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

Percentage Accurate: 97.9% → 98.9%

Time: 12.7s

Alternatives: 13

Speedup: 1.0×

• 32.6% 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: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around 0 50.0%

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

      1. +-commutative 50.0%

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

      2. *-commutative 50.0%

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

      3. fma-define 83.3%

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

      4. *-commutative 83.3%

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

   5. Applied egg-rr 83.3%

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

4. Final simplification 99.6%

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

Alternative 2: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. associate--l+ 97.6%

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

   2. fma-define 98.8%

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

   3. associate-/l* 98.8%

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

   4. fma-neg 98.8%

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

   5. distribute-neg-frac2 98.8%

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

   6. metadata-eval 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 3: 98.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. associate-+l- 97.6%

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

   2. *-commutative 97.6%

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

   3. associate-+l- 97.6%

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

   4. fma-define 98.4%

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

   5. *-commutative 98.4%

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

   6. associate-/l* 98.4%

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

   7. associate-/l* 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 4: 98.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ c + \mathsf{fma}\left(x, y, z \cdot \left(t \cdot 0.0625\right) - \frac{a}{\frac{4}{b}}\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ c (fma x y (- (* z (* t 0.0625)) (/ a (/ 4.0 b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + fma(x, y, ((z * (t * 0.0625)) - (a / (4.0 / b))));
}

Julia

function code(x, y, z, t, a, b, c)
	return Float64(c + fma(x, y, Float64(Float64(z * Float64(t * 0.0625)) - Float64(a / Float64(4.0 / b)))))
end

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. associate--l+ 97.6%

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

   2. fma-define 98.8%

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

   3. associate-/l* 98.8%

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

   4. fma-neg 98.8%

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

   5. distribute-neg-frac2 98.8%

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

   6. metadata-eval 98.8%

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

3. Simplified 98.8%

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

   1. fma-undefine 98.8%

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

   2. associate-*r/ 98.8%

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

   3. frac-2neg 98.8%

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

   4. metadata-eval 98.8%

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

   5. div-inv 98.8%

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

   6. cancel-sign-sub-inv 98.8%

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

   7. div-inv 98.8%

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

   8. associate-*r/ 98.8%

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

   9. div-inv 98.8%

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

   10. metadata-eval 98.8%

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

   11. associate-*r/ 98.8%

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

   12. clear-num 98.8%

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

   13. un-div-inv 98.8%

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

6. Applied egg-rr 98.8%

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

7. Final simplification 98.8%

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

Alternative 5: 64.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + b \cdot \left(a \cdot -0.25\right)\\ t_2 := c + 0.0625 \cdot \left(z \cdot t\right)\\ t_3 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -2.4 \cdot 10^{+42}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.95 \cdot 10^{-289}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 1.7 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 3.4 \cdot 10^{+147}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* b (* a -0.25))))
        (t_2 (+ c (* 0.0625 (* z t))))
        (t_3 (+ c (* x y))))
   (if (<= (* x y) -2.4e+42)
     t_3
     (if (<= (* x y) 0.0)
       t_1
       (if (<= (* x y) 1.95e-289)
         t_2
         (if (<= (* x y) 1.7e-128) t_1 (if (<= (* x y) 3.4e+147) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double t_2 = c + (0.0625 * (z * t));
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -2.4e+42) {
		tmp = t_3;
	} else if ((x * y) <= 0.0) {
		tmp = t_1;
	} else if ((x * y) <= 1.95e-289) {
		tmp = t_2;
	} else if ((x * y) <= 1.7e-128) {
		tmp = t_1;
	} else if ((x * y) <= 3.4e+147) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c + (b * (a * (-0.25d0)))
    t_2 = c + (0.0625d0 * (z * t))
    t_3 = c + (x * y)
    if ((x * y) <= (-2.4d+42)) then
        tmp = t_3
    else if ((x * y) <= 0.0d0) then
        tmp = t_1
    else if ((x * y) <= 1.95d-289) then
        tmp = t_2
    else if ((x * y) <= 1.7d-128) then
        tmp = t_1
    else if ((x * y) <= 3.4d+147) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double t_2 = c + (0.0625 * (z * t));
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -2.4e+42) {
		tmp = t_3;
	} else if ((x * y) <= 0.0) {
		tmp = t_1;
	} else if ((x * y) <= 1.95e-289) {
		tmp = t_2;
	} else if ((x * y) <= 1.7e-128) {
		tmp = t_1;
	} else if ((x * y) <= 3.4e+147) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (b * (a * -0.25))
	t_2 = c + (0.0625 * (z * t))
	t_3 = c + (x * y)
	tmp = 0
	if (x * y) <= -2.4e+42:
		tmp = t_3
	elif (x * y) <= 0.0:
		tmp = t_1
	elif (x * y) <= 1.95e-289:
		tmp = t_2
	elif (x * y) <= 1.7e-128:
		tmp = t_1
	elif (x * y) <= 3.4e+147:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(b * Float64(a * -0.25)))
	t_2 = Float64(c + Float64(0.0625 * Float64(z * t)))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -2.4e+42)
		tmp = t_3;
	elseif (Float64(x * y) <= 0.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.95e-289)
		tmp = t_2;
	elseif (Float64(x * y) <= 1.7e-128)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.4e+147)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (b * (a * -0.25));
	t_2 = c + (0.0625 * (z * t));
	t_3 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -2.4e+42)
		tmp = t_3;
	elseif ((x * y) <= 0.0)
		tmp = t_1;
	elseif ((x * y) <= 1.95e-289)
		tmp = t_2;
	elseif ((x * y) <= 1.7e-128)
		tmp = t_1;
	elseif ((x * y) <= 3.4e+147)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.4e+42], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 0.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.95e-289], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1.7e-128], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.4e+147], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.3999999999999999e42 or 3.4e147 < (*.f64 x y)

