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

Percentage Accurate: 97.5% → 98.3%

Time: 8.6s

Alternatives: 16

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: 97.5% 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: 98.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot z}{16} + x \cdot y\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+300}:\\ \;\;\;\;c + \left(t_1 - \frac{b \cdot a}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z}{16}, c + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (/ (* t z) 16.0) (* x y))))
   (if (<= t_1 5e+300)
     (+ c (- t_1 (/ (* b a) 4.0)))
     (fma t (/ z 16.0) (+ c (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * z) / 16.0) + (x * y);
	double tmp;
	if (t_1 <= 5e+300) {
		tmp = c + (t_1 - ((b * a) / 4.0));
	} else {
		tmp = fma(t, (z / 16.0), (c + (x * y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t * z) / 16.0) + Float64(x * y))
	tmp = 0.0
	if (t_1 <= 5e+300)
		tmp = Float64(c + Float64(t_1 - Float64(Float64(b * a) / 4.0)));
	else
		tmp = fma(t, Float64(z / 16.0), Float64(c + Float64(x * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * z), $MachinePrecision] / 16.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+300], N[(c + N[(t$95$1 - N[(N[(b * a), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z / 16.0), $MachinePrecision] + N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16)) < 5.00000000000000026e300

   1. Initial program 100.0%

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

   if 5.00000000000000026e300 < (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16))

   1. Initial program 75.8%

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

      1. associate-+l- 75.8%

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

      2. +-commutative 75.8%

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

      3. associate--l+ 75.8%

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

      4. associate-*l/ 75.8%

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

      5. *-commutative 75.8%

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

      6. fma-def 87.9%

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

      7. fma-neg 87.9%

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

      8. neg-sub0 87.9%

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

      9. associate-+l- 87.9%

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

      10. neg-sub0 87.9%

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

      11. +-commutative 87.9%

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

      12. unsub-neg 87.9%

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

      13. *-commutative 87.9%

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

      14. associate-*r/ 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in b around 0 90.9%

      \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \color{blue}{c + y \cdot x}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t \cdot z}{16} + x \cdot y \leq 5 \cdot 10^{+300}:\\ \;\;\;\;c + \left(\left(\frac{t \cdot z}{16} + x \cdot y\right) - \frac{b \cdot a}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z}{16}, c + x \cdot y\right)\\ \end{array} \]

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 96.9%

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

   1. associate-+l- 96.9%

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

   2. +-commutative 96.9%

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

   3. associate--l+ 96.9%

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

   4. associate-*l/ 96.9%

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

   5. *-commutative 96.9%

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

   6. fma-def 98.4%

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

   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: 97.9% 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 96.9%

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

   1. associate-+l- 96.9%

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

   2. sub-neg 96.9%

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

   3. neg-mul-1 96.9%

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

   4. metadata-eval 96.9%

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

   5. metadata-eval 96.9%

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

   6. cancel-sign-sub-inv 96.9%

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

   7. fma-def 98.0%

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

   8. associate-/l* 98.0%

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

   9. metadata-eval 98.0%

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

   10. *-lft-identity 98.0%

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

   11. associate-/l* 97.9%

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

3. Simplified 97.9%

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

4. Final simplification 97.9%

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

Alternative 4: 98.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(t * z) / 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(c + Float64(x * y));
	end
	return tmp
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(t * z), $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[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

   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 0 12.5%

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

   3. Taylor expanded in t around 0 62.5%

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

4. Final simplification 98.8%

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

Alternative 5: 64.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + \left(t \cdot z\right) \cdot 0.0625\\ t_3 := c + \left(b \cdot a\right) \cdot -0.25\\ \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+145}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{-291}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{-106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq 1:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y)))
        (t_2 (+ c (* (* t z) 0.0625)))
        (t_3 (+ c (* (* b a) -0.25))))
   (if (<= (* b a) -5e+145)
     t_3
     (if (<= (* b a) -2e-57)
       t_1
       (if (<= (* b a) -2e-120)
         t_2
         (if (<= (* b a) 2e-291)
           t_1
           (if (<= (* b a) 2e-106) t_2 (if (<= (* b a) 1.0) t_1 t_3))))))))

