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

   2. Taylor expanded in a around inf 68.3%

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

      1. associate-*r* 68.3%

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

      2. *-commutative 68.3%

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

   4. Simplified 68.3%

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

   if 5.9999999999999999e83 < t

   1. Initial program 85.8%

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

   2. Taylor expanded in z around inf 66.1%

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

      1. *-commutative 66.1%

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

      2. associate-*r* 68.5%

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

      3. *-commutative 68.5%

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

   4. Simplified 68.5%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.14:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-287}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-122}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+83}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]

Alternative 14: 63.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.46 \cdot 10^{+181} \lor \neg \left(a \cdot b \leq 2.9 \cdot 10^{+138}\right):\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -1.46e+181) (not (<= (* a b) 2.9e+138)))
   (* (* a b) -0.25)
   (+ c (* x y))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -1.46e+181) || !((a * b) <= 2.9e+138)) {
		tmp = (a * b) * -0.25;
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
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) <= (-1.46d+181)) .or. (.not. ((a * b) <= 2.9d+138))) then
        tmp = (a * b) * (-0.25d0)
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -1.46e+181) || !((a * b) <= 2.9e+138)) {
		tmp = (a * b) * -0.25;
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -1.46e+181) or not ((a * b) <= 2.9e+138):
		tmp = (a * b) * -0.25
	else:
		tmp = c + (x * y)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -1.46e+181) || !(Float64(a * b) <= 2.9e+138))
		tmp = Float64(Float64(a * b) * -0.25);
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -1.46e+181) || ~(((a * b) <= 2.9e+138)))
		tmp = (a * b) * -0.25;
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1.46e+181], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2.9e+138]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.46000000000000008e181 or 2.9000000000000001e138 < (*.f64 a b)

   1. Initial program 90.6%

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

      1. associate-+l- 90.6%

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

      2. associate--l+ 90.6%

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

      3. fma-def 95.3%

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

      4. associate-*l/ 95.3%

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

      5. fma-neg 96.9%

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

      6. sub-neg 96.9%

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

      7. distribute-neg-in 96.9%

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

      8. remove-double-neg 96.9%

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

      9. associate-/l* 96.8%

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

      10. distribute-frac-neg 96.8%

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

      11. associate-/r/ 96.9%

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

      12. fma-def 96.9%

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

      13. neg-mul-1 96.9%

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

      14. *-commutative 96.9%

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

      15. associate-/l* 96.9%

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

      16. metadata-eval 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in z around 0 86.1%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c + -0.25 \cdot \left(a \cdot b\right)}\right) \]
   5. Step-by-step derivation

      1. metadata-eval 86.1%

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

      2. distribute-lft-neg-in 86.1%

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

      3. +-commutative 86.1%

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

      4. distribute-lft-neg-in 86.1%

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

      5. metadata-eval 86.1%

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

      6. associate-*r* 86.1%

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

      7. *-commutative 86.1%

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

      8. fma-udef 86.1%

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

   6. Simplified 86.1%

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

   7. Taylor expanded in a around inf 75.2%

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

   if -1.46000000000000008e181 < (*.f64 a b) < 2.9000000000000001e138

   1. Initial program 98.5%

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

   2. Taylor expanded in x around inf 63.2%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.46 \cdot 10^{+181} \lor \neg \left(a \cdot b \leq 2.9 \cdot 10^{+138}\right):\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 15: 37.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+45}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-34}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -4.6e+45) (* x y) (if (<= x 2.8e-34) c (* x y))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -4.6e+45) {
		tmp = x * y;
	} else if (x <= 2.8e-34) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
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 <= (-4.6d+45)) then
        tmp = x * y
    else if (x <= 2.8d-34) then
        tmp = c
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -4.6e+45) {
		tmp = x * y;
	} else if (x <= 2.8e-34) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -4.6e+45:
		tmp = x * y
	elif x <= 2.8e-34:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -4.6e+45)
		tmp = Float64(x * y);
	elseif (x <= 2.8e-34)
		tmp = c;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (x <= -4.6e+45)
		tmp = x * y;
	elseif (x <= 2.8e-34)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -4.6e+45], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.8e-34], c, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.60000000000000025e45 or 2.79999999999999997e-34 < x

   1. Initial program 94.4%

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

      1. associate-+l- 94.4%

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

      2. associate--l+ 94.4%

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

      3. fma-def 96.8%

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

      4. associate-*l/ 96.8%

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

      5. fma-neg 96.8%

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

      6. sub-neg 96.8%

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

      7. distribute-neg-in 96.8%

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

      8. remove-double-neg 96.8%

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

      9. associate-/l* 96.8%

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

      10. distribute-frac-neg 96.8%

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

      11. associate-/r/ 96.8%

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

      12. fma-def 96.8%

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

      13. neg-mul-1 96.8%

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

      14. *-commutative 96.8%

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

      15. associate-/l* 96.8%

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

      16. metadata-eval 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around 0 84.4%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c + -0.25 \cdot \left(a \cdot b\right)}\right) \]
   5. Step-by-step derivation

      1. metadata-eval 84.4%

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

      2. distribute-lft-neg-in 84.4%

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

      3. +-commutative 84.4%

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

      4. distribute-lft-neg-in 84.4%

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

      5. metadata-eval 84.4%

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

      6. associate-*r* 84.4%

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

      7. *-commutative 84.4%

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

      8. fma-udef 84.4%

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

   6. Simplified 84.4%

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

   7. Taylor expanded in x around inf 48.5%

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

   if -4.60000000000000025e45 < x < 2.79999999999999997e-34

   1. Initial program 98.6%

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

   2. Taylor expanded in c around inf 31.0%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+45}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-34}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 16: 22.4% accurate, 17.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ c \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 c)

C

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

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
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

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

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	return c

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	return c
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = c;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := c

Derivation

1. Initial program 96.5%

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

2. Taylor expanded in c around inf 23.7%

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

3. Final simplification 23.7%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023268 
(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))