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

Percentage Accurate: 97.6% → 98.8%

Time: 11.2s

Alternatives: 14

Speedup: 0.5×

• 33.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.6% 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: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - t\_1 \leq \infty:\\ \;\;\;\;c + \left(\mathsf{fma}\left(z \cdot 0.0625, t, x \cdot y\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;c + \mathsf{fma}\left(t \cdot 0.0625, z, x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

      1. +-commutative 100.0%

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

      2. associate-/l* 99.9%

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

      3. associate-/r/ 100.0%

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

      4. fma-def 100.0%

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

      5. div-inv 100.0%

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

      6. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

   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. Add Preprocessing

   3. Taylor expanded in a around 0 40.0%

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

      1. associate-*r* 40.0%

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

      2. fma-def 70.0%

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

   5. Applied egg-rr 70.0%

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

4. Final simplification 98.8%

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

Alternative 2: 98.9% 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 96.1%

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

   1. associate-+l- 96.1%

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

   2. associate--l+ 96.1%

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

   3. fma-def 96.9%

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

   4. associate-*l/ 96.9%

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

   5. fma-neg 97.3%

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

   6. sub-neg 97.3%

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

   7. distribute-neg-in 97.3%

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

   8. remove-double-neg 97.3%

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

   9. associate-/l* 97.2%

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

   10. distribute-frac-neg 97.2%

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

   11. associate-/r/ 97.3%

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

   12. fma-def 97.3%

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

   13. neg-mul-1 97.3%

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

   14. *-commutative 97.3%

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

   15. associate-/l* 97.3%

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

   16. metadata-eval 97.3%

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

3. Simplified 97.3%

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

5. Final simplification 97.3%

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

Alternative 3: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;c + t\_1\\ \mathbf{else}:\\ \;\;\;\;c + \mathsf{fma}\left(t \cdot 0.0625, z, x \cdot y\right)\\ \end{array} \end{array} \]

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 (fma (* t 0.0625) z (* x y))))))

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 + fma((t * 0.0625), z, (x * y));
	}
	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 + fma(Float64(t * 0.0625), z, Float64(x * y)));
	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[(c + N[(N[(t * 0.0625), $MachinePrecision] * z + N[(x * y), $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. Add Preprocessing

