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

Percentage Accurate: 97.7% → 98.8%

Time: 12.0s

Alternatives: 15

Speedup: 1.0×

• 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: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.8% accurate, 0.1× speedup

Math

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

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 y x (* -0.25 (* a b))))))

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(y, x, (-0.25 * (a * b)));
	}
	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(y, x, Float64(-0.25 * Float64(a * b)));
	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[(y * x + N[(-0.25 * N[(a * b), $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 z around 0 60.0%

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

   4. Taylor expanded in c around 0 60.0%

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

      1. *-commutative 60.0%

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

      2. fma-neg 80.0%

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

      3. *-commutative 80.0%

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

      4. distribute-rgt-neg-in 80.0%

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

      5. metadata-eval 80.0%

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

   6. Applied egg-rr 80.0%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, -0.25 \cdot \left(a \cdot b\right)\right)\\ \end{array} \]
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 98.0%

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

   1. associate-+l- 98.0%

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

   2. associate--l+ 98.0%

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

   3. fma-def 98.8%

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

   4. associate-*l/ 98.8%

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

   5. fma-neg 99.2%

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

   6. sub-neg 99.2%

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

   7. distribute-neg-in 99.2%

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

   8. remove-double-neg 99.2%

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

   9. associate-/l* 99.2%

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

   10. distribute-frac-neg 99.2%

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

   11. associate-/r/ 99.2%

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

   12. fma-def 99.2%

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

   13. neg-mul-1 99.2%

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

   14. *-commutative 99.2%

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

   15. associate-/l* 99.2%

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

   16. metadata-eval 99.2%

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

3. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 3: 98.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. associate--l+ 98.0%

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

   2. associate-/l* 97.9%

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

   3. div-inv 98.0%

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

   4. fma-neg 98.4%

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

   5. clear-num 98.4%

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

   6. div-inv 98.4%

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

   7. metadata-eval 98.4%

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

   8. associate-/l* 98.3%

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

   9. associate-/r/ 98.4%

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

   10. distribute-lft-neg-in 98.4%

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

   11. distribute-frac-neg 98.4%

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

   12. metadata-eval 98.4%

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

   13. frac-2neg 98.4%

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

   14. div-inv 98.4%

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

   15. associate-*l* 98.4%

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

   16. metadata-eval 98.4%

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

4. Applied egg-rr 98.4%

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

5. Final simplification 98.4%

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

Alternative 4: 88.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -1.45 \cdot 10^{+87}:\\ \;\;\;\;\left(c + x \cdot y\right) - t_1\\ \mathbf{elif}\;x \cdot y \leq 1.46 \cdot 10^{-55}:\\ \;\;\;\;\left(c + t_2\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + t_2\right)\\ \end{array} \end{array} \]

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) -1.45e+87)
     (- (+ c (* x y)) t_1)
     (if (<= (* x y) 1.46e-55) (- (+ 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) <= -1.45e+87) {
		tmp = (c + (x * y)) - t_1;
	} else if ((x * y) <= 1.46e-55) {
		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) <= (-1.45d+87)) then
        tmp = (c + (x * y)) - t_1
    else if ((x * y) <= 1.46d-55) 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) <= -1.45e+87) {
		tmp = (c + (x * y)) - t_1;
	} else if ((x * y) <= 1.46e-55) {
		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) <= -1.45e+87:
		tmp = (c + (x * y)) - t_1
	elif (x * y) <= 1.46e-55:
		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) <= -1.45e+87)
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	elseif (Float64(x * y) <= 1.46e-55)
		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) <= -1.45e+87)
		tmp = (c + (x * y)) - t_1;
	elseif ((x * y) <= 1.46e-55)
		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], -1.45e+87], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.46e-55], 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) < -1.4499999999999999e87

   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 z around 0 89.7%

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

   if -1.4499999999999999e87 < (*.f64 x y) < 1.46000000000000009e-55

   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. Taylor expanded in x around 0 97.0%

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

   if 1.46000000000000009e-55 < (*.f64 x y)

