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

Percentage Accurate: 97.6% → 98.7%

Time: 12.1s

Alternatives: 13

Speedup: 0.5×

• 33.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(t, z \cdot 0.0625, a \cdot \left(b \cdot -0.25\right)\right) + \left(c + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, c + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) INFINITY)
   (+ (fma t (* z 0.0625) (* a (* b -0.25))) (+ c (* x y)))
   (fma x y (+ c (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) <= ((double) INFINITY)) {
		tmp = fma(t, (z * 0.0625), (a * (b * -0.25))) + (c + (x * y));
	} else {
		tmp = fma(x, y, (c + (0.0625 * (z * t))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) <= Inf)
		tmp = Float64(fma(t, Float64(z * 0.0625), Float64(a * Float64(b * -0.25))) + Float64(c + Float64(x * y)));
	else
		tmp = fma(x, y, Float64(c + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(t * N[(z * 0.0625), $MachinePrecision] + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * y + N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. fma-def 100.0%

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

      4. associate-/l* 99.9%

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

      5. sub-neg 99.9%

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

      6. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. associate--r- 99.9%

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

      2. fma-udef 99.9%

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

      3. associate-/l* 99.9%

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

      4. associate-/l* 100.0%

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

      5. associate--l+ 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+l+ 100.0%

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

   5. Applied egg-rr 100.0%

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

   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 28.6%

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

      4. associate-*l/ 28.6%

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

      5. fma-neg 28.6%

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

      6. neg-sub0 28.6%

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

      7. associate-+l- 28.6%

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

      8. neg-sub0 28.6%

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

      9. associate-/l* 28.6%

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

      10. distribute-frac-neg 28.6%

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

      11. associate-/r/ 28.6%

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

      12. fma-def 28.6%

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

      13. neg-mul-1 28.6%

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

      14. *-commutative 28.6%

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

      15. associate-/l* 28.6%

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

      16. metadata-eval 28.6%

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

   3. Simplified 28.6%

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

   4. Taylor expanded in a around 0 85.7%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(t, z \cdot 0.0625, a \cdot \left(b \cdot -0.25\right)\right) + \left(c + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, c + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 2: 98.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. associate-+l- 97.2%

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

   2. associate--l+ 97.2%

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

   3. fma-def 98.0%

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

   4. associate-*l/ 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 98.0%

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

   6. neg-sub0 98.0%

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

   7. associate-+l- 98.0%

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

   8. neg-sub0 98.0%

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

   9. associate-/l* 98.0%

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

   10. distribute-frac-neg 98.0%

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

   11. associate-/r/ 98.0%

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

   12. fma-def 98.0%

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

   13. neg-mul-1 98.0%

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

   14. *-commutative 98.0%

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

   15. associate-/l* 98.0%

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

   16. metadata-eval 98.0%

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

3. Simplified 98.0%

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

4. Final simplification 98.0%

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

Alternative 3: 98.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. 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 28.6%

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

      4. associate-*l/ 28.6%

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

      5. fma-neg 28.6%

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

      6. neg-sub0 28.6%

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

      7. associate-+l- 28.6%

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

      8. neg-sub0 28.6%

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

      9. associate-/l* 28.6%

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

      10. distribute-frac-neg 28.6%

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

      11. associate-/r/ 28.6%

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

      12. fma-def 28.6%

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

      13. neg-mul-1 28.6%

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

      14. *-commutative 28.6%

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

      15. associate-/l* 28.6%

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

      16. metadata-eval 28.6%

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

   3. Simplified 28.6%

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

   4. Taylor expanded in a around 0 85.7%

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

4. Final simplification 99.6%

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

Alternative 4: 98.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = c + t_1;
	} else {
		tmp = c + (z * (t * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)
	tmp = 0
	if t_1 <= math.inf:
		tmp = c + t_1
	else:
		tmp = c + (z * (t * 0.0625))
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = c + t_1;
	else
		tmp = c + (z * (t * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around inf 73.5%