   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. Add Preprocessing

   3. Taylor expanded in a around 0 40.0%

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

      1. associate-*r* 40.0%

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

      2. fma-def 70.0%

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

   5. Applied egg-rr 70.0%

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

4. Final simplification 98.8%

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

Alternative 4: 84.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot t\right) \cdot 0.0625\\ t_2 := c + \left(x \cdot y + t\_1\right)\\ t_3 := c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+154}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+181}:\\ \;\;\;\;t\_1 - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+219}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* z t) 0.0625))
        (t_2 (+ c (+ (* x y) t_1)))
        (t_3 (+ c (* a (* b -0.25)))))
   (if (<= (* a b) -5e+154)
     t_3
     (if (<= (* a b) 5e+30)
       t_2
       (if (<= (* a b) 5e+181)
         (- t_1 (* (* a b) 0.25))
         (if (<= (* a b) 2e+219) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * t) * 0.0625;
	double t_2 = c + ((x * y) + t_1);
	double t_3 = c + (a * (b * -0.25));
	double tmp;
	if ((a * b) <= -5e+154) {
		tmp = t_3;
	} else if ((a * b) <= 5e+30) {
		tmp = t_2;
	} else if ((a * b) <= 5e+181) {
		tmp = t_1 - ((a * b) * 0.25);
	} else if ((a * b) <= 2e+219) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z * t) * 0.0625d0
    t_2 = c + ((x * y) + t_1)
    t_3 = c + (a * (b * (-0.25d0)))
    if ((a * b) <= (-5d+154)) then
        tmp = t_3
    else if ((a * b) <= 5d+30) then
        tmp = t_2
    else if ((a * b) <= 5d+181) then
        tmp = t_1 - ((a * b) * 0.25d0)
    else if ((a * b) <= 2d+219) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * t) * 0.0625;
	double t_2 = c + ((x * y) + t_1);
	double t_3 = c + (a * (b * -0.25));
	double tmp;
	if ((a * b) <= -5e+154) {
		tmp = t_3;
	} else if ((a * b) <= 5e+30) {
		tmp = t_2;
	} else if ((a * b) <= 5e+181) {
		tmp = t_1 - ((a * b) * 0.25);
	} else if ((a * b) <= 2e+219) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (z * t) * 0.0625
	t_2 = c + ((x * y) + t_1)
	t_3 = c + (a * (b * -0.25))
	tmp = 0
	if (a * b) <= -5e+154:
		tmp = t_3
	elif (a * b) <= 5e+30:
		tmp = t_2
	elif (a * b) <= 5e+181:
		tmp = t_1 - ((a * b) * 0.25)
	elif (a * b) <= 2e+219:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(z * t) * 0.0625)
	t_2 = Float64(c + Float64(Float64(x * y) + t_1))
	t_3 = Float64(c + Float64(a * Float64(b * -0.25)))
	tmp = 0.0
	if (Float64(a * b) <= -5e+154)
		tmp = t_3;
	elseif (Float64(a * b) <= 5e+30)
		tmp = t_2;
	elseif (Float64(a * b) <= 5e+181)
		tmp = Float64(t_1 - Float64(Float64(a * b) * 0.25));
	elseif (Float64(a * b) <= 2e+219)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (z * t) * 0.0625;
	t_2 = c + ((x * y) + t_1);
	t_3 = c + (a * (b * -0.25));
	tmp = 0.0;
	if ((a * b) <= -5e+154)
		tmp = t_3;
	elseif ((a * b) <= 5e+30)
		tmp = t_2;
	elseif ((a * b) <= 5e+181)
		tmp = t_1 - ((a * b) * 0.25);
	elseif ((a * b) <= 2e+219)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+154], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], 5e+30], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 5e+181], N[(t$95$1 - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+219], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.00000000000000004e154 or 1.99999999999999993e219 < (*.f64 a b)

   1. Initial program 93.0%

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

   3. Taylor expanded in a around inf 81.1%

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

      1. *-commutative 81.1%

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

      2. associate-*r* 81.1%

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

   5. Simplified 81.1%

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

   if -5.00000000000000004e154 < (*.f64 a b) < 4.9999999999999998e30 or 5.0000000000000003e181 < (*.f64 a b) < 1.99999999999999993e219

   1. Initial program 97.6%

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

   3. Taylor expanded in a around 0 94.6%

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

   if 4.9999999999999998e30 < (*.f64 a b) < 5.0000000000000003e181

   1. Initial program 95.0%

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

   3. Taylor expanded in x around 0 92.5%

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

      1. +-commutative 92.5%

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

      2. associate-*r* 92.5%

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

      3. fma-def 92.5%

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

   5. Applied egg-rr 92.5%

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

   6. Taylor expanded in c around 0 83.1%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+154}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+30}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+181}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625 - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+219}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;c + t\_1\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

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 (* x y)))))

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 + (x * y);
	}
	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 + (x * y);
	}
	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 + (x * y)
	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(x * y));
	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 + (x * y);
	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[(x * y), $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. Add Preprocessing

   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. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 0.0%