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 + ((t * z) * 0.0625);
	double t_3 = c + ((b * a) * -0.25);
	double tmp;
	if ((b * a) <= -5e+145) {
		tmp = t_3;
	} else if ((b * a) <= -2e-57) {
		tmp = t_1;
	} else if ((b * a) <= -2e-120) {
		tmp = t_2;
	} else if ((b * a) <= 2e-291) {
		tmp = t_1;
	} else if ((b * a) <= 2e-106) {
		tmp = t_2;
	} else if ((b * a) <= 1.0) {
		tmp = t_1;
	} 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 = c + (x * y)
    t_2 = c + ((t * z) * 0.0625d0)
    t_3 = c + ((b * a) * (-0.25d0))
    if ((b * a) <= (-5d+145)) then
        tmp = t_3
    else if ((b * a) <= (-2d-57)) then
        tmp = t_1
    else if ((b * a) <= (-2d-120)) then
        tmp = t_2
    else if ((b * a) <= 2d-291) then
        tmp = t_1
    else if ((b * a) <= 2d-106) then
        tmp = t_2
    else if ((b * a) <= 1.0d0) then
        tmp = t_1
    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 = c + (x * y);
	double t_2 = c + ((t * z) * 0.0625);
	double t_3 = c + ((b * a) * -0.25);
	double tmp;
	if ((b * a) <= -5e+145) {
		tmp = t_3;
	} else if ((b * a) <= -2e-57) {
		tmp = t_1;
	} else if ((b * a) <= -2e-120) {
		tmp = t_2;
	} else if ((b * a) <= 2e-291) {
		tmp = t_1;
	} else if ((b * a) <= 2e-106) {
		tmp = t_2;
	} else if ((b * a) <= 1.0) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = c + ((t * z) * 0.0625)
	t_3 = c + ((b * a) * -0.25)
	tmp = 0
	if (b * a) <= -5e+145:
		tmp = t_3
	elif (b * a) <= -2e-57:
		tmp = t_1
	elif (b * a) <= -2e-120:
		tmp = t_2
	elif (b * a) <= 2e-291:
		tmp = t_1
	elif (b * a) <= 2e-106:
		tmp = t_2
	elif (b * a) <= 1.0:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(c + Float64(Float64(t * z) * 0.0625))
	t_3 = Float64(c + Float64(Float64(b * a) * -0.25))
	tmp = 0.0
	if (Float64(b * a) <= -5e+145)
		tmp = t_3;
	elseif (Float64(b * a) <= -2e-57)
		tmp = t_1;
	elseif (Float64(b * a) <= -2e-120)
		tmp = t_2;
	elseif (Float64(b * a) <= 2e-291)
		tmp = t_1;
	elseif (Float64(b * a) <= 2e-106)
		tmp = t_2;
	elseif (Float64(b * a) <= 1.0)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = c + ((t * z) * 0.0625);
	t_3 = c + ((b * a) * -0.25);
	tmp = 0.0;
	if ((b * a) <= -5e+145)
		tmp = t_3;
	elseif ((b * a) <= -2e-57)
		tmp = t_1;
	elseif ((b * a) <= -2e-120)
		tmp = t_2;
	elseif ((b * a) <= 2e-291)
		tmp = t_1;
	elseif ((b * a) <= 2e-106)
		tmp = t_2;
	elseif ((b * a) <= 1.0)
		tmp = t_1;
	else
		tmp = t_3;
	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[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -5e+145], t$95$3, If[LessEqual[N[(b * a), $MachinePrecision], -2e-57], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -2e-120], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], 2e-291], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 2e-106], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], 1.0], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.99999999999999967e145 or 1 < (*.f64 a b)

   1. Initial program 95.9%

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

   2. Taylor expanded in a around inf 78.8%

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

      1. *-commutative 78.8%

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

   4. Simplified 78.8%

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

   if -4.99999999999999967e145 < (*.f64 a b) < -1.99999999999999991e-57 or -1.99999999999999996e-120 < (*.f64 a b) < 1.99999999999999992e-291 or 1.99999999999999988e-106 < (*.f64 a b) < 1

   1. Initial program 97.5%

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

   2. Taylor expanded in a around 0 92.1%

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

   3. Taylor expanded in t around 0 73.0%

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

   if -1.99999999999999991e-57 < (*.f64 a b) < -1.99999999999999996e-120 or 1.99999999999999992e-291 < (*.f64 a b) < 1.99999999999999988e-106

   1. Initial program 97.2%

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

   2. Taylor expanded in a around 0 92.0%

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

   3. Taylor expanded in y around 0 76.2%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+145}:\\ \;\;\;\;c + \left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-57}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-120}:\\ \;\;\;\;c + \left(t \cdot z\right) \cdot 0.0625\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{-291}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{-106}:\\ \;\;\;\;c + \left(t \cdot z\right) \cdot 0.0625\\ \mathbf{elif}\;b \cdot a \leq 1:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + \left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 6: 88.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot z\right) \cdot 0.0625\\ \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+145} \lor \neg \left(b \cdot a \leq 1\right):\\ \;\;\;\;t_1 + \left(c - \frac{a}{\frac{4}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* t z) 0.0625)))
   (if (or (<= (* b a) -5e+145) (not (<= (* b a) 1.0)))
     (+ t_1 (- c (/ a (/ 4.0 b))))
     (+ c (+ (* x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * z) * 0.0625;
	double tmp;
	if (((b * a) <= -5e+145) || !((b * a) <= 1.0)) {
		tmp = t_1 + (c - (a / (4.0 / b)));
	} else {
		tmp = c + ((x * y) + 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 = (t * z) * 0.0625d0
    if (((b * a) <= (-5d+145)) .or. (.not. ((b * a) <= 1.0d0))) then
        tmp = t_1 + (c - (a / (4.0d0 / b)))
    else
        tmp = c + ((x * y) + 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 = (t * z) * 0.0625;
	double tmp;
	if (((b * a) <= -5e+145) || !((b * a) <= 1.0)) {
		tmp = t_1 + (c - (a / (4.0 / b)));
	} else {
		tmp = c + ((x * y) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (t * z) * 0.0625
	tmp = 0
	if ((b * a) <= -5e+145) or not ((b * a) <= 1.0):
		tmp = t_1 + (c - (a / (4.0 / b)))
	else:
		tmp = c + ((x * y) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(t * z) * 0.0625)
	tmp = 0.0
	if ((Float64(b * a) <= -5e+145) || !(Float64(b * a) <= 1.0))
		tmp = Float64(t_1 + Float64(c - Float64(a / Float64(4.0 / b))));
	else
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (t * z) * 0.0625;
	tmp = 0.0;
	if (((b * a) <= -5e+145) || ~(((b * a) <= 1.0)))
		tmp = t_1 + (c - (a / (4.0 / b)));
	else
		tmp = c + ((x * y) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]}, If[Or[LessEqual[N[(b * a), $MachinePrecision], -5e+145], N[Not[LessEqual[N[(b * a), $MachinePrecision], 1.0]], $MachinePrecision]], N[(t$95$1 + N[(c - N[(a / N[(4.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.99999999999999967e145 or 1 < (*.f64 a b)