   1. Initial program 96.8%

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

   3. Taylor expanded in a around 0 86.9%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.45 \cdot 10^{+87}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 1.46 \cdot 10^{-55}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+133} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+97}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -5e+133) (not (<= (* a b) 5e+97)))
   (- (+ c (* x y)) (* (* a b) 0.25))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+133) || !((a * b) <= 5e+97)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((a * b) <= (-5d+133)) .or. (.not. ((a * b) <= 5d+97))) then
        tmp = (c + (x * y)) - ((a * b) * 0.25d0)
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+133) || !((a * b) <= 5e+97)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -5e+133) or not ((a * b) <= 5e+97):
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -5e+133) || !(Float64(a * b) <= 5e+97))
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -5e+133) || ~(((a * b) <= 5e+97)))
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -5e+133], N[Not[LessEqual[N[(a * b), $MachinePrecision], 5e+97]], $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[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.99999999999999961e133 or 4.99999999999999999e97 < (*.f64 a b)

   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 z around 0 87.2%

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

   if -4.99999999999999961e133 < (*.f64 a b) < 4.99999999999999999e97

   1. Initial program 98.3%

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

   3. Taylor expanded in a around 0 93.3%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+133} \lor \neg \left(a \cdot b \leq 5 \cdot 10^{+97}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+162}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+212}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -5e+162)
   (- (* x y) (* (* a b) 0.25))
   (if (<= (* a b) 2e+212)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (* -0.25 (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -5e+162) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((a * b) <= 2e+212) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = -0.25 * (a * b);
	}
	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+162)) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    else if ((a * b) <= 2d+212) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = (-0.25d0) * (a * b)
    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+162) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((a * b) <= 2e+212) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = -0.25 * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -5e+162:
		tmp = (x * y) - ((a * b) * 0.25)
	elif (a * b) <= 2e+212:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = -0.25 * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -5e+162)
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	elseif (Float64(a * b) <= 2e+212)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(-0.25 * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -5e+162)
		tmp = (x * y) - ((a * b) * 0.25);
	elseif ((a * b) <= 2e+212)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = -0.25 * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -5e+162], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+212], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.9999999999999997e162

   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 z around 0 89.2%

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

   4. Taylor expanded in c around 0 89.5%

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

   if -4.9999999999999997e162 < (*.f64 a b) < 1.9999999999999998e212

   1. Initial program 98.5%

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

   3. Taylor expanded in a around 0 90.9%

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

   if 1.9999999999999998e212 < (*.f64 a b)

   1. Initial program 94.4%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in a around inf 95.0%

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

      1. *-commutative 95.0%

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

   6. Simplified 95.0%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+162}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+212}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+162}:\\ \;\;\;\;x \cdot y - t_1\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+212}:\\ \;\;\;\;c + \left(x \cdot y + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)) (t_2 (* 0.0625 (* z t))))
   (if (<= (* a b) -5e+162)
     (- (* x y) t_1)
     (if (<= (* a b) 2e+212) (+ c (+ (* x y) t_2)) (- t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -5e+162) {
		tmp = (x * y) - t_1;
	} else if ((a * b) <= 2e+212) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    t_2 = 0.0625d0 * (z * t)
    if ((a * b) <= (-5d+162)) then
        tmp = (x * y) - t_1
    else if ((a * b) <= 2d+212) then
        tmp = c + ((x * y) + t_2)
    else
        tmp = t_2 - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -5e+162) {
		tmp = (x * y) - t_1;
	} else if ((a * b) <= 2e+212) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	t_2 = 0.0625 * (z * t)
	tmp = 0
	if (a * b) <= -5e+162:
		tmp = (x * y) - t_1
	elif (a * b) <= 2e+212:
		tmp = c + ((x * y) + t_2)
	else:
		tmp = t_2 - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	t_2 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -5e+162)
		tmp = Float64(Float64(x * y) - t_1);
	elseif (Float64(a * b) <= 2e+212)
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	else
		tmp = Float64(t_2 - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	t_2 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((a * b) <= -5e+162)
		tmp = (x * y) - t_1;
	elseif ((a * b) <= 2e+212)
		tmp = c + ((x * y) + t_2);
	else
		tmp = t_2 - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+162], N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+212], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(t$95$2 - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.9999999999999997e162