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

      2. associate-/l* 0.0%

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

      3. associate-/r/ 0.0%

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

      4. fma-def 30.0%

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

      5. div-inv 30.0%

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

      6. metadata-eval 30.0%

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

   4. Applied egg-rr 30.0%

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

   5. Taylor expanded in x around inf 60.4%

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

4. Final simplification 98.4%

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

Alternative 6: 88.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot t\right) \cdot 0.0625\\ t_2 := \left(a \cdot b\right) \cdot 0.25\\ t_3 := \left(c + t\_1\right) - t\_2\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+136}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+30}:\\ \;\;\;\;c + \left(x \cdot y + t\_1\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+170}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* z t) 0.0625))
        (t_2 (* (* a b) 0.25))
        (t_3 (- (+ c t_1) t_2)))
   (if (<= (* a b) -2e+136)
     t_3
     (if (<= (* a b) 5e+30)
       (+ c (+ (* x y) t_1))
       (if (<= (* a b) 5e+170) t_3 (- (+ 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 = (z * t) * 0.0625;
	double t_2 = (a * b) * 0.25;
	double t_3 = (c + t_1) - t_2;
	double tmp;
	if ((a * b) <= -2e+136) {
		tmp = t_3;
	} else if ((a * b) <= 5e+30) {
		tmp = c + ((x * y) + t_1);
	} else if ((a * b) <= 5e+170) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = (z * t) * 0.0625d0
    t_2 = (a * b) * 0.25d0
    t_3 = (c + t_1) - t_2
    if ((a * b) <= (-2d+136)) then
        tmp = t_3
    else if ((a * b) <= 5d+30) then
        tmp = c + ((x * y) + t_1)
    else if ((a * b) <= 5d+170) then
        tmp = t_3
    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 = (z * t) * 0.0625;
	double t_2 = (a * b) * 0.25;
	double t_3 = (c + t_1) - t_2;
	double tmp;
	if ((a * b) <= -2e+136) {
		tmp = t_3;
	} else if ((a * b) <= 5e+30) {
		tmp = c + ((x * y) + t_1);
	} else if ((a * b) <= 5e+170) {
		tmp = t_3;
	} else {
		tmp = (c + (x * y)) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (z * t) * 0.0625
	t_2 = (a * b) * 0.25
	t_3 = (c + t_1) - t_2
	tmp = 0
	if (a * b) <= -2e+136:
		tmp = t_3
	elif (a * b) <= 5e+30:
		tmp = c + ((x * y) + t_1)
	elif (a * b) <= 5e+170:
		tmp = t_3
	else:
		tmp = (c + (x * y)) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(z * t) * 0.0625)
	t_2 = Float64(Float64(a * b) * 0.25)
	t_3 = Float64(Float64(c + t_1) - t_2)
	tmp = 0.0
	if (Float64(a * b) <= -2e+136)
		tmp = t_3;
	elseif (Float64(a * b) <= 5e+30)
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	elseif (Float64(a * b) <= 5e+170)
		tmp = t_3;
	else
		tmp = Float64(Float64(c + Float64(x * y)) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (z * t) * 0.0625;
	t_2 = (a * b) * 0.25;
	t_3 = (c + t_1) - t_2;
	tmp = 0.0;
	if ((a * b) <= -2e+136)
		tmp = t_3;
	elseif ((a * b) <= 5e+30)
		tmp = c + ((x * y) + t_1);
	elseif ((a * b) <= 5e+170)
		tmp = t_3;
	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[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+136], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], 5e+30], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+170], t$95$3, N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.00000000000000012e136 or 4.9999999999999998e30 < (*.f64 a b) < 4.99999999999999977e170

   1. Initial program 93.3%

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

   3. Taylor expanded in x around 0 90.9%

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

   if -2.00000000000000012e136 < (*.f64 a b) < 4.9999999999999998e30

   1. Initial program 97.4%

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

   3. Taylor expanded in a around 0 94.9%

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

   if 4.99999999999999977e170 < (*.f64 a b)