   1. Initial program 94.9%

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

   3. Taylor expanded in x around inf 77.4%

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

   if -2.3999999999999999e42 < (*.f64 x y) < 0.0 or 1.9499999999999999e-289 < (*.f64 x y) < 1.69999999999999987e-128

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 68.8%

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

      1. associate-*r* 68.8%

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

   5. Simplified 68.8%

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

   if 0.0 < (*.f64 x y) < 1.9499999999999999e-289 or 1.69999999999999987e-128 < (*.f64 x y) < 3.4e147

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf 75.2%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.4 \cdot 10^{+42}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.95 \cdot 10^{-289}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 1.7 \cdot 10^{-128}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 3.4 \cdot 10^{+147}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+149} \lor \neg \left(z \leq 1.4 \cdot 10^{-170} \lor \neg \left(z \leq 2.3 \cdot 10^{-115}\right) \land z \leq 3.7 \cdot 10^{-37}\right):\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -9.6e+149)
         (not (or (<= z 1.4e-170) (and (not (<= z 2.3e-115)) (<= z 3.7e-37)))))
   (+ c (* 0.0625 (* z t)))
   (- (* x y) (* (* a b) 0.25))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -9.6e+149) || !((z <= 1.4e-170) || (!(z <= 2.3e-115) && (z <= 3.7e-37)))) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-9.6d+149)) .or. (.not. (z <= 1.4d-170) .or. (.not. (z <= 2.3d-115)) .and. (z <= 3.7d-37))) then
        tmp = c + (0.0625d0 * (z * t))
    else
        tmp = (x * y) - ((a * b) * 0.25d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -9.6e+149) || !((z <= 1.4e-170) || (!(z <= 2.3e-115) && (z <= 3.7e-37)))) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -9.6e+149) or not ((z <= 1.4e-170) or (not (z <= 2.3e-115) and (z <= 3.7e-37))):
		tmp = c + (0.0625 * (z * t))
	else:
		tmp = (x * y) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -9.6e+149) || !((z <= 1.4e-170) || (!(z <= 2.3e-115) && (z <= 3.7e-37))))
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	else
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -9.6e+149) || ~(((z <= 1.4e-170) || (~((z <= 2.3e-115)) && (z <= 3.7e-37)))))
		tmp = c + (0.0625 * (z * t));
	else
		tmp = (x * y) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -9.6e+149], N[Not[Or[LessEqual[z, 1.4e-170], And[N[Not[LessEqual[z, 2.3e-115]], $MachinePrecision], LessEqual[z, 3.7e-37]]]], $MachinePrecision]], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.60000000000000047e149 or 1.39999999999999998e-170 < z < 2.29999999999999985e-115 or 3.7e-37 < z

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 59.4%

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

   if -9.60000000000000047e149 < z < 1.39999999999999998e-170 or 2.29999999999999985e-115 < z < 3.7e-37