   1. Initial program 95.9%

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

      1. associate-+l- 95.9%

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

      2. sub-neg 95.9%

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

      3. neg-mul-1 95.9%

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

      4. metadata-eval 95.9%

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

      5. metadata-eval 95.9%

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

      6. cancel-sign-sub-inv 95.9%

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

      7. fma-def 97.9%

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

      8. associate-/l* 97.9%

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

      9. metadata-eval 97.9%

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

      10. *-lft-identity 97.9%

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

      11. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

      1. fma-udef 95.7%

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

      2. associate-/l* 95.7%

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

      3. +-commutative 95.7%

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

      4. div-inv 95.7%

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

      5. metadata-eval 95.7%

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

   5. Applied egg-rr 95.7%

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

   6. Taylor expanded in z around inf 93.1%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   if -4.99999999999999967e145 < (*.f64 a b) < 1

   1. Initial program 97.5%

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

   2. Taylor expanded in a around 0 92.1%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+145} \lor \neg \left(b \cdot a \leq 1\right):\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625 + \left(c - \frac{a}{\frac{4}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(t \cdot z\right) \cdot 0.0625\right)\\ \end{array} \]

Alternative 7: 88.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot z\right) \cdot 0.0625\\ \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+145} \lor \neg \left(b \cdot a \leq 1\right):\\ \;\;\;\;\left(c + t_1\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* t z) 0.0625)))
   (if (or (<= (* b a) -5e+145) (not (<= (* b a) 1.0)))
     (- (+ c t_1) (* (* b a) 0.25))
     (+ c (+ (* x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * z) * 0.0625;
	double tmp;
	if (((b * a) <= -5e+145) || !((b * a) <= 1.0)) {
		tmp = (c + t_1) - ((b * a) * 0.25);
	} else {
		tmp = c + ((x * y) + 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 = (t * z) * 0.0625d0
    if (((b * a) <= (-5d+145)) .or. (.not. ((b * a) <= 1.0d0))) then
        tmp = (c + t_1) - ((b * a) * 0.25d0)
    else
        tmp = c + ((x * y) + 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 = (t * z) * 0.0625;
	double tmp;
	if (((b * a) <= -5e+145) || !((b * a) <= 1.0)) {
		tmp = (c + t_1) - ((b * a) * 0.25);
	} else {
		tmp = c + ((x * y) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (t * z) * 0.0625
	tmp = 0
	if ((b * a) <= -5e+145) or not ((b * a) <= 1.0):
		tmp = (c + t_1) - ((b * a) * 0.25)
	else:
		tmp = c + ((x * y) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(t * z) * 0.0625)
	tmp = 0.0
	if ((Float64(b * a) <= -5e+145) || !(Float64(b * a) <= 1.0))
		tmp = Float64(Float64(c + t_1) - Float64(Float64(b * a) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (t * z) * 0.0625;
	tmp = 0.0;
	if (((b * a) <= -5e+145) || ~(((b * a) <= 1.0)))
		tmp = (c + t_1) - ((b * a) * 0.25);
	else
		tmp = c + ((x * y) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]}, If[Or[LessEqual[N[(b * a), $MachinePrecision], -5e+145], N[Not[LessEqual[N[(b * a), $MachinePrecision], 1.0]], $MachinePrecision]], N[(N[(c + t$95$1), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.99999999999999967e145 or 1 < (*.f64 a b)

   1. Initial program 95.9%

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

   2. Taylor expanded in x around 0 93.2%

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

   if -4.99999999999999967e145 < (*.f64 a b) < 1

   1. Initial program 97.5%

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

   2. Taylor expanded in a around 0 92.1%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+145} \lor \neg \left(b \cdot a \leq 1\right):\\ \;\;\;\;\left(c + \left(t \cdot z\right) \cdot 0.0625\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(t \cdot z\right) \cdot 0.0625\right)\\ \end{array} \]