   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 z around 0 89.2%

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

   4. Taylor expanded in c around 0 89.5%

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

   if -4.9999999999999997e162 < (*.f64 a b) < 1.9999999999999998e212

   1. Initial program 98.5%

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

   3. Taylor expanded in a around 0 90.9%

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

   if 1.9999999999999998e212 < (*.f64 a b)

   1. Initial program 94.4%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in c around 0 100.0%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+162}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+212}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = c + ((x * y) + ((z / (16.0d0 / t)) - ((a * b) * 0.25d0)))
end function

Java

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

Python

def code(x, y, z, t, a, b, c):
	return c + ((x * y) + ((z / (16.0 / t)) - ((a * b) * 0.25)))

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = c + ((x * y) + ((z / (16.0 / t)) - ((a * b) * 0.25)));
end

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. associate-/l* 97.9%

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

   2. add-cube-cbrt 97.6%

      \[\leadsto \left(\left(x \cdot y + \frac{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}{\frac{16}{t}}\right) - \frac{a \cdot b}{4}\right) + c \]

   3. div-inv 97.6%

      \[\leadsto \left(\left(x \cdot y + \frac{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}{\color{blue}{16 \cdot \frac{1}{t}}}\right) - \frac{a \cdot b}{4}\right) + c \]

   4. times-frac 97.6%

      \[\leadsto \left(\left(x \cdot y + \color{blue}{\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{16} \cdot \frac{\sqrt[3]{z}}{\frac{1}{t}}}\right) - \frac{a \cdot b}{4}\right) + c \]

   5. pow2 97.6%

      \[\leadsto \left(\left(x \cdot y + \frac{\color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}}{16} \cdot \frac{\sqrt[3]{z}}{\frac{1}{t}}\right) - \frac{a \cdot b}{4}\right) + c \]

4. Applied egg-rr 97.6%

   \[\leadsto \left(\left(x \cdot y + \color{blue}{\frac{{\left(\sqrt[3]{z}\right)}^{2}}{16} \cdot \frac{\sqrt[3]{z}}{\frac{1}{t}}}\right) - \frac{a \cdot b}{4}\right) + c \]
5. Step-by-step derivation

   1. associate-/r/ 97.6%

      \[\leadsto \left(\left(x \cdot y + \frac{{\left(\sqrt[3]{z}\right)}^{2}}{16} \cdot \color{blue}{\left(\frac{\sqrt[3]{z}}{1} \cdot t\right)}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. /-rgt-identity 97.6%

      \[\leadsto \left(\left(x \cdot y + \frac{{\left(\sqrt[3]{z}\right)}^{2}}{16} \cdot \left(\color{blue}{\sqrt[3]{z}} \cdot t\right)\right) - \frac{a \cdot b}{4}\right) + c \]

   3. associate-*r* 97.6%

      \[\leadsto \left(\left(x \cdot y + \color{blue}{\left(\frac{{\left(\sqrt[3]{z}\right)}^{2}}{16} \cdot \sqrt[3]{z}\right) \cdot t}\right) - \frac{a \cdot b}{4}\right) + c \]

   4. associate-*l/ 97.6%

      \[\leadsto \left(\left(x \cdot y + \color{blue}{\frac{{\left(\sqrt[3]{z}\right)}^{2} \cdot \sqrt[3]{z}}{16}} \cdot t\right) - \frac{a \cdot b}{4}\right) + c \]

   5. unpow2 97.6%

      \[\leadsto \left(\left(x \cdot y + \frac{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)} \cdot \sqrt[3]{z}}{16} \cdot t\right) - \frac{a \cdot b}{4}\right) + c \]

   6. rem-3cbrt-lft 98.0%

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

   7. associate-/r/ 97.9%

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

6. Simplified 97.9%

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

   1. associate--l+ 97.9%

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

   2. div-inv 97.9%

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

   3. metadata-eval 97.9%

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

   4. *-commutative 97.9%

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

8. Applied egg-rr 97.9%

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

9. Final simplification 97.9%

   \[\leadsto c + \left(x \cdot y + \left(\frac{z}{\frac{16}{t}} - \left(a \cdot b\right) \cdot 0.25\right)\right) \]
10. Add Preprocessing

Alternative 9: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Final simplification 98.0%