   1. Initial program 95.1%

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

   3. Taylor expanded in z around 0 90.5%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+136}:\\ \;\;\;\;\left(c + \left(z \cdot t\right) \cdot 0.0625\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+30}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+170}:\\ \;\;\;\;\left(c + \left(z \cdot t\right) \cdot 0.0625\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{-112}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-31}:\\ \;\;\;\;c + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (+ c (* a (* b -0.25)))))
   (if (<= b -5.5e-112)
     t_2
     (if (<= b 2.6e-110)
       t_1
       (if (<= b 3e-31)
         (+ c (* (* z t) 0.0625))
         (if (<= b 7.6e+89) 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 + (a * (b * -0.25));
	double tmp;
	if (b <= -5.5e-112) {
		tmp = t_2;
	} else if (b <= 2.6e-110) {
		tmp = t_1;
	} else if (b <= 3e-31) {
		tmp = c + ((z * t) * 0.0625);
	} else if (b <= 7.6e+89) {
		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 + (a * (b * (-0.25d0)))
    if (b <= (-5.5d-112)) then
        tmp = t_2
    else if (b <= 2.6d-110) then
        tmp = t_1
    else if (b <= 3d-31) then
        tmp = c + ((z * t) * 0.0625d0)
    else if (b <= 7.6d+89) 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 + (a * (b * -0.25));
	double tmp;
	if (b <= -5.5e-112) {
		tmp = t_2;
	} else if (b <= 2.6e-110) {
		tmp = t_1;
	} else if (b <= 3e-31) {
		tmp = c + ((z * t) * 0.0625);
	} else if (b <= 7.6e+89) {
		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 + (a * (b * -0.25))
	tmp = 0
	if b <= -5.5e-112:
		tmp = t_2
	elif b <= 2.6e-110:
		tmp = t_1
	elif b <= 3e-31:
		tmp = c + ((z * t) * 0.0625)
	elif b <= 7.6e+89:
		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(a * Float64(b * -0.25)))
	tmp = 0.0
	if (b <= -5.5e-112)
		tmp = t_2;
	elseif (b <= 2.6e-110)
		tmp = t_1;
	elseif (b <= 3e-31)
		tmp = Float64(c + Float64(Float64(z * t) * 0.0625));
	elseif (b <= 7.6e+89)
		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 + (a * (b * -0.25));
	tmp = 0.0;
	if (b <= -5.5e-112)
		tmp = t_2;
	elseif (b <= 2.6e-110)
		tmp = t_1;
	elseif (b <= 3e-31)
		tmp = c + ((z * t) * 0.0625);
	elseif (b <= 7.6e+89)
		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[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.5e-112], t$95$2, If[LessEqual[b, 2.6e-110], t$95$1, If[LessEqual[b, 3e-31], N[(c + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.6e+89], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.5e-112 or 7.60000000000000047e89 < b

   1. Initial program 94.6%

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

   3. Taylor expanded in a around inf 60.9%

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

      1. *-commutative 60.9%

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

      2. associate-*r* 60.9%

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

   5. Simplified 60.9%

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

   if -5.5e-112 < b < 2.5999999999999999e-110 or 2.99999999999999981e-31 < b < 7.60000000000000047e89

   1. Initial program 97.0%

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

      1. +-commutative 97.0%

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

      2. associate-/l* 96.9%

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

      3. associate-/r/ 97.0%

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

      4. fma-def 98.0%

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

      5. div-inv 98.0%

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

      6. metadata-eval 98.0%

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

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in x around inf 69.3%

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

   if 2.5999999999999999e-110 < b < 2.99999999999999981e-31

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-/l* 99.9%

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

      3. associate-/r/ 100.0%

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

      4. fma-def 100.0%

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

      5. div-inv 100.0%

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

      6. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around inf 61.5%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-112}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-110}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-31}:\\ \;\;\;\;c + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{+89}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+71} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{-7}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -5e+71) (not (<= (* a b) 5e-7)))
   (- (+ c (* x y)) (* (* a b) 0.25))
   (+ c (+ (* x y) (* (* z t) 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+71) || !((a * b) <= 5e-7)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	}
	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) <= (-5d+71)) .or. (.not. ((a * b) <= 5d-7))) 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

