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

Percentage Accurate: 97.7% → 98.9%

Time: 9.1s

Alternatives: 14

Speedup: 0.5×

• 33.2% 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: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. associate-+l- 96.5%

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

   2. +-commutative 96.5%

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

   3. associate--l+ 96.5%

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

   4. +-commutative 96.5%

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

   5. associate-+l- 96.5%

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

   6. fma-neg 98.0%

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

   7. neg-sub0 98.0%

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

   8. associate--l- 98.0%

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

   9. associate-+l- 98.0%

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

   10. neg-sub0 98.0%

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

   11. *-commutative 98.0%

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

   12. associate-*r/ 98.0%

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

   13. distribute-rgt-neg-in 98.0%

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

   14. fma-def 98.4%

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

   15. distribute-frac-neg 98.4%

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

   16. neg-mul-1 98.4%

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

   17. associate-/l* 98.4%

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

   18. associate-/r/ 98.4%

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

   19. metadata-eval 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 2: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. associate-+l- 96.5%

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

   2. +-commutative 96.5%

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

   3. associate--l+ 96.5%

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

   4. associate-*l/ 96.5%

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

   5. *-commutative 96.5%

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

   6. fma-def 97.7%

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

   7. fma-neg 98.4%

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

   8. neg-sub0 98.4%

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

   9. associate-+l- 98.4%

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

   10. neg-sub0 98.4%

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

   11. +-commutative 98.4%

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

   12. unsub-neg 98.4%

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

   13. *-commutative 98.4%

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

   14. associate-*r/ 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 3: 98.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. associate-+l- 96.5%

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

   2. sub-neg 96.5%

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

   3. neg-mul-1 96.5%

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

   4. metadata-eval 96.5%

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

   5. metadata-eval 96.5%

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

   6. cancel-sign-sub-inv 96.5%

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

   7. fma-def 97.3%

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

   8. associate-/l* 97.2%

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

   9. metadata-eval 97.2%

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

   10. *-lft-identity 97.2%

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

   11. associate-/l* 97.1%

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

3. Simplified 97.1%

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

4. Final simplification 97.1%

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

Alternative 4: 98.6% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (+ (/ (* z t) 16.0) (* x y)) (/ (* b a) 4.0))))
   (if (<= t_1 INFINITY) (+ c t_1) (* b (* -0.25 a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((z * t) / 16.0) + (x * y)) - ((b * a) / 4.0);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = c + t_1;
	} else {
		tmp = b * (-0.25 * a);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((z * t) / 16.0) + (x * y)) - ((b * a) / 4.0);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = c + t_1;
	} else {
		tmp = b * (-0.25 * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (((z * t) / 16.0) + (x * y)) - ((b * a) / 4.0)
	tmp = 0
	if t_1 <= math.inf:
		tmp = c + t_1
	else:
		tmp = b * (-0.25 * a)
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (((z * t) / 16.0) + (x * y)) - ((b * a) / 4.0);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = c + t_1;
	else
		tmp = b * (-0.25 * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(c + t$95$1), $MachinePrecision], N[(b * N[(-0.25 * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in a around inf 55.9%