Alternative 8: 85.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+145} \lor \neg \left(b \cdot a \leq 2 \cdot 10^{+66}\right):\\ \;\;\;\;c + \left(b \cdot a\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(t \cdot z\right) \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -5e+145) (not (<= (* b a) 2e+66)))
   (+ c (* (* b a) -0.25))
   (+ c (+ (* x y) (* (* t z) 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -5e+145) || !((b * a) <= 2e+66)) {
		tmp = c + ((b * a) * -0.25);
	} else {
		tmp = c + ((x * y) + ((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 (((b * a) <= (-5d+145)) .or. (.not. ((b * a) <= 2d+66))) then
        tmp = c + ((b * a) * (-0.25d0))
    else
        tmp = c + ((x * y) + ((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 (((b * a) <= -5e+145) || !((b * a) <= 2e+66)) {
		tmp = c + ((b * a) * -0.25);
	} else {
		tmp = c + ((x * y) + ((t * z) * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((b * a) <= -5e+145) or not ((b * a) <= 2e+66):
		tmp = c + ((b * a) * -0.25)
	else:
		tmp = c + ((x * y) + ((t * z) * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(b * a) <= -5e+145) || !(Float64(b * a) <= 2e+66))
		tmp = Float64(c + Float64(Float64(b * a) * -0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(Float64(t * z) * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((b * a) <= -5e+145) || ~(((b * a) <= 2e+66)))
		tmp = c + ((b * a) * -0.25);
	else
		tmp = c + ((x * y) + ((t * z) * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -5e+145], N[Not[LessEqual[N[(b * a), $MachinePrecision], 2e+66]], $MachinePrecision]], N[(c + N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.99999999999999967e145 or 1.99999999999999989e66 < (*.f64 a b)

   1. Initial program 95.2%

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

   2. Taylor expanded in a around inf 81.3%

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

      1. *-commutative 81.3%

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

   4. Simplified 81.3%

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

   if -4.99999999999999967e145 < (*.f64 a b) < 1.99999999999999989e66

   1. Initial program 97.7%

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

   2. Taylor expanded in a around 0 90.4%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+145} \lor \neg \left(b \cdot a \leq 2 \cdot 10^{+66}\right):\\ \;\;\;\;c + \left(b \cdot a\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(t \cdot z\right) \cdot 0.0625\right)\\ \end{array} \]

Alternative 9: 86.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t \cdot z\right) \cdot 0.0625\\ \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+145} \lor \neg \left(b \cdot a \leq 2 \cdot 10^{+66}\right):\\ \;\;\;\;t_1 - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* t z) 0.0625)))
   (if (or (<= (* b a) -5e+145) (not (<= (* b a) 2e+66)))
     (- t_1 (* (* b a) 0.25))
     (+ c (+ (* x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * z) * 0.0625;
	double tmp;
	if (((b * a) <= -5e+145) || !((b * a) <= 2e+66)) {
		tmp = t_1 - ((b * a) * 0.25);
	} else {
		tmp = c + ((x * y) + 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 = (t * z) * 0.0625d0
    if (((b * a) <= (-5d+145)) .or. (.not. ((b * a) <= 2d+66))) then
        tmp = t_1 - ((b * a) * 0.25d0)
    else
        tmp = c + ((x * y) + 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 = (t * z) * 0.0625;
	double tmp;
	if (((b * a) <= -5e+145) || !((b * a) <= 2e+66)) {
		tmp = t_1 - ((b * a) * 0.25);
	} else {
		tmp = c + ((x * y) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (t * z) * 0.0625
	tmp = 0
	if ((b * a) <= -5e+145) or not ((b * a) <= 2e+66):
		tmp = t_1 - ((b * a) * 0.25)
	else:
		tmp = c + ((x * y) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(t * z) * 0.0625)
	tmp = 0.0
	if ((Float64(b * a) <= -5e+145) || !(Float64(b * a) <= 2e+66))
		tmp = Float64(t_1 - Float64(Float64(b * a) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (t * z) * 0.0625;
	tmp = 0.0;
	if (((b * a) <= -5e+145) || ~(((b * a) <= 2e+66)))
		tmp = t_1 - ((b * a) * 0.25);
	else
		tmp = c + ((x * y) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]}, If[Or[LessEqual[N[(b * a), $MachinePrecision], -5e+145], N[Not[LessEqual[N[(b * a), $MachinePrecision], 2e+66]], $MachinePrecision]], N[(t$95$1 - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.99999999999999967e145 or 1.99999999999999989e66 < (*.f64 a b)

   1. Initial program 95.2%

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

   2. Taylor expanded in x around 0 94.5%

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

   3. Taylor expanded in c around 0 84.2%

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

   if -4.99999999999999967e145 < (*.f64 a b) < 1.99999999999999989e66

   1. Initial program 97.7%

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

   2. Taylor expanded in a around 0 90.4%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+145} \lor \neg \left(b \cdot a \leq 2 \cdot 10^{+66}\right):\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625 - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(t \cdot z\right) \cdot 0.0625\right)\\ \end{array} \]