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+71) || !((a * b) <= 5e-7)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -5e+71) or not ((a * b) <= 5e-7):
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + ((z * t) * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -5e+71) || !(Float64(a * b) <= 5e-7))
		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

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -5e+71) || ~(((a * b) <= 5e-7)))
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -5e+71], N[Not[LessEqual[N[(a * b), $MachinePrecision], 5e-7]], $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) < -4.99999999999999972e71 or 4.99999999999999977e-7 < (*.f64 a b)

   1. Initial program 94.9%

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

   3. Taylor expanded in z around 0 85.3%

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

   if -4.99999999999999972e71 < (*.f64 a b) < 4.99999999999999977e-7

   1. Initial program 97.1%

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

   3. Taylor expanded in a around 0 95.7%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+71} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{-7}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+24} \lor \neg \left(b \leq 8.8 \cdot 10^{+89}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -4.2e+24) (not (<= b 8.8e+89)))
   (+ c (* a (* b -0.25)))
   (+ c (+ (* x y) (* (* z t) 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -4.2e+24) || !(b <= 8.8e+89)) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-4.2d+24)) .or. (.not. (b <= 8.8d+89))) then
        tmp = c + (a * (b * (-0.25d0)))
    else
        tmp = c + ((x * y) + ((z * t) * 0.0625d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -4.2e+24) || !(b <= 8.8e+89)) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -4.2e+24) or not (b <= 8.8e+89):
		tmp = c + (a * (b * -0.25))
	else:
		tmp = c + ((x * y) + ((z * t) * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -4.2e+24) || !(b <= 8.8e+89))
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -4.2e+24) || ~((b <= 8.8e+89)))
		tmp = c + (a * (b * -0.25));
	else
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -4.2e+24], N[Not[LessEqual[b, 8.8e+89]], $MachinePrecision]], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $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 b < -4.2000000000000003e24 or 8.8000000000000001e89 < b

   1. Initial program 92.6%

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

   3. Taylor expanded in a around inf 68.0%

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

      1. *-commutative 68.0%

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

      2. associate-*r* 68.0%

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

   5. Simplified 68.0%

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

   if -4.2000000000000003e24 < b < 8.8000000000000001e89

   1. Initial program 98.1%

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

   3. Taylor expanded in a around 0 86.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+24} \lor \neg \left(b \leq 8.8 \cdot 10^{+89}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;a \leq -3 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-240}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-101}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (* a -0.25))))
   (if (<= a -3e+95)
     t_1
     (if (<= a -7e-240) (* t (* z 0.0625)) (if (<= a 5.2e-101) c t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (a * -0.25);
	double tmp;
	if (a <= -3e+95) {
		tmp = t_1;
	} else if (a <= -7e-240) {
		tmp = t * (z * 0.0625);
	} else if (a <= 5.2e-101) {
		tmp = c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * (-0.25d0))
    if (a <= (-3d+95)) then
        tmp = t_1
    else if (a <= (-7d-240)) then
        tmp = t * (z * 0.0625d0)
    else if (a <= 5.2d-101) then
        tmp = c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (a * -0.25);
	double tmp;
	if (a <= -3e+95) {
		tmp = t_1;
	} else if (a <= -7e-240) {
		tmp = t * (z * 0.0625);
	} else if (a <= 5.2e-101) {
		tmp = c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b * (a * -0.25)
	tmp = 0
	if a <= -3e+95:
		tmp = t_1
	elif a <= -7e-240:
		tmp = t * (z * 0.0625)
	elif a <= 5.2e-101:
		tmp = c
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(a * -0.25))
	tmp = 0.0
	if (a <= -3e+95)
		tmp = t_1;
	elseif (a <= -7e-240)
		tmp = Float64(t * Float64(z * 0.0625));
	elseif (a <= 5.2e-101)
		tmp = c;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b * (a * -0.25);
	tmp = 0.0;
	if (a <= -3e+95)
		tmp = t_1;
	elseif (a <= -7e-240)
		tmp = t * (z * 0.0625);
	elseif (a <= 5.2e-101)
		tmp = c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3e+95], t$95$1, If[LessEqual[a, -7e-240], N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e-101], c, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.99999999999999991e95 or 5.2000000000000002e-101 < a