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

      1. *-commutative 55.9%

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

   4. Simplified 55.9%

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

   5. Taylor expanded in a around inf 55.9%

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

      1. associate-*r* 55.9%

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

   7. Simplified 55.9%

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

4. Final simplification 98.4%

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

Alternative 5: 37.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t \cdot 0.0625\right)\\ t_2 := b \cdot \left(-0.25 \cdot a\right)\\ \mathbf{if}\;b \leq -2.95 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-279}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-175}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-104}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-33}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{+46}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+174}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (* t 0.0625))) (t_2 (* b (* -0.25 a))))
   (if (<= b -2.95e-15)
     t_2
     (if (<= b -1.8e-114)
       t_1
       (if (<= b -4.5e-279)
         (* x y)
         (if (<= b 7e-247)
           t_1
           (if (<= b 4e-175)
             c
             (if (<= b 3e-125)
               t_1
               (if (<= b 1.2e-104)
                 c
                 (if (<= b 3.5e-33)
                   (* x y)
                   (if (<= b 2.95e+46)
                     c
                     (if (<= b 5.4e+174) (* 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 = b * (-0.25 * a);
	double tmp;
	if (b <= -2.95e-15) {
		tmp = t_2;
	} else if (b <= -1.8e-114) {
		tmp = t_1;
	} else if (b <= -4.5e-279) {
		tmp = x * y;
	} else if (b <= 7e-247) {
		tmp = t_1;
	} else if (b <= 4e-175) {
		tmp = c;
	} else if (b <= 3e-125) {
		tmp = t_1;
	} else if (b <= 1.2e-104) {
		tmp = c;
	} else if (b <= 3.5e-33) {
		tmp = x * y;
	} else if (b <= 2.95e+46) {
		tmp = c;
	} else if (b <= 5.4e+174) {
		tmp = x * y;
	} 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 = z * (t * 0.0625d0)
    t_2 = b * ((-0.25d0) * a)
    if (b <= (-2.95d-15)) then
        tmp = t_2
    else if (b <= (-1.8d-114)) then
        tmp = t_1
    else if (b <= (-4.5d-279)) then
        tmp = x * y
    else if (b <= 7d-247) then
        tmp = t_1
    else if (b <= 4d-175) then
        tmp = c
    else if (b <= 3d-125) then
        tmp = t_1
    else if (b <= 1.2d-104) then
        tmp = c
    else if (b <= 3.5d-33) then
        tmp = x * y
    else if (b <= 2.95d+46) then
        tmp = c
    else if (b <= 5.4d+174) then
        tmp = x * y
    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 = z * (t * 0.0625);
	double t_2 = b * (-0.25 * a);
	double tmp;
	if (b <= -2.95e-15) {
		tmp = t_2;
	} else if (b <= -1.8e-114) {
		tmp = t_1;
	} else if (b <= -4.5e-279) {
		tmp = x * y;
	} else if (b <= 7e-247) {
		tmp = t_1;
	} else if (b <= 4e-175) {
		tmp = c;
	} else if (b <= 3e-125) {
		tmp = t_1;
	} else if (b <= 1.2e-104) {
		tmp = c;
	} else if (b <= 3.5e-33) {
		tmp = x * y;
	} else if (b <= 2.95e+46) {
		tmp = c;
	} else if (b <= 5.4e+174) {
		tmp = x * y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = z * (t * 0.0625)
	t_2 = b * (-0.25 * a)
	tmp = 0
	if b <= -2.95e-15:
		tmp = t_2
	elif b <= -1.8e-114:
		tmp = t_1
	elif b <= -4.5e-279:
		tmp = x * y
	elif b <= 7e-247:
		tmp = t_1
	elif b <= 4e-175:
		tmp = c
	elif b <= 3e-125:
		tmp = t_1
	elif b <= 1.2e-104:
		tmp = c
	elif b <= 3.5e-33:
		tmp = x * y
	elif b <= 2.95e+46:
		tmp = c
	elif b <= 5.4e+174:
		tmp = x * y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(z * Float64(t * 0.0625))
	t_2 = Float64(b * Float64(-0.25 * a))
	tmp = 0.0
	if (b <= -2.95e-15)
		tmp = t_2;
	elseif (b <= -1.8e-114)
		tmp = t_1;
	elseif (b <= -4.5e-279)
		tmp = Float64(x * y);
	elseif (b <= 7e-247)
		tmp = t_1;
	elseif (b <= 4e-175)
		tmp = c;
	elseif (b <= 3e-125)
		tmp = t_1;
	elseif (b <= 1.2e-104)
		tmp = c;
	elseif (b <= 3.5e-33)
		tmp = Float64(x * y);
	elseif (b <= 2.95e+46)
		tmp = c;
	elseif (b <= 5.4e+174)
		tmp = Float64(x * y);
	else
		tmp = 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 = b * (-0.25 * a);
	tmp = 0.0;
	if (b <= -2.95e-15)
		tmp = t_2;
	elseif (b <= -1.8e-114)
		tmp = t_1;
	elseif (b <= -4.5e-279)
		tmp = x * y;
	elseif (b <= 7e-247)
		tmp = t_1;
	elseif (b <= 4e-175)
		tmp = c;
	elseif (b <= 3e-125)
		tmp = t_1;
	elseif (b <= 1.2e-104)
		tmp = c;
	elseif (b <= 3.5e-33)
		tmp = x * y;
	elseif (b <= 2.95e+46)
		tmp = c;
	elseif (b <= 5.4e+174)
		tmp = x * y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(-0.25 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.95e-15], t$95$2, If[LessEqual[b, -1.8e-114], t$95$1, If[LessEqual[b, -4.5e-279], N[(x * y), $MachinePrecision], If[LessEqual[b, 7e-247], t$95$1, If[LessEqual[b, 4e-175], c, If[LessEqual[b, 3e-125], t$95$1, If[LessEqual[b, 1.2e-104], c, If[LessEqual[b, 3.5e-33], N[(x * y), $MachinePrecision], If[LessEqual[b, 2.95e+46], c, If[LessEqual[b, 5.4e+174], N[(x * y), $MachinePrecision], t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.94999999999999982e-15 or 5.3999999999999998e174 < b