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

      1. associate-*r* 73.5%

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

      2. *-commutative 73.5%

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

      3. *-commutative 73.5%

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

      4. *-commutative 73.5%

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

   4. Simplified 73.5%

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

4. Final simplification 99.3%

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

Alternative 5: 89.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -3.3 \cdot 10^{+60}:\\ \;\;\;\;\left(c + x \cdot y\right) - t_1\\ \mathbf{elif}\;x \cdot y \leq 0.8:\\ \;\;\;\;\left(c + t_2\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + t_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)) (t_2 (* 0.0625 (* z t))))
   (if (<= (* x y) -3.3e+60)
     (- (+ c (* x y)) t_1)
     (if (<= (* x y) 0.8) (- (+ c t_2) t_1) (+ c (+ (* x y) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = 0.0625 * (z * t);
	double tmp;
	if ((x * y) <= -3.3e+60) {
		tmp = (c + (x * y)) - t_1;
	} else if ((x * y) <= 0.8) {
		tmp = (c + t_2) - t_1;
	} else {
		tmp = c + ((x * y) + t_2);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    t_2 = 0.0625d0 * (z * t)
    if ((x * y) <= (-3.3d+60)) then
        tmp = (c + (x * y)) - t_1
    else if ((x * y) <= 0.8d0) then
        tmp = (c + t_2) - t_1
    else
        tmp = c + ((x * y) + t_2)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = 0.0625 * (z * t);
	double tmp;
	if ((x * y) <= -3.3e+60) {
		tmp = (c + (x * y)) - t_1;
	} else if ((x * y) <= 0.8) {
		tmp = (c + t_2) - t_1;
	} else {
		tmp = c + ((x * y) + t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	t_2 = 0.0625 * (z * t)
	tmp = 0
	if (x * y) <= -3.3e+60:
		tmp = (c + (x * y)) - t_1
	elif (x * y) <= 0.8:
		tmp = (c + t_2) - t_1
	else:
		tmp = c + ((x * y) + t_2)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	t_2 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -3.3e+60)
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	elseif (Float64(x * y) <= 0.8)
		tmp = Float64(Float64(c + t_2) - t_1);
	else
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	t_2 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((x * y) <= -3.3e+60)
		tmp = (c + (x * y)) - t_1;
	elseif ((x * y) <= 0.8)
		tmp = (c + t_2) - t_1;
	else
		tmp = c + ((x * y) + t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.3e+60], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 0.8], N[(N[(c + t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.2999999999999998e60

   1. Initial program 97.7%

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

      1. associate-+l- 97.7%

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

      2. sub-neg 97.7%

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

      3. fma-def 97.7%

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

      4. associate-/l* 97.7%

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

      5. sub-neg 97.7%

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

      6. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around 0 87.8%

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

   if -3.2999999999999998e60 < (*.f64 x y) < 0.80000000000000004

   1. Initial program 98.6%

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

      1. associate-+l- 98.6%

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

      2. sub-neg 98.6%

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

      3. fma-def 98.6%

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

      4. associate-/l* 98.5%

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

      5. sub-neg 98.5%

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

      6. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in x around 0 95.2%

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

   if 0.80000000000000004 < (*.f64 x y)

   1. Initial program 94.2%

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

   2. Taylor expanded in a around 0 88.8%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.3 \cdot 10^{+60}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 0.8:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 6: 61.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ t_2 := c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{-287}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-138}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* a b) 0.25))) (t_2 (+ c (* z (* t 0.0625)))))
   (if (<= z -5.4e+88)
     t_2
     (if (<= z -3.5e-74)
       t_1
       (if (<= z -1.04e-287)
         (+ c (* b (* a -0.25)))
         (if (<= z 1.3e-138) (+ c (* x y)) (if (<= z 2.7e+49) t_1 t_2)))))))