   1. Initial program 95.5%

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

   3. Taylor expanded in x around 0 75.2%

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

      1. +-commutative 75.2%

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

      2. associate-*r* 75.2%

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

      3. fma-def 75.2%

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

   5. Applied egg-rr 75.2%

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

   6. Taylor expanded in a around inf 43.9%

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

      1. associate-*r* 43.9%

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

      2. *-commutative 43.9%

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

      3. *-commutative 43.9%

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

   8. Simplified 43.9%

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

   if -2.99999999999999991e95 < a < -7.00000000000000032e-240

   1. Initial program 97.0%

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

   3. Taylor expanded in x around 0 74.7%

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

      1. +-commutative 74.7%

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

      2. associate-*r* 74.7%

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

      3. fma-def 74.7%

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

   5. Applied egg-rr 74.7%

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

   6. Taylor expanded in c around 0 47.7%

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

   7. Taylor expanded in t around inf 35.2%

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

      1. *-commutative 35.2%

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

      2. associate-*l* 35.2%

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

      3. *-commutative 35.2%

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

   9. Simplified 35.2%

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

   if -7.00000000000000032e-240 < a < 5.2000000000000002e-101

   1. Initial program 96.3%

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

   3. Taylor expanded in c around inf 32.6%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+95}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-240}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-101}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-38} \lor \neg \left(t \leq 9 \cdot 10^{+84}\right):\\ \;\;\;\;c + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -1.25e-38) (not (<= t 9e+84)))
   (+ c (* (* z t) 0.0625))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.25e-38) || !(t <= 9e+84)) {
		tmp = c + ((z * t) * 0.0625);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-1.25d-38)) .or. (.not. (t <= 9d+84))) then
        tmp = c + ((z * t) * 0.0625d0)
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.25e-38) || !(t <= 9e+84)) {
		tmp = c + ((z * t) * 0.0625);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -1.25e-38) or not (t <= 9e+84):
		tmp = c + ((z * t) * 0.0625)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -1.25e-38) || !(t <= 9e+84))
		tmp = Float64(c + Float64(Float64(z * t) * 0.0625));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -1.25e-38) || ~((t <= 9e+84)))
		tmp = c + ((z * t) * 0.0625);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -1.25e-38], N[Not[LessEqual[t, 9e+84]], $MachinePrecision]], N[(c + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.25000000000000008e-38 or 8.9999999999999994e84 < t