   1. Initial program 92.6%

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

   2. Taylor expanded in a around inf 59.7%

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

      1. *-commutative 59.7%

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

   4. Simplified 59.7%

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

   5. Taylor expanded in a around inf 45.0%

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

      1. associate-*r* 45.0%

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

   7. Simplified 45.0%

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

   if -2.94999999999999982e-15 < b < -1.80000000000000009e-114 or -4.49999999999999995e-279 < b < 6.9999999999999998e-247 or 4e-175 < b < 2.9999999999999999e-125

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. +-commutative 100.0%

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

      3. associate--l+ 100.0%

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

      4. associate-*l/ 100.0%

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

      5. *-commutative 100.0%

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

      6. fma-def 100.0%

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

      7. fma-neg 100.0%

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

      8. neg-sub0 100.0%

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

      9. associate-+l- 100.0%

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

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. unsub-neg 100.0%

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

      13. *-commutative 100.0%

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

      14. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in b around 0 96.0%

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

   5. Taylor expanded in t around inf 40.8%

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

      1. associate-*r* 40.8%

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

      2. *-commutative 40.8%

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

      3. *-commutative 40.8%

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

      4. *-commutative 40.8%

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

   7. Simplified 40.8%

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

   if -1.80000000000000009e-114 < b < -4.49999999999999995e-279 or 1.2e-104 < b < 3.4999999999999999e-33 or 2.95e46 < b < 5.3999999999999998e174

   1. Initial program 97.5%

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

      1. associate-+l- 97.5%

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

      2. +-commutative 97.5%

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

      3. associate--l+ 97.5%

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

      4. associate-*l/ 97.5%

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

      5. *-commutative 97.5%

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

      6. fma-def 97.5%

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

      7. fma-neg 97.5%

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

      8. neg-sub0 97.5%

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

      9. associate-+l- 97.5%

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

      10. neg-sub0 97.5%

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

      11. +-commutative 97.5%

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

      12. unsub-neg 97.5%

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

      13. *-commutative 97.5%

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

      14. associate-*r/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in b around 0 83.1%

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

   5. Taylor expanded in y around inf 41.3%

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

   if 6.9999999999999998e-247 < b < 4e-175 or 2.9999999999999999e-125 < b < 1.2e-104 or 3.4999999999999999e-33 < b < 2.95e46

   1. Initial program 100.0%

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

   2. Taylor expanded in c around inf 40.1%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.95 \cdot 10^{-15}:\\ \;\;\;\;b \cdot \left(-0.25 \cdot a\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-279}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-247}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-175}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-104}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-33}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{+46}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+174}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-0.25 \cdot a\right)\\ \end{array} \]

Alternative 6: 65.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + -0.25 \cdot \left(b \cdot a\right)\\ \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 20000000000000:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+175}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (+ c (* -0.25 (* b a)))))
   (if (<= (* b a) -1e+130)
     t_2
     (if (<= (* b a) -2e-231)
       t_1
       (if (<= (* b a) 20000000000000.0)
         (+ c (* t (* z 0.0625)))
         (if (<= (* b a) 2e+175) 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 + (-0.25 * (b * a));
	double tmp;
	if ((b * a) <= -1e+130) {
		tmp = t_2;
	} else if ((b * a) <= -2e-231) {
		tmp = t_1;
	} else if ((b * a) <= 20000000000000.0) {
		tmp = c + (t * (z * 0.0625));
	} else if ((b * a) <= 2e+175) {
		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 + ((-0.25d0) * (b * a))
    if ((b * a) <= (-1d+130)) then
        tmp = t_2
    else if ((b * a) <= (-2d-231)) then
        tmp = t_1
    else if ((b * a) <= 20000000000000.0d0) then
        tmp = c + (t * (z * 0.0625d0))
    else if ((b * a) <= 2d+175) 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 + (-0.25 * (b * a));
	double tmp;
	if ((b * a) <= -1e+130) {
		tmp = t_2;
	} else if ((b * a) <= -2e-231) {
		tmp = t_1;
	} else if ((b * a) <= 20000000000000.0) {
		tmp = c + (t * (z * 0.0625));
	} else if ((b * a) <= 2e+175) {
		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 + (-0.25 * (b * a))
	tmp = 0
	if (b * a) <= -1e+130:
		tmp = t_2
	elif (b * a) <= -2e-231:
		tmp = t_1
	elif (b * a) <= 20000000000000.0:
		tmp = c + (t * (z * 0.0625))
	elif (b * a) <= 2e+175:
		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(-0.25 * Float64(b * a)))
	tmp = 0.0
	if (Float64(b * a) <= -1e+130)
		tmp = t_2;
	elseif (Float64(b * a) <= -2e-231)
		tmp = t_1;
	elseif (Float64(b * a) <= 20000000000000.0)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (Float64(b * a) <= 2e+175)
		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 + (-0.25 * (b * a));
	tmp = 0.0;
	if ((b * a) <= -1e+130)
		tmp = t_2;
	elseif ((b * a) <= -2e-231)
		tmp = t_1;
	elseif ((b * a) <= 20000000000000.0)
		tmp = c + (t * (z * 0.0625));
	elseif ((b * a) <= 2e+175)
		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[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -1e+130], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -2e-231], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 20000000000000.0], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 2e+175], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.0000000000000001e130 or 1.9999999999999999e175 < (*.f64 a b)