C

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 t_2 = c + (z * (t * 0.0625));
	double tmp;
	if (z <= -5.4e+88) {
		tmp = t_2;
	} else if (z <= -3.5e-74) {
		tmp = t_1;
	} else if (z <= -1.04e-287) {
		tmp = c + (b * (a * -0.25));
	} else if (z <= 1.3e-138) {
		tmp = c + (x * y);
	} else if (z <= 2.7e+49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * y) - ((a * b) * 0.25d0)
    t_2 = c + (z * (t * 0.0625d0))
    if (z <= (-5.4d+88)) then
        tmp = t_2
    else if (z <= (-3.5d-74)) then
        tmp = t_1
    else if (z <= (-1.04d-287)) then
        tmp = c + (b * (a * (-0.25d0)))
    else if (z <= 1.3d-138) then
        tmp = c + (x * y)
    else if (z <= 2.7d+49) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) - ((a * b) * 0.25);
	double t_2 = c + (z * (t * 0.0625));
	double tmp;
	if (z <= -5.4e+88) {
		tmp = t_2;
	} else if (z <= -3.5e-74) {
		tmp = t_1;
	} else if (z <= -1.04e-287) {
		tmp = c + (b * (a * -0.25));
	} else if (z <= 1.3e-138) {
		tmp = c + (x * y);
	} else if (z <= 2.7e+49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) - ((a * b) * 0.25)
	t_2 = c + (z * (t * 0.0625))
	tmp = 0
	if z <= -5.4e+88:
		tmp = t_2
	elif z <= -3.5e-74:
		tmp = t_1
	elif z <= -1.04e-287:
		tmp = c + (b * (a * -0.25))
	elif z <= 1.3e-138:
		tmp = c + (x * y)
	elif z <= 2.7e+49:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25))
	t_2 = Float64(c + Float64(z * Float64(t * 0.0625)))
	tmp = 0.0
	if (z <= -5.4e+88)
		tmp = t_2;
	elseif (z <= -3.5e-74)
		tmp = t_1;
	elseif (z <= -1.04e-287)
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	elseif (z <= 1.3e-138)
		tmp = Float64(c + Float64(x * y));
	elseif (z <= 2.7e+49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) - ((a * b) * 0.25);
	t_2 = c + (z * (t * 0.0625));
	tmp = 0.0;
	if (z <= -5.4e+88)
		tmp = t_2;
	elseif (z <= -3.5e-74)
		tmp = t_1;
	elseif (z <= -1.04e-287)
		tmp = c + (b * (a * -0.25));
	elseif (z <= 1.3e-138)
		tmp = c + (x * y);
	elseif (z <= 2.7e+49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e+88], t$95$2, If[LessEqual[z, -3.5e-74], t$95$1, If[LessEqual[z, -1.04e-287], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-138], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+49], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.40000000000000031e88 or 2.7000000000000001e49 < z

   1. Initial program 95.4%

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

   2. Taylor expanded in z around inf 67.6%

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

      1. associate-*r* 67.6%

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

      2. *-commutative 67.6%

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

      3. *-commutative 67.6%

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

      4. *-commutative 67.6%

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

   4. Simplified 67.6%

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

   if -5.40000000000000031e88 < z < -3.50000000000000015e-74 or 1.3e-138 < z < 2.7000000000000001e49

   1. Initial program 97.1%

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

      1. associate-+l- 97.1%

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

      2. sub-neg 97.1%

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

      3. fma-def 97.1%

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

      4. associate-/l* 97.0%

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

      5. sub-neg 97.0%

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

      6. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in z around 0 71.8%

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

   5. Taylor expanded in c around 0 58.4%

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

   if -3.50000000000000015e-74 < z < -1.03999999999999996e-287

   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 84.9%

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

      1. associate-*r* 84.9%

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

      2. *-commutative 84.9%

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

      3. *-commutative 84.9%

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

   4. Simplified 84.9%

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

   if -1.03999999999999996e-287 < z < 1.3e-138

   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 67.5%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+88}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-74}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{-287}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-138}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+49}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \]

Alternative 7: 86.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.5 \cdot 10^{+186}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+214}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -2.5e+186)
   (+ c (* b (* a -0.25)))
   (if (<= (* a b) 1e+214)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (- (* x y) (* (* a b) 0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -2.5e+186) {
		tmp = c + (b * (a * -0.25));
	} else if ((a * b) <= 1e+214) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a * b) <= (-2.5d+186)) then
        tmp = c + (b * (a * (-0.25d0)))
    else if ((a * b) <= 1d+214) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = (x * y) - ((a * b) * 0.25d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -2.5e+186) {
		tmp = c + (b * (a * -0.25));
	} else if ((a * b) <= 1e+214) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -2.5e+186:
		tmp = c + (b * (a * -0.25))
	elif (a * b) <= 1e+214:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = (x * y) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -2.5e+186)
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	elseif (Float64(a * b) <= 1e+214)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -2.5e+186)
		tmp = c + (b * (a * -0.25));
	elseif ((a * b) <= 1e+214)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = (x * y) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -2.5e+186], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+214], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.49999999999999977e186

   1. Initial program 89.1%

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

   2. Taylor expanded in a around inf 79.5%

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

      1. associate-*r* 79.5%

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

      2. *-commutative 79.5%

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

      3. *-commutative 79.5%

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

   4. Simplified 79.5%

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

   if -2.49999999999999977e186 < (*.f64 a b) < 9.9999999999999995e213

   1. Initial program 99.4%

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

   2. Taylor expanded in a around 0 91.2%

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

   if 9.9999999999999995e213 < (*.f64 a b)