   1. Initial program 94.1%

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

      1. +-commutative 94.1%

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

      2. associate-/l* 94.0%

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

      3. associate-/r/ 94.1%

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

      4. fma-def 96.6%

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

      5. div-inv 96.6%

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

      6. metadata-eval 96.6%

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

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in z around inf 57.9%

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

   if -1.25000000000000008e-38 < t < 8.9999999999999994e84

   1. Initial program 97.8%

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

      1. +-commutative 97.8%

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

      2. associate-/l* 97.8%

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

      3. associate-/r/ 97.8%

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

      4. fma-def 97.8%

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

      5. div-inv 97.8%

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

      6. metadata-eval 97.8%

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

   4. Applied egg-rr 97.8%

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

   5. Taylor expanded in x around inf 63.4%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-38} \lor \neg \left(t \leq 9 \cdot 10^{+84}\right):\\ \;\;\;\;c + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.7 \cdot 10^{+40} \lor \neg \left(a \leq 4.9 \cdot 10^{-101}\right):\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -6.7e+40) (not (<= a 4.9e-101))) (* b (* a -0.25)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -6.7e+40) || !(a <= 4.9e-101)) {
		tmp = b * (a * -0.25);
	} else {
		tmp = c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a <= (-6.7d+40)) .or. (.not. (a <= 4.9d-101))) then
        tmp = b * (a * (-0.25d0))
    else
        tmp = c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -6.7e+40) || !(a <= 4.9e-101)) {
		tmp = b * (a * -0.25);
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -6.7e+40) or not (a <= 4.9e-101):
		tmp = b * (a * -0.25)
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -6.7e+40) || !(a <= 4.9e-101))
		tmp = Float64(b * Float64(a * -0.25));
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -6.7e+40) || ~((a <= 4.9e-101)))
		tmp = b * (a * -0.25);
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -6.7e+40], N[Not[LessEqual[a, 4.9e-101]], $MachinePrecision]], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if a < -6.70000000000000022e40 or 4.9e-101 < a

   1. Initial program 95.2%

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

   3. Taylor expanded in x around 0 75.8%

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

      1. +-commutative 75.8%

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

      2. associate-*r* 75.8%

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

      3. fma-def 75.8%

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

   5. Applied egg-rr 75.8%

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

   6. Taylor expanded in a around inf 42.8%

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

      1. associate-*r* 42.8%

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

      2. *-commutative 42.8%

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

      3. *-commutative 42.8%

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

   8. Simplified 42.8%

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

   if -6.70000000000000022e40 < a < 4.9e-101

   1. Initial program 97.3%

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

   3. Taylor expanded in c around inf 31.7%

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

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.7 \cdot 10^{+40} \lor \neg \left(a \leq 4.9 \cdot 10^{-101}\right):\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-38} \lor \neg \left(t \leq 1.6 \cdot 10^{+85}\right):\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -1.25e-38) (not (<= t 1.6e+85)))
   (* t (* z 0.0625))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.25e-38) || !(t <= 1.6e+85)) {
		tmp = t * (z * 0.0625);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-1.25d-38)) .or. (.not. (t <= 1.6d+85))) then
        tmp = t * (z * 0.0625d0)
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.25e-38) || !(t <= 1.6e+85)) {
		tmp = t * (z * 0.0625);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -1.25e-38) or not (t <= 1.6e+85):
		tmp = t * (z * 0.0625)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -1.25e-38) || !(t <= 1.6e+85))
		tmp = Float64(t * Float64(z * 0.0625));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -1.25e-38) || ~((t <= 1.6e+85)))
		tmp = t * (z * 0.0625);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -1.25e-38], N[Not[LessEqual[t, 1.6e+85]], $MachinePrecision]], N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.25000000000000008e-38 or 1.60000000000000009e85 < t

   1. Initial program 94.1%

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

   3. Taylor expanded in x around 0 77.4%

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

      1. +-commutative 77.4%

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

      2. associate-*r* 77.4%

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

      3. fma-def 77.4%

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

   5. Applied egg-rr 77.4%

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

   6. Taylor expanded in c around 0 64.1%

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

   7. Taylor expanded in t around inf 44.4%

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

      1. *-commutative 44.4%

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

      2. associate-*l* 44.4%

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

      3. *-commutative 44.4%

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

   9. Simplified 44.4%

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

   if -1.25000000000000008e-38 < t < 1.60000000000000009e85

   1. Initial program 97.8%

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

      1. +-commutative 97.8%

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

      2. associate-/l* 97.8%

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

      3. associate-/r/ 97.8%

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

      4. fma-def 97.8%

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

      5. div-inv 97.8%

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

      6. metadata-eval 97.8%

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

   4. Applied egg-rr 97.8%

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

   5. Taylor expanded in x around inf 63.4%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-38} \lor \neg \left(t \leq 1.6 \cdot 10^{+85}\right):\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 21.2% 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 96.1%

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

3. Taylor expanded in c around inf 23.6%

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

4. Final simplification 23.6%

   \[\leadsto c \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024036 
(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))