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

Alternative 10: 65.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.05 \cdot 10^{+76} \lor \neg \left(x \cdot y \leq 1.55 \cdot 10^{+68}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.05e+76) (not (<= (* x y) 1.55e+68)))
   (+ c (* x y))
   (+ c (* a (* b -0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.05e+76) || !((x * y) <= 1.55e+68)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (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 (((x * y) <= (-1.05d+76)) .or. (.not. ((x * y) <= 1.55d+68))) then
        tmp = c + (x * y)
    else
        tmp = c + (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 (((x * y) <= -1.05e+76) || !((x * y) <= 1.55e+68)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.05e+76) or not ((x * y) <= 1.55e+68):
		tmp = c + (x * y)
	else:
		tmp = c + (a * (b * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1.05e+76) || !(Float64(x * y) <= 1.55e+68))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1.05e+76) || ~(((x * y) <= 1.55e+68)))
		tmp = c + (x * y);
	else
		tmp = c + (a * (b * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.05e+76], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.55e+68]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.05000000000000003e76 or 1.5499999999999999e68 < (*.f64 x y)

   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. Step-by-step derivation

      1. associate--l+ 95.2%

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

      2. associate-/l* 95.2%

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

      3. div-inv 95.2%

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

      4. fma-neg 96.2%

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

      5. clear-num 96.2%

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

      6. div-inv 96.2%

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

      7. metadata-eval 96.2%

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

      8. associate-/l* 96.2%

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

      9. associate-/r/ 96.2%

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

      10. distribute-lft-neg-in 96.2%

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

      11. distribute-frac-neg 96.2%

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

      12. metadata-eval 96.2%

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

      13. frac-2neg 96.2%

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

      14. div-inv 96.2%

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

      15. associate-*l* 96.2%

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

      16. metadata-eval 96.2%

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

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in x around inf 78.1%

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

   if -1.05000000000000003e76 < (*.f64 x y) < 1.5499999999999999e68

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 54.3%

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

      1. *-commutative 54.3%

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

      2. associate-*r* 54.3%

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

   5. Simplified 54.3%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.05 \cdot 10^{+76} \lor \neg \left(x \cdot y \leq 1.55 \cdot 10^{+68}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.5 \cdot 10^{+89} \lor \neg \left(x \cdot y \leq 10^{+51}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -2.5e+89) (not (<= (* x y) 1e+51)))
   (+ c (* x y))
   (+ c (* z (* t 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -2.5e+89) || !((x * y) <= 1e+51)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (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 (((x * y) <= (-2.5d+89)) .or. (.not. ((x * y) <= 1d+51))) then
        tmp = c + (x * y)
    else
        tmp = c + (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 (((x * y) <= -2.5e+89) || !((x * y) <= 1e+51)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (z * (t * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -2.5e+89) or not ((x * y) <= 1e+51):
		tmp = c + (x * y)
	else:
		tmp = c + (z * (t * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -2.5e+89) || !(Float64(x * y) <= 1e+51))
		tmp = Float64(c + Float64(x * y));
	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)
	tmp = 0.0;
	if (((x * y) <= -2.5e+89) || ~(((x * y) <= 1e+51)))
		tmp = c + (x * y);
	else
		tmp = c + (z * (t * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2.5e+89], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+51]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.49999999999999992e89 or 1e51 < (*.f64 x y)