Alternative 10: 88.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1.5 \cdot 10^{+91} \lor \neg \left(b \cdot a \leq 5 \cdot 10^{-37}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(t \cdot z\right) \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -1.5e+91) (not (<= (* b a) 5e-37)))
   (- (+ c (* x y)) (* (* b a) 0.25))
   (+ c (+ (* x y) (* (* t z) 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -1.5e+91) || !((b * a) <= 5e-37)) {
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	} else {
		tmp = c + ((x * y) + ((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 (((b * a) <= (-1.5d+91)) .or. (.not. ((b * a) <= 5d-37))) then
        tmp = (c + (x * y)) - ((b * a) * 0.25d0)
    else
        tmp = c + ((x * y) + ((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 (((b * a) <= -1.5e+91) || !((b * a) <= 5e-37)) {
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	} else {
		tmp = c + ((x * y) + ((t * z) * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((b * a) <= -1.5e+91) or not ((b * a) <= 5e-37):
		tmp = (c + (x * y)) - ((b * a) * 0.25)
	else:
		tmp = c + ((x * y) + ((t * z) * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(b * a) <= -1.5e+91) || !(Float64(b * a) <= 5e-37))
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(b * a) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(Float64(t * z) * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((b * a) <= -1.5e+91) || ~(((b * a) <= 5e-37)))
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	else
		tmp = c + ((x * y) + ((t * z) * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -1.5e+91], N[Not[LessEqual[N[(b * a), $MachinePrecision], 5e-37]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.50000000000000003e91 or 4.9999999999999997e-37 < (*.f64 a b)

   1. Initial program 95.5%

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

   2. Taylor expanded in z around 0 83.9%

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

   if -1.50000000000000003e91 < (*.f64 a b) < 4.9999999999999997e-37

   1. Initial program 97.9%

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

   2. Taylor expanded in a around 0 93.4%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1.5 \cdot 10^{+91} \lor \neg \left(b \cdot a \leq 5 \cdot 10^{-37}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(t \cdot z\right) \cdot 0.0625\right)\\ \end{array} \]

Alternative 11: 39.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+31}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-214}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-47}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625\\ \mathbf{elif}\;y \leq 3600000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+70}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (* a -0.25))))
   (if (<= y -2.9e+31)
     (* x y)
     (if (<= y 5.2e-267)
       t_1
       (if (<= y 2.4e-214)
         c
         (if (<= y 1.05e-101)
           t_1
           (if (<= y 4.8e-47)
             (* (* t z) 0.0625)
             (if (<= y 3600000.0) t_1 (if (<= y 9.5e+70) c (* x y))))))))))

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 (y <= -2.9e+31) {
		tmp = x * y;
	} else if (y <= 5.2e-267) {
		tmp = t_1;
	} else if (y <= 2.4e-214) {
		tmp = c;
	} else if (y <= 1.05e-101) {
		tmp = t_1;
	} else if (y <= 4.8e-47) {
		tmp = (t * z) * 0.0625;
	} else if (y <= 3600000.0) {
		tmp = t_1;
	} else if (y <= 9.5e+70) {
		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) :: t_1
    real(8) :: tmp
    t_1 = b * (a * (-0.25d0))
    if (y <= (-2.9d+31)) then
        tmp = x * y
    else if (y <= 5.2d-267) then
        tmp = t_1
    else if (y <= 2.4d-214) then
        tmp = c
    else if (y <= 1.05d-101) then
        tmp = t_1
    else if (y <= 4.8d-47) then
        tmp = (t * z) * 0.0625d0
    else if (y <= 3600000.0d0) then
        tmp = t_1
    else if (y <= 9.5d+70) 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 t_1 = b * (a * -0.25);
	double tmp;
	if (y <= -2.9e+31) {
		tmp = x * y;
	} else if (y <= 5.2e-267) {
		tmp = t_1;
	} else if (y <= 2.4e-214) {
		tmp = c;
	} else if (y <= 1.05e-101) {
		tmp = t_1;
	} else if (y <= 4.8e-47) {
		tmp = (t * z) * 0.0625;
	} else if (y <= 3600000.0) {
		tmp = t_1;
	} else if (y <= 9.5e+70) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b * (a * -0.25)
	tmp = 0
	if y <= -2.9e+31:
		tmp = x * y
	elif y <= 5.2e-267:
		tmp = t_1
	elif y <= 2.4e-214:
		tmp = c
	elif y <= 1.05e-101:
		tmp = t_1
	elif y <= 4.8e-47:
		tmp = (t * z) * 0.0625
	elif y <= 3600000.0:
		tmp = t_1
	elif y <= 9.5e+70:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(a * -0.25))
	tmp = 0.0
	if (y <= -2.9e+31)
		tmp = Float64(x * y);
	elseif (y <= 5.2e-267)
		tmp = t_1;
	elseif (y <= 2.4e-214)
		tmp = c;
	elseif (y <= 1.05e-101)
		tmp = t_1;
	elseif (y <= 4.8e-47)
		tmp = Float64(Float64(t * z) * 0.0625);
	elseif (y <= 3600000.0)
		tmp = t_1;
	elseif (y <= 9.5e+70)
		tmp = c;
	else
		tmp = Float64(x * y);
	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 (y <= -2.9e+31)
		tmp = x * y;
	elseif (y <= 5.2e-267)
		tmp = t_1;
	elseif (y <= 2.4e-214)
		tmp = c;
	elseif (y <= 1.05e-101)
		tmp = t_1;
	elseif (y <= 4.8e-47)
		tmp = (t * z) * 0.0625;
	elseif (y <= 3600000.0)
		tmp = t_1;
	elseif (y <= 9.5e+70)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.9e+31], N[(x * y), $MachinePrecision], If[LessEqual[y, 5.2e-267], t$95$1, If[LessEqual[y, 2.4e-214], c, If[LessEqual[y, 1.05e-101], t$95$1, If[LessEqual[y, 4.8e-47], N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision], If[LessEqual[y, 3600000.0], t$95$1, If[LessEqual[y, 9.5e+70], c, N[(x * y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.9e31 or 9.5000000000000002e70 < y