   1. Initial program 89.3%

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

   2. Taylor expanded in a around inf 80.8%

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

      1. *-commutative 80.8%

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

   4. Simplified 80.8%

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

   if -1.0000000000000001e130 < (*.f64 a b) < -2e-231 or 2e13 < (*.f64 a b) < 1.9999999999999999e175

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 66.9%

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

   if -2e-231 < (*.f64 a b) < 2e13

   1. Initial program 98.9%

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

   2. Taylor expanded in z around inf 68.9%

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

      1. *-commutative 68.9%

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

      2. associate-*r* 68.9%

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

      3. *-commutative 68.9%

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

   4. Simplified 68.9%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+130}:\\ \;\;\;\;c + -0.25 \cdot \left(b \cdot a\right)\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-231}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 20000000000000:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+175}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + -0.25 \cdot \left(b \cdot a\right)\\ \end{array} \]

Alternative 7: 81.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot 0.25\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+99} \lor \neg \left(x \leq -4 \cdot 10^{+46} \lor \neg \left(x \leq -7 \cdot 10^{-76}\right) \land x \leq 3.1 \cdot 10^{-142}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(c + \left(z \cdot t\right) \cdot 0.0625\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) 0.25)))
   (if (or (<= x -1.45e+99)
           (not (or (<= x -4e+46) (and (not (<= x -7e-76)) (<= x 3.1e-142)))))
     (- (+ c (* x y)) t_1)
     (- (+ c (* (* z t) 0.0625)) 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 ((x <= -1.45e+99) || !((x <= -4e+46) || (!(x <= -7e-76) && (x <= 3.1e-142)))) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = (c + ((z * t) * 0.0625)) - 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 ((x <= (-1.45d+99)) .or. (.not. (x <= (-4d+46)) .or. (.not. (x <= (-7d-76))) .and. (x <= 3.1d-142))) then
        tmp = (c + (x * y)) - t_1
    else
        tmp = (c + ((z * t) * 0.0625d0)) - 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 ((x <= -1.45e+99) || !((x <= -4e+46) || (!(x <= -7e-76) && (x <= 3.1e-142)))) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = (c + ((z * t) * 0.0625)) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * 0.25
	tmp = 0
	if (x <= -1.45e+99) or not ((x <= -4e+46) or (not (x <= -7e-76) and (x <= 3.1e-142))):
		tmp = (c + (x * y)) - t_1
	else:
		tmp = (c + ((z * t) * 0.0625)) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b * a) * 0.25)
	tmp = 0.0
	if ((x <= -1.45e+99) || !((x <= -4e+46) || (!(x <= -7e-76) && (x <= 3.1e-142))))
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	else
		tmp = Float64(Float64(c + Float64(Float64(z * t) * 0.0625)) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b * a) * 0.25;
	tmp = 0.0;
	if ((x <= -1.45e+99) || ~(((x <= -4e+46) || (~((x <= -7e-76)) && (x <= 3.1e-142)))))
		tmp = (c + (x * y)) - t_1;
	else
		tmp = (c + ((z * t) * 0.0625)) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]}, If[Or[LessEqual[x, -1.45e+99], N[Not[Or[LessEqual[x, -4e+46], And[N[Not[LessEqual[x, -7e-76]], $MachinePrecision], LessEqual[x, 3.1e-142]]]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(c + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4500000000000001e99 or -4e46 < x < -6.99999999999999995e-76 or 3.1e-142 < x