   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. Step-by-step derivation

      1. associate--l+ 95.1%

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

      2. associate-/l* 95.1%

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

      3. div-inv 95.1%

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

      4. fma-neg 96.1%

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

      5. clear-num 96.1%

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

      6. div-inv 96.1%

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

      7. metadata-eval 96.1%

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

      8. associate-/l* 96.1%

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

      9. associate-/r/ 96.1%

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

      10. distribute-lft-neg-in 96.1%

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

      11. distribute-frac-neg 96.1%

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

      12. metadata-eval 96.1%

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

      13. frac-2neg 96.1%

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

      14. div-inv 96.1%

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

      15. associate-*l* 96.1%

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

      16. metadata-eval 96.1%

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

   4. Applied egg-rr 96.1%

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

   5. Taylor expanded in x around inf 79.1%

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

   if -2.49999999999999992e89 < (*.f64 x y) < 1e51

   1. Initial program 99.9%

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

      1. associate--l+ 100.0%

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

      2. associate-/l* 99.8%

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

      3. div-inv 99.9%

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

      4. fma-neg 99.9%

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

      5. clear-num 100.0%

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

      6. div-inv 100.0%

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

      7. metadata-eval 100.0%

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

      8. associate-/l* 99.9%

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

      9. associate-/r/ 100.0%

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

      10. distribute-lft-neg-in 100.0%

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

      11. distribute-frac-neg 100.0%

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

      12. metadata-eval 100.0%

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

      13. frac-2neg 100.0%

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

      14. div-inv 100.0%

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

      15. associate-*l* 100.0%

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

      16. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around inf 67.9%

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

      1. *-commutative 67.9%

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

      2. *-commutative 67.9%

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

      3. associate-*r* 67.9%

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

      4. *-commutative 67.9%

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

   7. Simplified 67.9%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.5 \cdot 10^{+89} \lor \neg \left(x \cdot y \leq 10^{+51}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+126}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 6.2 \cdot 10^{+51}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -5e+126)
   (- (* x y) (* (* a b) 0.25))
   (if (<= (* x y) 6.2e+51) (+ 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 ((x * y) <= -5e+126) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((x * y) <= 6.2e+51) {
		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 ((x * y) <= (-5d+126)) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    else if ((x * y) <= 6.2d+51) 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 ((x * y) <= -5e+126) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((x * y) <= 6.2e+51) {
		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 (x * y) <= -5e+126:
		tmp = (x * y) - ((a * b) * 0.25)
	elif (x * y) <= 6.2e+51:
		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 (Float64(x * y) <= -5e+126)
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	elseif (Float64(x * y) <= 6.2e+51)
		tmp = Float64(c + Float64(z * Float64(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 ((x * y) <= -5e+126)
		tmp = (x * y) - ((a * b) * 0.25);
	elseif ((x * y) <= 6.2e+51)
		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[LessEqual[N[(x * y), $MachinePrecision], -5e+126], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.2e+51], N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.99999999999999977e126

   1. Initial program 93.7%

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

   3. Taylor expanded in z around 0 88.1%

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

   4. Taylor expanded in c around 0 88.1%

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

   if -4.99999999999999977e126 < (*.f64 x y) < 6.20000000000000022e51

   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. associate--l+ 100.0%

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

      2. associate-/l* 99.8%

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

      3. div-inv 99.9%

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

      4. fma-neg 99.9%

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

      5. clear-num 100.0%

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

      6. div-inv 100.0%

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

      7. metadata-eval 100.0%

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

      8. associate-/l* 99.9%

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

      9. associate-/r/ 100.0%

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

      10. distribute-lft-neg-in 100.0%

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

      11. distribute-frac-neg 100.0%

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

      12. metadata-eval 100.0%

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

      13. frac-2neg 100.0%

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

      14. div-inv 100.0%

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

      15. associate-*l* 100.0%

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

      16. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around inf 67.4%

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

      1. *-commutative 67.4%

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

      2. *-commutative 67.4%

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

      3. associate-*r* 67.4%

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

      4. *-commutative 67.4%

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

   7. Simplified 67.4%

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

   if 6.20000000000000022e51 < (*.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. Add Preprocessing
   3. Step-by-step derivation