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 85.7%

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

   3. Taylor expanded in c around 0 70.4%

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

   4. Taylor expanded in y around inf 52.4%

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

   if -2.9e31 < y < 5.2000000000000003e-267 or 2.4000000000000002e-214 < y < 1.05000000000000008e-101 or 4.7999999999999999e-47 < y < 3.6e6

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. cancel-sign-sub-inv 100.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 99.9%

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

      9. metadata-eval 99.9%

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

      10. *-lft-identity 99.9%

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

      11. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

      2. associate-/l* 99.9%

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

      3. +-commutative 99.9%

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

      4. div-inv 99.9%

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

      5. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in a around inf 40.5%

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

      1. associate-*r* 40.5%

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

   8. Simplified 40.5%

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

   if 5.2000000000000003e-267 < y < 2.4000000000000002e-214 or 3.6e6 < y < 9.5000000000000002e70

   1. Initial program 99.9%

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

   2. Taylor expanded in c around inf 39.2%

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

   if 1.05000000000000008e-101 < y < 4.7999999999999999e-47

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. cancel-sign-sub-inv 100.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 100.0%

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

      9. metadata-eval 100.0%

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

      10. *-lft-identity 100.0%

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

      11. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

      2. associate-/l* 99.8%

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

      3. +-commutative 99.8%

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

      4. div-inv 99.8%

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

      5. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around inf 99.8%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   7. Taylor expanded in t around inf 51.0%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+31}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-267}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-214}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-47}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625\\ \mathbf{elif}\;y \leq 3600000:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+70}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 12: 52.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + \left(t \cdot z\right) \cdot 0.0625\\ t_3 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{-52}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 7.9 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+206}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y)))
        (t_2 (+ c (* (* t z) 0.0625)))
        (t_3 (* b (* a -0.25))))
   (if (<= b -1.25e-52)
     t_3
     (if (<= b 7.9e-221)
       t_1
       (if (<= b 1.3e-145)
         t_2
         (if (<= b 8e-76)
           t_1
           (if (<= b 2.5e-9) t_2 (if (<= b 1.5e+206) t_1 t_3))))))))

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 + ((t * z) * 0.0625);
	double t_3 = b * (a * -0.25);
	double tmp;
	if (b <= -1.25e-52) {
		tmp = t_3;
	} else if (b <= 7.9e-221) {
		tmp = t_1;
	} else if (b <= 1.3e-145) {
		tmp = t_2;
	} else if (b <= 8e-76) {
		tmp = t_1;
	} else if (b <= 2.5e-9) {
		tmp = t_2;
	} else if (b <= 1.5e+206) {
		tmp = t_1;
	} 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 = c + (x * y)
    t_2 = c + ((t * z) * 0.0625d0)
    t_3 = b * (a * (-0.25d0))
    if (b <= (-1.25d-52)) then
        tmp = t_3
    else if (b <= 7.9d-221) then
        tmp = t_1
    else if (b <= 1.3d-145) then
        tmp = t_2
    else if (b <= 8d-76) then
        tmp = t_1
    else if (b <= 2.5d-9) then
        tmp = t_2
    else if (b <= 1.5d+206) then
        tmp = t_1
    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 = c + (x * y);
	double t_2 = c + ((t * z) * 0.0625);
	double t_3 = b * (a * -0.25);
	double tmp;
	if (b <= -1.25e-52) {
		tmp = t_3;
	} else if (b <= 7.9e-221) {
		tmp = t_1;
	} else if (b <= 1.3e-145) {
		tmp = t_2;
	} else if (b <= 8e-76) {
		tmp = t_1;
	} else if (b <= 2.5e-9) {
		tmp = t_2;
	} else if (b <= 1.5e+206) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = c + ((t * z) * 0.0625)
	t_3 = b * (a * -0.25)
	tmp = 0
	if b <= -1.25e-52:
		tmp = t_3
	elif b <= 7.9e-221:
		tmp = t_1
	elif b <= 1.3e-145:
		tmp = t_2
	elif b <= 8e-76:
		tmp = t_1
	elif b <= 2.5e-9:
		tmp = t_2
	elif b <= 1.5e+206:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(c + Float64(Float64(t * z) * 0.0625))
	t_3 = Float64(b * Float64(a * -0.25))
	tmp = 0.0
	if (b <= -1.25e-52)
		tmp = t_3;
	elseif (b <= 7.9e-221)
		tmp = t_1;
	elseif (b <= 1.3e-145)
		tmp = t_2;
	elseif (b <= 8e-76)
		tmp = t_1;
	elseif (b <= 2.5e-9)
		tmp = t_2;
	elseif (b <= 1.5e+206)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = c + ((t * z) * 0.0625);
	t_3 = b * (a * -0.25);
	tmp = 0.0;
	if (b <= -1.25e-52)
		tmp = t_3;
	elseif (b <= 7.9e-221)
		tmp = t_1;
	elseif (b <= 1.3e-145)
		tmp = t_2;
	elseif (b <= 8e-76)
		tmp = t_1;
	elseif (b <= 2.5e-9)
		tmp = t_2;
	elseif (b <= 1.5e+206)
		tmp = t_1;
	else
		tmp = t_3;
	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[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e-52], t$95$3, If[LessEqual[b, 7.9e-221], t$95$1, If[LessEqual[b, 1.3e-145], t$95$2, If[LessEqual[b, 8e-76], t$95$1, If[LessEqual[b, 2.5e-9], t$95$2, If[LessEqual[b, 1.5e+206], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.25e-52 or 1.5000000000000001e206 < b