   1. Initial program 95.4%

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

   2. Taylor expanded in z around 0 78.8%

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

   if -1.4500000000000001e99 < x < -4e46 or -6.99999999999999995e-76 < x < 3.1e-142

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0 92.4%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+99} \lor \neg \left(x \leq -4 \cdot 10^{+46} \lor \neg \left(x \leq -7 \cdot 10^{-76}\right) \land x \leq 3.1 \cdot 10^{-142}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(c + \left(z \cdot t\right) \cdot 0.0625\right) - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 8: 66.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+130}:\\ \;\;\;\;c + -0.25 \cdot \left(b \cdot a\right)\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-231}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 20000000000000:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* b a) -1e+130)
   (+ c (* -0.25 (* b a)))
   (if (<= (* b a) -2e-231)
     (+ c (* x y))
     (if (<= (* b a) 20000000000000.0)
       (+ c (* t (* z 0.0625)))
       (- (* x y) (* (* b a) 0.25))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b * a) <= -1e+130) {
		tmp = c + (-0.25 * (b * a));
	} else if ((b * a) <= -2e-231) {
		tmp = c + (x * y);
	} else if ((b * a) <= 20000000000000.0) {
		tmp = c + (t * (z * 0.0625));
	} else {
		tmp = (x * y) - ((b * a) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b * a) <= (-1d+130)) then
        tmp = c + ((-0.25d0) * (b * a))
    else if ((b * a) <= (-2d-231)) then
        tmp = c + (x * y)
    else if ((b * a) <= 20000000000000.0d0) then
        tmp = c + (t * (z * 0.0625d0))
    else
        tmp = (x * y) - ((b * a) * 0.25d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b * a) <= -1e+130) {
		tmp = c + (-0.25 * (b * a));
	} else if ((b * a) <= -2e-231) {
		tmp = c + (x * y);
	} else if ((b * a) <= 20000000000000.0) {
		tmp = c + (t * (z * 0.0625));
	} else {
		tmp = (x * y) - ((b * a) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b * a) <= -1e+130:
		tmp = c + (-0.25 * (b * a))
	elif (b * a) <= -2e-231:
		tmp = c + (x * y)
	elif (b * a) <= 20000000000000.0:
		tmp = c + (t * (z * 0.0625))
	else:
		tmp = (x * y) - ((b * a) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(b * a) <= -1e+130)
		tmp = Float64(c + Float64(-0.25 * Float64(b * a)));
	elseif (Float64(b * a) <= -2e-231)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(b * a) <= 20000000000000.0)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	else
		tmp = Float64(Float64(x * y) - Float64(Float64(b * a) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b * a) <= -1e+130)
		tmp = c + (-0.25 * (b * a));
	elseif ((b * a) <= -2e-231)
		tmp = c + (x * y);
	elseif ((b * a) <= 20000000000000.0)
		tmp = c + (t * (z * 0.0625));
	else
		tmp = (x * y) - ((b * a) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(b * a), $MachinePrecision], -1e+130], N[(c + N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], -2e-231], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 20000000000000.0], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -1.0000000000000001e130

   1. Initial program 90.2%

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

   2. Taylor expanded in a around inf 81.7%

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

      1. *-commutative 81.7%

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

   4. Simplified 81.7%

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

   if -1.0000000000000001e130 < (*.f64 a b) < -2e-231

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 66.1%

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

   if -2e-231 < (*.f64 a b) < 2e13

   1. Initial program 98.9%

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

   2. Taylor expanded in z around inf 68.9%

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

      1. *-commutative 68.9%

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

      2. associate-*r* 68.9%

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

      3. *-commutative 68.9%

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

   4. Simplified 68.9%

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

   if 2e13 < (*.f64 a b)

   1. Initial program 93.3%

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

   2. Taylor expanded in z around 0 83.6%

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

   3. Taylor expanded in c around 0 70.2%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+130}:\\ \;\;\;\;c + -0.25 \cdot \left(b \cdot a\right)\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-231}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 20000000000000:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 9: 35.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-112}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+20}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+44}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+67}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+90}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -5.8e-112)
   (* x y)
   (if (<= y 1.8e+20)
     c
     (if (<= y 1.7e+44)
       (* x y)
       (if (<= y 1.35e+67)
         c
         (if (<= y 9.2e+90) (* z (* t 0.0625)) (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -5.8e-112) {
		tmp = x * y;
	} else if (y <= 1.8e+20) {
		tmp = c;
	} else if (y <= 1.7e+44) {
		tmp = x * y;
	} else if (y <= 1.35e+67) {
		tmp = c;
	} else if (y <= 9.2e+90) {
		tmp = z * (t * 0.0625);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= (-5.8d-112)) then
        tmp = x * y
    else if (y <= 1.8d+20) then
        tmp = c
    else if (y <= 1.7d+44) then
        tmp = x * y
    else if (y <= 1.35d+67) then
        tmp = c
    else if (y <= 9.2d+90) then
        tmp = z * (t * 0.0625d0)
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -5.8e-112) {
		tmp = x * y;
	} else if (y <= 1.8e+20) {
		tmp = c;
	} else if (y <= 1.7e+44) {
		tmp = x * y;
	} else if (y <= 1.35e+67) {
		tmp = c;
	} else if (y <= 9.2e+90) {
		tmp = z * (t * 0.0625);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -5.8e-112:
		tmp = x * y
	elif y <= 1.8e+20:
		tmp = c
	elif y <= 1.7e+44:
		tmp = x * y
	elif y <= 1.35e+67:
		tmp = c
	elif y <= 9.2e+90:
		tmp = z * (t * 0.0625)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -5.8e-112)
		tmp = Float64(x * y);
	elseif (y <= 1.8e+20)
		tmp = c;
	elseif (y <= 1.7e+44)
		tmp = Float64(x * y);
	elseif (y <= 1.35e+67)
		tmp = c;
	elseif (y <= 9.2e+90)
		tmp = Float64(z * Float64(t * 0.0625));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -5.8e-112)
		tmp = x * y;
	elseif (y <= 1.8e+20)
		tmp = c;
	elseif (y <= 1.7e+44)
		tmp = x * y;
	elseif (y <= 1.35e+67)
		tmp = c;
	elseif (y <= 9.2e+90)
		tmp = z * (t * 0.0625);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -5.8e-112], N[(x * y), $MachinePrecision], If[LessEqual[y, 1.8e+20], c, If[LessEqual[y, 1.7e+44], N[(x * y), $MachinePrecision], If[LessEqual[y, 1.35e+67], c, If[LessEqual[y, 9.2e+90], N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.79999999999999985e-112 or 1.8e20 < y < 1.7e44 or 9.20000000000000001e90 < y