      1. associate--l+ 95.4%

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

      2. associate-/l* 95.4%

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

      3. div-inv 95.4%

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

      4. fma-neg 96.9%

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

      5. clear-num 96.9%

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

      6. div-inv 96.9%

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

      7. metadata-eval 96.9%

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

      8. associate-/l* 96.9%

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

      9. associate-/r/ 96.9%

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

      10. distribute-lft-neg-in 96.9%

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

      11. distribute-frac-neg 96.9%

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

      12. metadata-eval 96.9%

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

      13. frac-2neg 96.9%

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

      14. div-inv 96.9%

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

      15. associate-*l* 96.9%

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

      16. metadata-eval 96.9%

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

   4. Applied egg-rr 96.9%

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

   5. Taylor expanded in x around inf 78.0%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+126}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 6.2 \cdot 10^{+51}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 41.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.5 \cdot 10^{+131} \lor \neg \left(a \cdot b \leq 2.6 \cdot 10^{+103}\right):\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -1.5e+131) (not (<= (* a b) 2.6e+103)))
   (* -0.25 (* a b))
   c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -1.5e+131) || !((a * b) <= 2.6e+103)) {
		tmp = -0.25 * (a * b);
	} 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 * b) <= (-1.5d+131)) .or. (.not. ((a * b) <= 2.6d+103))) then
        tmp = (-0.25d0) * (a * b)
    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 * b) <= -1.5e+131) || !((a * b) <= 2.6e+103)) {
		tmp = -0.25 * (a * b);
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -1.5e+131) or not ((a * b) <= 2.6e+103):
		tmp = -0.25 * (a * b)
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -1.5e+131) || !(Float64(a * b) <= 2.6e+103))
		tmp = Float64(-0.25 * Float64(a * b));
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -1.5e+131) || ~(((a * b) <= 2.6e+103)))
		tmp = -0.25 * (a * b);
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1.5e+131], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2.6e+103]], $MachinePrecision]], N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.5000000000000001e131 or 2.6000000000000002e103 < (*.f64 a b)

   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 84.6%

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

   4. Taylor expanded in a around inf 65.2%

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

      1. *-commutative 65.2%

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

   6. Simplified 65.2%

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

   if -1.5000000000000001e131 < (*.f64 a b) < 2.6000000000000002e103

   1. Initial program 98.4%

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

   3. Taylor expanded in c around inf 24.0%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.5 \cdot 10^{+131} \lor \neg \left(a \cdot b \leq 2.6 \cdot 10^{+103}\right):\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -7 \cdot 10^{+162} \lor \neg \left(a \cdot b \leq 7.2 \cdot 10^{+213}\right):\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -7e+162) (not (<= (* a b) 7.2e+213)))
   (* -0.25 (* a b))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -7e+162) || !((a * b) <= 7.2e+213)) {
		tmp = -0.25 * (a * b);
	} 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 (((a * b) <= (-7d+162)) .or. (.not. ((a * b) <= 7.2d+213))) then
        tmp = (-0.25d0) * (a * b)
    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 (((a * b) <= -7e+162) || !((a * b) <= 7.2e+213)) {
		tmp = -0.25 * (a * b);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -7e+162) or not ((a * b) <= 7.2e+213):
		tmp = -0.25 * (a * b)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -7e+162) || !(Float64(a * b) <= 7.2e+213))
		tmp = Float64(-0.25 * Float64(a * b));
	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 (((a * b) <= -7e+162) || ~(((a * b) <= 7.2e+213)))
		tmp = -0.25 * (a * b);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -7e+162], N[Not[LessEqual[N[(a * b), $MachinePrecision], 7.2e+213]], $MachinePrecision]], N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -7.00000000000000036e162 or 7.2000000000000002e213 < (*.f64 a b)

   1. Initial program 95.6%

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

   3. Taylor expanded in x around 0 89.2%

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

   4. Taylor expanded in a around inf 83.2%

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

      1. *-commutative 83.2%

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

   6. Simplified 83.2%

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

   if -7.00000000000000036e162 < (*.f64 a b) < 7.2000000000000002e213

   1. Initial program 98.5%

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

      1. associate--l+ 98.5%

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

      2. associate-/l* 98.4%

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

      3. div-inv 98.5%

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

      4. fma-neg 98.5%

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

      5. clear-num 98.5%

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

      6. div-inv 98.5%

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

      7. metadata-eval 98.5%

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

      8. associate-/l* 98.5%

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

      9. associate-/r/ 98.5%

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

      10. distribute-lft-neg-in 98.5%

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

      11. distribute-frac-neg 98.5%

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

      12. metadata-eval 98.5%

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

      13. frac-2neg 98.5%

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

      14. div-inv 98.5%

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

      15. associate-*l* 98.5%

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

      16. metadata-eval 98.5%

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

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in x around inf 58.4%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -7 \cdot 10^{+162} \lor \neg \left(a \cdot b \leq 7.2 \cdot 10^{+213}\right):\\ \;\;\;\;-0.25 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 22.3% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in c around inf 20.3%

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

4. Final simplification 20.3%

   \[\leadsto c \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024011 
(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))