   1. Initial program 95.8%

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

      1. associate-+l- 95.8%

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

      2. sub-neg 95.8%

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

      3. neg-mul-1 95.8%

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

      4. metadata-eval 95.8%

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

      5. metadata-eval 95.8%

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

      6. cancel-sign-sub-inv 95.8%

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

      7. fma-def 97.9%

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

      8. associate-/l* 97.9%

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

      9. metadata-eval 97.9%

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

      10. *-lft-identity 97.9%

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

      11. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

      1. fma-udef 95.7%

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

      2. associate-/l* 95.7%

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

      3. +-commutative 95.7%

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

      4. div-inv 95.7%

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

      5. metadata-eval 95.7%

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

   5. Applied egg-rr 95.7%

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

   6. Taylor expanded in a around inf 51.7%

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

      1. associate-*r* 51.7%

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

   8. Simplified 51.7%

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

   if -1.25e-52 < b < 7.9000000000000004e-221 or 1.3e-145 < b < 7.99999999999999942e-76 or 2.5000000000000001e-9 < b < 1.5000000000000001e206

   1. Initial program 97.6%

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

   2. Taylor expanded in a around 0 83.3%

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

   3. Taylor expanded in t around 0 66.7%

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

   if 7.9000000000000004e-221 < b < 1.3e-145 or 7.99999999999999942e-76 < b < 2.5000000000000001e-9

   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 a around 0 85.3%

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

   3. Taylor expanded in y around 0 61.8%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{-52}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \leq 7.9 \cdot 10^{-221}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-145}:\\ \;\;\;\;c + \left(t \cdot z\right) \cdot 0.0625\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-76}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-9}:\\ \;\;\;\;c + \left(t \cdot z\right) \cdot 0.0625\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+206}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 13: 51.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.16 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-147}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+206}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* b (* a -0.25))))
   (if (<= b -1.25e-52)
     t_2
     (if (<= b 1.16e-200)
       t_1
       (if (<= b 1.2e-147) (* (* t z) 0.0625) (if (<= b 1.5e+206) 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 = b * (a * -0.25);
	double tmp;
	if (b <= -1.25e-52) {
		tmp = t_2;
	} else if (b <= 1.16e-200) {
		tmp = t_1;
	} else if (b <= 1.2e-147) {
		tmp = (t * z) * 0.0625;
	} else if (b <= 1.5e+206) {
		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 = b * (a * (-0.25d0))
    if (b <= (-1.25d-52)) then
        tmp = t_2
    else if (b <= 1.16d-200) then
        tmp = t_1
    else if (b <= 1.2d-147) then
        tmp = (t * z) * 0.0625d0
    else if (b <= 1.5d+206) 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 = b * (a * -0.25);
	double tmp;
	if (b <= -1.25e-52) {
		tmp = t_2;
	} else if (b <= 1.16e-200) {
		tmp = t_1;
	} else if (b <= 1.2e-147) {
		tmp = (t * z) * 0.0625;
	} else if (b <= 1.5e+206) {
		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 = b * (a * -0.25)
	tmp = 0
	if b <= -1.25e-52:
		tmp = t_2
	elif b <= 1.16e-200:
		tmp = t_1
	elif b <= 1.2e-147:
		tmp = (t * z) * 0.0625
	elif b <= 1.5e+206:
		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(b * Float64(a * -0.25))
	tmp = 0.0
	if (b <= -1.25e-52)
		tmp = t_2;
	elseif (b <= 1.16e-200)
		tmp = t_1;
	elseif (b <= 1.2e-147)
		tmp = Float64(Float64(t * z) * 0.0625);
	elseif (b <= 1.5e+206)
		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 = b * (a * -0.25);
	tmp = 0.0;
	if (b <= -1.25e-52)
		tmp = t_2;
	elseif (b <= 1.16e-200)
		tmp = t_1;
	elseif (b <= 1.2e-147)
		tmp = (t * z) * 0.0625;
	elseif (b <= 1.5e+206)
		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[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e-52], t$95$2, If[LessEqual[b, 1.16e-200], t$95$1, If[LessEqual[b, 1.2e-147], N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision], If[LessEqual[b, 1.5e+206], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.25e-52 or 1.5000000000000001e206 < b