   1. Initial program 96.0%

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

      1. associate-+l- 96.0%

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

      2. +-commutative 96.0%

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

      3. associate--l+ 96.0%

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

      4. associate-*l/ 96.0%

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

      5. *-commutative 96.0%

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

      6. fma-def 96.7%

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

      7. fma-neg 98.0%

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

      8. neg-sub0 98.0%

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

      9. associate-+l- 98.0%

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

      10. neg-sub0 98.0%

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

      11. +-commutative 98.0%

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

      12. unsub-neg 98.0%

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

      13. *-commutative 98.0%

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

      14. associate-*r/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in b around 0 75.2%

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

   5. Taylor expanded in y around inf 44.2%

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

   if -5.79999999999999985e-112 < y < 1.8e20 or 1.7e44 < y < 1.35e67

   1. Initial program 97.1%

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

   2. Taylor expanded in c around inf 34.0%

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

   if 1.35e67 < y < 9.20000000000000001e90

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. +-commutative 100.0%

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

      3. associate--l+ 100.0%

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

      4. associate-*l/ 100.0%

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

      5. *-commutative 100.0%

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

      6. fma-def 100.0%

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

      7. fma-neg 100.0%

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

      8. neg-sub0 100.0%

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

      9. associate-+l- 100.0%

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

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. unsub-neg 100.0%

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

      13. *-commutative 100.0%

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

      14. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in b around 0 100.0%

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

   5. Taylor expanded in t around inf 50.8%

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

      1. associate-*r* 50.8%

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

      2. *-commutative 50.8%

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

      3. *-commutative 50.8%

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

      4. *-commutative 50.8%

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

   7. Simplified 50.8%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-112}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+20}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+44}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+67}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+90}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 10: 50.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t \cdot 0.0625\right)\\ t_2 := c + x \cdot y\\ t_3 := b \cdot \left(-0.25 \cdot a\right)\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{-16}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-279}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+175}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (* t 0.0625))) (t_2 (+ c (* x y))) (t_3 (* b (* -0.25 a))))
   (if (<= b -3.4e-16)
     t_3
     (if (<= b -2.7e-114)
       t_1
       (if (<= b -2.4e-279)
         t_2
         (if (<= b 1.1e-285) t_1 (if (<= b 1.8e+175) 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);
	double t_3 = b * (-0.25 * a);
	double tmp;
	if (b <= -3.4e-16) {
		tmp = t_3;
	} else if (b <= -2.7e-114) {
		tmp = t_1;
	} else if (b <= -2.4e-279) {
		tmp = t_2;
	} else if (b <= 1.1e-285) {
		tmp = t_1;
	} else if (b <= 1.8e+175) {
		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_3 = b * ((-0.25d0) * a)
    if (b <= (-3.4d-16)) then
        tmp = t_3
    else if (b <= (-2.7d-114)) then
        tmp = t_1
    else if (b <= (-2.4d-279)) then
        tmp = t_2
    else if (b <= 1.1d-285) then
        tmp = t_1
    else if (b <= 1.8d+175) 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);
	double t_3 = b * (-0.25 * a);
	double tmp;
	if (b <= -3.4e-16) {
		tmp = t_3;
	} else if (b <= -2.7e-114) {
		tmp = t_1;
	} else if (b <= -2.4e-279) {
		tmp = t_2;
	} else if (b <= 1.1e-285) {
		tmp = t_1;
	} else if (b <= 1.8e+175) {
		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_3 = b * (-0.25 * a)
	tmp = 0
	if b <= -3.4e-16:
		tmp = t_3
	elif b <= -2.7e-114:
		tmp = t_1
	elif b <= -2.4e-279:
		tmp = t_2
	elif b <= 1.1e-285:
		tmp = t_1
	elif b <= 1.8e+175:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(z * Float64(t * 0.0625))
	t_2 = Float64(c + Float64(x * y))
	t_3 = Float64(b * Float64(-0.25 * a))
	tmp = 0.0
	if (b <= -3.4e-16)
		tmp = t_3;
	elseif (b <= -2.7e-114)
		tmp = t_1;
	elseif (b <= -2.4e-279)
		tmp = t_2;
	elseif (b <= 1.1e-285)
		tmp = t_1;
	elseif (b <= 1.8e+175)
		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_3 = b * (-0.25 * a);
	tmp = 0.0;
	if (b <= -3.4e-16)
		tmp = t_3;
	elseif (b <= -2.7e-114)
		tmp = t_1;
	elseif (b <= -2.4e-279)
		tmp = t_2;
	elseif (b <= 1.1e-285)
		tmp = t_1;
	elseif (b <= 1.8e+175)
		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[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(-0.25 * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.4e-16], t$95$3, If[LessEqual[b, -2.7e-114], t$95$1, If[LessEqual[b, -2.4e-279], t$95$2, If[LessEqual[b, 1.1e-285], t$95$1, If[LessEqual[b, 1.8e+175], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.4e-16 or 1.80000000000000017e175 < b