   1. Initial program 95.0%

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

      1. associate-+l- 95.0%

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

      2. sub-neg 95.0%

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

      3. fma-def 95.0%

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

      4. associate-/l* 94.9%

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

      5. sub-neg 94.9%

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

      6. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in z around 0 80.3%

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

   5. Taylor expanded in c around 0 80.3%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.5 \cdot 10^{+186}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+214}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 8: 60.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-287}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (+ c (* z (* t 0.0625)))))
   (if (<= z -4.4e+129)
     t_2
     (if (<= z -1.02e-82)
       t_1
       (if (<= z -1.22e-287)
         (+ c (* b (* a -0.25)))
         (if (<= z 2.1e+49) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = c + (z * (t * 0.0625));
	double tmp;
	if (z <= -4.4e+129) {
		tmp = t_2;
	} else if (z <= -1.02e-82) {
		tmp = t_1;
	} else if (z <= -1.22e-287) {
		tmp = c + (b * (a * -0.25));
	} else if (z <= 2.1e+49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = c + (z * (t * 0.0625d0))
    if (z <= (-4.4d+129)) then
        tmp = t_2
    else if (z <= (-1.02d-82)) then
        tmp = t_1
    else if (z <= (-1.22d-287)) then
        tmp = c + (b * (a * (-0.25d0)))
    else if (z <= 2.1d+49) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = c + (z * (t * 0.0625));
	double tmp;
	if (z <= -4.4e+129) {
		tmp = t_2;
	} else if (z <= -1.02e-82) {
		tmp = t_1;
	} else if (z <= -1.22e-287) {
		tmp = c + (b * (a * -0.25));
	} else if (z <= 2.1e+49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = c + (z * (t * 0.0625))
	tmp = 0
	if z <= -4.4e+129:
		tmp = t_2
	elif z <= -1.02e-82:
		tmp = t_1
	elif z <= -1.22e-287:
		tmp = c + (b * (a * -0.25))
	elif z <= 2.1e+49:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(c + Float64(z * Float64(t * 0.0625)))
	tmp = 0.0
	if (z <= -4.4e+129)
		tmp = t_2;
	elseif (z <= -1.02e-82)
		tmp = t_1;
	elseif (z <= -1.22e-287)
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	elseif (z <= 2.1e+49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = c + (z * (t * 0.0625));
	tmp = 0.0;
	if (z <= -4.4e+129)
		tmp = t_2;
	elseif (z <= -1.02e-82)
		tmp = t_1;
	elseif (z <= -1.22e-287)
		tmp = c + (b * (a * -0.25));
	elseif (z <= 2.1e+49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.4e+129], t$95$2, If[LessEqual[z, -1.02e-82], t$95$1, If[LessEqual[z, -1.22e-287], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+49], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.3999999999999999e129 or 2.10000000000000011e49 < z

   1. Initial program 95.1%

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

   2. Taylor expanded in z around inf 67.3%

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

      1. associate-*r* 67.3%

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

      2. *-commutative 67.3%

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

      3. *-commutative 67.3%

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

      4. *-commutative 67.3%

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

   4. Simplified 67.3%

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

   if -4.3999999999999999e129 < z < -1.02000000000000007e-82 or -1.21999999999999996e-287 < z < 2.10000000000000011e49

   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 x around inf 60.0%

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

   if -1.02000000000000007e-82 < z < -1.21999999999999996e-287

   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 86.0%

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

      1. associate-*r* 86.0%

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

      2. *-commutative 86.0%

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

      3. *-commutative 86.0%

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

   4. Simplified 86.0%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+129}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-82}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-287}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+49}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \]

Alternative 9: 64.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.6 \cdot 10^{+100} \lor \neg \left(x \cdot y \leq 5.2 \cdot 10^{+22}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -9.6e+100) (not (<= (* x y) 5.2e+22)))
   (+ c (* x y))
   (+ c (* b (* a -0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -9.6e+100) || !((x * y) <= 5.2e+22)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (b * (a * -0.25));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-9.6d+100)) .or. (.not. ((x * y) <= 5.2d+22))) then
        tmp = c + (x * y)
    else
        tmp = c + (b * (a * (-0.25d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -9.6e+100) || !((x * y) <= 5.2e+22)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (b * (a * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -9.6e+100) or not ((x * y) <= 5.2e+22):
		tmp = c + (x * y)
	else:
		tmp = c + (b * (a * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -9.6e+100) || !(Float64(x * y) <= 5.2e+22))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -9.6e+100) || ~(((x * y) <= 5.2e+22)))
		tmp = c + (x * y);
	else
		tmp = c + (b * (a * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -9.6e+100], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5.2e+22]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.60000000000000046e100 or 5.2e22 < (*.f64 x y)