   1. Initial program 95.8%

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

      1. associate-+l- 95.8%

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

      2. sub-neg 95.8%

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

      3. neg-mul-1 95.8%

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

      4. metadata-eval 95.8%

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

      5. metadata-eval 95.8%

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

      6. cancel-sign-sub-inv 95.8%

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

      7. fma-def 97.9%

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

      8. associate-/l* 97.9%

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

      9. metadata-eval 97.9%

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

      10. *-lft-identity 97.9%

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

      11. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

      1. fma-udef 95.7%

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

      2. associate-/l* 95.7%

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

      3. +-commutative 95.7%

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

      4. div-inv 95.7%

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

      5. metadata-eval 95.7%

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

   5. Applied egg-rr 95.7%

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

   6. Taylor expanded in a around inf 51.7%

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

      1. associate-*r* 51.7%

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

   8. Simplified 51.7%

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

   if -1.25e-52 < b < 1.1600000000000001e-200 or 1.19999999999999999e-147 < b < 1.5000000000000001e206

   1. Initial program 97.3%

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

   2. Taylor expanded in a around 0 84.0%

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

   3. Taylor expanded in t around 0 64.1%

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

   if 1.1600000000000001e-200 < b < 1.19999999999999999e-147

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. cancel-sign-sub-inv 100.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 99.8%

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

      9. metadata-eval 99.8%

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

      10. *-lft-identity 99.8%

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

      11. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

      1. fma-udef 99.5%

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

      2. associate-/l* 99.7%

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

      3. +-commutative 99.7%

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

      4. div-inv 99.7%

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

      5. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in z around inf 77.7%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   7. Taylor expanded in t around inf 57.6%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{-52}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \leq 1.16 \cdot 10^{-200}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-147}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+206}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 14: 37.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-180}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-9}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625\\ \mathbf{elif}\;y \leq 10^{+71}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -7e-180)
   (* x y)
   (if (<= y 9.6e-9) (* (* t z) 0.0625) (if (<= y 1e+71) c (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -7e-180) {
		tmp = x * y;
	} else if (y <= 9.6e-9) {
		tmp = (t * z) * 0.0625;
	} else if (y <= 1e+71) {
		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 <= (-7d-180)) then
        tmp = x * y
    else if (y <= 9.6d-9) then
        tmp = (t * z) * 0.0625d0
    else if (y <= 1d+71) 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 <= -7e-180) {
		tmp = x * y;
	} else if (y <= 9.6e-9) {
		tmp = (t * z) * 0.0625;
	} else if (y <= 1e+71) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -7e-180:
		tmp = x * y
	elif y <= 9.6e-9:
		tmp = (t * z) * 0.0625
	elif y <= 1e+71:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -7e-180)
		tmp = Float64(x * y);
	elseif (y <= 9.6e-9)
		tmp = Float64(Float64(t * z) * 0.0625);
	elseif (y <= 1e+71)
		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 <= -7e-180)
		tmp = x * y;
	elseif (y <= 9.6e-9)
		tmp = (t * z) * 0.0625;
	elseif (y <= 1e+71)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -7e-180], N[(x * y), $MachinePrecision], If[LessEqual[y, 9.6e-9], N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision], If[LessEqual[y, 1e+71], c, N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.0000000000000001e-180 or 1e71 < y

   1. Initial program 94.6%

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

   2. Taylor expanded in z around 0 85.1%

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

   3. Taylor expanded in c around 0 68.8%

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

   4. Taylor expanded in y around inf 43.8%

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

   if -7.0000000000000001e-180 < y < 9.5999999999999999e-9

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. cancel-sign-sub-inv 100.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 99.8%

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

      9. metadata-eval 99.8%

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

      10. *-lft-identity 99.8%

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

      11. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. fma-udef 99.7%

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

      2. associate-/l* 99.8%

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

      3. +-commutative 99.8%

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

      4. div-inv 99.8%

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

      5. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around inf 90.4%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   7. Taylor expanded in t around inf 35.6%

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

   if 9.5999999999999999e-9 < y < 1e71

   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 43.7%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-180}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-9}:\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625\\ \mathbf{elif}\;y \leq 10^{+71}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 15: 35.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{-150}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+70}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -9.6e-150) (* x y) (if (<= y 9.5e+70) c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -9.6e-150) {
		tmp = x * y;
	} else if (y <= 9.5e+70) {
		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 <= (-9.6d-150)) then
        tmp = x * y
    else if (y <= 9.5d+70) 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 <= -9.6e-150) {
		tmp = x * y;
	} else if (y <= 9.5e+70) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -9.6e-150:
		tmp = x * y
	elif y <= 9.5e+70:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -9.6e-150)
		tmp = Float64(x * y);
	elseif (y <= 9.5e+70)
		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 <= -9.6e-150)
		tmp = x * y;
	elseif (y <= 9.5e+70)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -9.6e-150], N[(x * y), $MachinePrecision], If[LessEqual[y, 9.5e+70], c, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.6e-150 or 9.5000000000000002e70 < y

   1. Initial program 94.3%

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

   2. Taylor expanded in z around 0 85.8%

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

   3. Taylor expanded in c around 0 70.7%

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

   4. Taylor expanded in y around inf 45.9%

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

   if -9.6e-150 < y < 9.5000000000000002e70

   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 28.9%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{-150}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+70}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 16: 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 96.9%

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

2. Taylor expanded in c around inf 22.5%

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

3. Final simplification 22.5%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023240 
(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))