   1. Initial program 92.6%

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

   2. Taylor expanded in a around inf 59.7%

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

      1. *-commutative 59.7%

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

   4. Simplified 59.7%

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

   5. Taylor expanded in a around inf 45.0%

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

      1. associate-*r* 45.0%

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

   7. Simplified 45.0%

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

   if -3.4e-16 < b < -2.7e-114 or -2.3999999999999999e-279 < b < 1.1e-285

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. +-commutative 99.9%

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

      3. associate--l+ 99.9%

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

      4. associate-*l/ 99.9%

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

      5. *-commutative 99.9%

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

      6. fma-def 100.0%

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

      7. fma-neg 100.0%

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

      8. neg-sub0 100.0%

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

      9. associate-+l- 100.0%

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

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. unsub-neg 100.0%

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

      13. *-commutative 100.0%

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

      14. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in b around 0 97.2%

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

   5. Taylor expanded in t around inf 45.7%

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

      1. associate-*r* 45.7%

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

      2. *-commutative 45.7%

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

      3. *-commutative 45.7%

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

      4. *-commutative 45.7%

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

   7. Simplified 45.7%

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

   if -2.7e-114 < b < -2.3999999999999999e-279 or 1.1e-285 < b < 1.80000000000000017e175

   1. Initial program 98.5%

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

   2. Taylor expanded in x around inf 60.3%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{-16}:\\ \;\;\;\;b \cdot \left(-0.25 \cdot a\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-279}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-285}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+175}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(-0.25 \cdot a\right)\\ \end{array} \]

Alternative 11: 58.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+100} \lor \neg \left(x \leq -2.6 \cdot 10^{-36} \lor \neg \left(x \leq -2.4 \cdot 10^{-51}\right) \land x \leq 82\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= x -1.55e+100)
         (not (or (<= x -2.6e-36) (and (not (<= x -2.4e-51)) (<= x 82.0)))))
   (+ c (* x y))
   (+ c (* t (* z 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x <= -1.55e+100) || !((x <= -2.6e-36) || (!(x <= -2.4e-51) && (x <= 82.0)))) {
		tmp = c + (x * y);
	} else {
		tmp = c + (t * (z * 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 <= (-1.55d+100)) .or. (.not. (x <= (-2.6d-36)) .or. (.not. (x <= (-2.4d-51))) .and. (x <= 82.0d0))) then
        tmp = c + (x * y)
    else
        tmp = c + (t * (z * 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 <= -1.55e+100) || !((x <= -2.6e-36) || (!(x <= -2.4e-51) && (x <= 82.0)))) {
		tmp = c + (x * y);
	} else {
		tmp = c + (t * (z * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x <= -1.55e+100) or not ((x <= -2.6e-36) or (not (x <= -2.4e-51) and (x <= 82.0))):
		tmp = c + (x * y)
	else:
		tmp = c + (t * (z * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((x <= -1.55e+100) || !((x <= -2.6e-36) || (!(x <= -2.4e-51) && (x <= 82.0))))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x <= -1.55e+100) || ~(((x <= -2.6e-36) || (~((x <= -2.4e-51)) && (x <= 82.0)))))
		tmp = c + (x * y);
	else
		tmp = c + (t * (z * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[x, -1.55e+100], N[Not[Or[LessEqual[x, -2.6e-36], And[N[Not[LessEqual[x, -2.4e-51]], $MachinePrecision], LessEqual[x, 82.0]]]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55000000000000003e100 or -2.6e-36 < x < -2.4e-51 or 82 < x