   1. Initial program 96.0%

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

   2. Taylor expanded in x around inf 70.3%

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

   if -9.60000000000000046e100 < (*.f64 x y) < 5.2e22

   1. Initial program 98.0%

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

   2. Taylor expanded in a around inf 61.8%

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

      1. associate-*r* 61.8%

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

      2. *-commutative 61.8%

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

      3. *-commutative 61.8%

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

   4. Simplified 61.8%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.6 \cdot 10^{+100} \lor \neg \left(x \cdot y \leq 5.2 \cdot 10^{+22}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 10: 84.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+70} \lor \neg \left(z \leq 10^{-50}\right):\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1e+70) (not (<= z 1e-50)))
   (+ c (+ (* x y) (* 0.0625 (* z t))))
   (- (+ c (* x y)) (* (* a b) 0.25))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1e+70) || !(z <= 1e-50)) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-1d+70)) .or. (.not. (z <= 1d-50))) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = (c + (x * y)) - ((a * b) * 0.25d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1e+70) || !(z <= 1e-50)) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1e+70) or not (z <= 1e-50):
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1e+70) || !(z <= 1e-50))
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(a * b) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1e+70) || ~((z <= 1e-50)))
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1e+70], N[Not[LessEqual[z, 1e-50]], $MachinePrecision]], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000007e70 or 1.00000000000000001e-50 < z

   1. Initial program 96.4%

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

   2. Taylor expanded in a around 0 85.8%

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

   if -1.00000000000000007e70 < z < 1.00000000000000001e-50

   1. Initial program 98.3%

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

      1. associate-+l- 98.3%

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

      2. sub-neg 98.3%

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

      3. fma-def 98.3%

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

      4. associate-/l* 98.2%

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

      5. sub-neg 98.2%

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

      6. associate-/l* 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in z around 0 88.3%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+70} \lor \neg \left(z \leq 10^{-50}\right):\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 11: 42.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.6 \cdot 10^{+100}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 4.5 \cdot 10^{+98}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -9.6e+100) (* x y) (if (<= (* x y) 4.5e+98) c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -9.6e+100) {
		tmp = x * y;
	} else if ((x * y) <= 4.5e+98) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((x * y) <= (-9.6d+100)) then
        tmp = x * y
    else if ((x * y) <= 4.5d+98) then
        tmp = c
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -9.6e+100) {
		tmp = x * y;
	} else if ((x * y) <= 4.5e+98) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -9.6e+100:
		tmp = x * y
	elif (x * y) <= 4.5e+98:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -9.6e+100)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 4.5e+98)
		tmp = c;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x * y) <= -9.6e+100)
		tmp = x * y;
	elseif ((x * y) <= 4.5e+98)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -9.6e+100], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4.5e+98], c, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.60000000000000046e100 or 4.5000000000000002e98 < (*.f64 x y)

   1. Initial program 95.4%

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

      1. associate-+l- 95.4%

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

      2. sub-neg 95.4%

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

      3. fma-def 96.5%

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

      4. associate-/l* 96.5%

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

      5. sub-neg 96.5%

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

      6. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

      1. associate--r- 96.5%

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

      2. fma-udef 95.3%

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

      3. associate-/l* 95.4%

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

      4. associate-/l* 95.4%

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

      5. associate--l+ 95.4%

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

      6. +-commutative 95.4%

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

      7. associate-+l+ 95.4%

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

   5. Applied egg-rr 95.4%

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

   6. Taylor expanded in x around inf 67.4%

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

   if -9.60000000000000046e100 < (*.f64 x y) < 4.5000000000000002e98

   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. sub-neg 98.2%

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

      3. fma-def 98.2%

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

      4. associate-/l* 98.1%

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

      5. sub-neg 98.1%

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

      6. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in c around inf 31.0%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.6 \cdot 10^{+100}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 4.5 \cdot 10^{+98}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 12: 49.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ c + x \cdot y \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.2%

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

2. Taylor expanded in x around inf 48.5%

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

3. Final simplification 48.5%

   \[\leadsto c + x \cdot y \]

Alternative 13: 22.4% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. associate-+l- 97.2%

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

   2. sub-neg 97.2%

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

   3. fma-def 97.6%

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

   4. associate-/l* 97.6%

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

   5. sub-neg 97.6%

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

   6. associate-/l* 97.5%

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

3. Simplified 97.5%

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

4. Taylor expanded in c around inf 23.3%

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

5. Final simplification 23.3%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023297 
(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))