   1. Initial program 93.4%

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

   2. Taylor expanded in x around inf 64.7%

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

   if -1.55000000000000003e100 < x < -2.6e-36 or -2.4e-51 < x < 82

   1. Initial program 98.6%

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

   2. Taylor expanded in z around inf 63.8%

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

      1. *-commutative 63.8%

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

      2. associate-*r* 63.8%

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

      3. *-commutative 63.8%

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

   4. Simplified 63.8%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+100} \lor \neg \left(x \leq -2.6 \cdot 10^{-36} \lor \neg \left(x \leq -2.4 \cdot 10^{-51}\right) \land x \leq 82\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]

Alternative 12: 77.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+45} \lor \neg \left(t \leq 3.9 \cdot 10^{+199}\right):\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -6.2e+45) (not (<= t 3.9e+199)))
   (+ c (* t (* z 0.0625)))
   (- (+ c (* x y)) (* (* b a) 0.25))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -6.2e+45) || !(t <= 3.9e+199)) {
		tmp = c + (t * (z * 0.0625));
	} else {
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-6.2d+45)) .or. (.not. (t <= 3.9d+199))) then
        tmp = c + (t * (z * 0.0625d0))
    else
        tmp = (c + (x * y)) - ((b * a) * 0.25d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -6.2e+45) || !(t <= 3.9e+199)) {
		tmp = c + (t * (z * 0.0625));
	} else {
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -6.2e+45) or not (t <= 3.9e+199):
		tmp = c + (t * (z * 0.0625))
	else:
		tmp = (c + (x * y)) - ((b * a) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -6.2e+45) || !(t <= 3.9e+199))
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	else
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(b * a) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -6.2e+45) || ~((t <= 3.9e+199)))
		tmp = c + (t * (z * 0.0625));
	else
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -6.2e+45], N[Not[LessEqual[t, 3.9e+199]], $MachinePrecision]], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.19999999999999975e45 or 3.9000000000000002e199 < t

   1. Initial program 93.5%

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

   2. Taylor expanded in z around inf 63.7%

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

      1. *-commutative 63.7%

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

      2. associate-*r* 63.7%

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

      3. *-commutative 63.7%

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

   4. Simplified 63.7%

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

   if -6.19999999999999975e45 < t < 3.9000000000000002e199

   1. Initial program 97.8%

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

   2. Taylor expanded in z around 0 80.8%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+45} \lor \neg \left(t \leq 3.9 \cdot 10^{+199}\right):\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 13: 36.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-112}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+19}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -6.5e-112) (* x y) (if (<= y 2.9e+19) c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -6.5e-112) {
		tmp = x * y;
	} else if (y <= 2.9e+19) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= (-6.5d-112)) then
        tmp = x * y
    else if (y <= 2.9d+19) then
        tmp = c
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -6.5e-112) {
		tmp = x * y;
	} else if (y <= 2.9e+19) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -6.5e-112:
		tmp = x * y
	elif y <= 2.9e+19:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -6.5e-112)
		tmp = Float64(x * y);
	elseif (y <= 2.9e+19)
		tmp = c;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -6.5e-112)
		tmp = x * y;
	elseif (y <= 2.9e+19)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -6.5e-112], N[(x * y), $MachinePrecision], If[LessEqual[y, 2.9e+19], c, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.49999999999999956e-112 or 2.9e19 < y

   1. Initial program 96.2%

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

      1. associate-+l- 96.2%

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

      2. +-commutative 96.2%

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

      3. associate--l+ 96.2%

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

      4. associate-*l/ 96.2%

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

      5. *-commutative 96.2%

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

      6. fma-def 96.8%

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

      7. fma-neg 98.1%

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

      8. neg-sub0 98.1%

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

      9. associate-+l- 98.1%

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

      10. neg-sub0 98.1%

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

      11. +-commutative 98.1%

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

      12. unsub-neg 98.1%

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

      13. *-commutative 98.1%

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

      14. associate-*r/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in b around 0 75.4%

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

   5. Taylor expanded in y around inf 43.6%

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

   if -6.49999999999999956e-112 < y < 2.9e19

   1. Initial program 97.0%

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

   2. Taylor expanded in c around inf 33.2%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-112}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+19}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 14: 22.0% 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 96.5%

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

2. Taylor expanded in c around inf 22.4%

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

3. Final simplification 22.4%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023192 
(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))