   1. Initial program 97.0%

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

   3. Taylor expanded in z around 0 85.3%

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

   4. Taylor expanded in c around 0 67.3%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+149} \lor \neg \left(z \leq 1.4 \cdot 10^{-170} \lor \neg \left(z \leq 2.3 \cdot 10^{-115}\right) \land z \leq 3.7 \cdot 10^{-37}\right):\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -2.6 \cdot 10^{+43} \lor \neg \left(x \cdot y \leq 8.2 \cdot 10^{-22}\right):\\ \;\;\;\;c + \left(x \cdot y + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + t\_1\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (or (<= (* x y) -2.6e+43) (not (<= (* x y) 8.2e-22)))
     (+ c (+ (* x y) t_1))
     (- (+ c t_1) (* (* a b) 0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if (((x * y) <= -2.6e+43) || !((x * y) <= 8.2e-22)) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + t_1) - ((a * b) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if (((x * y) <= (-2.6d+43)) .or. (.not. ((x * y) <= 8.2d-22))) then
        tmp = c + ((x * y) + t_1)
    else
        tmp = (c + t_1) - ((a * b) * 0.25d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if (((x * y) <= -2.6e+43) || !((x * y) <= 8.2e-22)) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + t_1) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if ((x * y) <= -2.6e+43) or not ((x * y) <= 8.2e-22):
		tmp = c + ((x * y) + t_1)
	else:
		tmp = (c + t_1) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if ((Float64(x * y) <= -2.6e+43) || !(Float64(x * y) <= 8.2e-22))
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	else
		tmp = Float64(Float64(c + t_1) - Float64(Float64(a * b) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if (((x * y) <= -2.6e+43) || ~(((x * y) <= 8.2e-22)))
		tmp = c + ((x * y) + t_1);
	else
		tmp = (c + t_1) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(x * y), $MachinePrecision], -2.6e+43], N[Not[LessEqual[N[(x * y), $MachinePrecision], 8.2e-22]], $MachinePrecision]], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(c + t$95$1), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.60000000000000021e43 or 8.1999999999999999e-22 < (*.f64 x y)

   1. Initial program 95.4%

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

   3. Taylor expanded in a around 0 88.1%

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

   if -2.60000000000000021e43 < (*.f64 x y) < 8.1999999999999999e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.1%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.6 \cdot 10^{+43} \lor \neg \left(x \cdot y \leq 8.2 \cdot 10^{-22}\right):\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+71} \lor \neg \left(a \cdot b \leq 10^{+262}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -1e+71) (not (<= (* a b) 1e+262)))
   (- (* x y) (* (* a b) 0.25))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -1e+71) || !((a * b) <= 1e+262)) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((a * b) <= (-1d+71)) .or. (.not. ((a * b) <= 1d+262))) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -1e+71) || !((a * b) <= 1e+262)) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -1e+71) or not ((a * b) <= 1e+262):
		tmp = (x * y) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -1e+71) || !(Float64(a * b) <= 1e+262))
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -1e+71) || ~(((a * b) <= 1e+262)))
		tmp = (x * y) - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -1e+71], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1e+262]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1e71 or 1e262 < (*.f64 a b)

   1. Initial program 92.9%

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

   3. Taylor expanded in z around 0 86.5%

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

   4. Taylor expanded in c around 0 82.2%

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

   if -1e71 < (*.f64 a b) < 1e262

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0 87.1%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+71} \lor \neg \left(a \cdot b \leq 10^{+262}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{-13} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+152}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -2e-13) (not (<= (* a b) 2e+152)))
   (- (+ c (* x y)) (* (* a b) 0.25))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -2e-13) || !((a * b) <= 2e+152)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((a * b) <= (-2d-13)) .or. (.not. ((a * b) <= 2d+152))) then
        tmp = (c + (x * y)) - ((a * b) * 0.25d0)
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -2e-13) || !((a * b) <= 2e+152)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -2e-13) or not ((a * b) <= 2e+152):
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -2e-13) || !(Float64(a * b) <= 2e+152))
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -2e-13) || ~(((a * b) <= 2e+152)))
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -2e-13], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e+152]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2.0000000000000001e-13 or 2.0000000000000001e152 < (*.f64 a b)

   1. Initial program 94.9%

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

   3. Taylor expanded in z around 0 82.6%

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

   if -2.0000000000000001e-13 < (*.f64 a b) < 2.0000000000000001e152

   1. Initial program 99.3%

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

   3. Taylor expanded in a around 0 90.6%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{-13} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+152}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.2 \cdot 10^{+77} \lor \neg \left(x \cdot y \leq 6 \cdot 10^{+147}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -5.2e+77) (not (<= (* x y) 6e+147)))
   (+ c (* x y))
   (+ c (* 0.0625 (* z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -5.2e+77) || !((x * y) <= 6e+147)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (0.0625 * (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-5.2d+77)) .or. (.not. ((x * y) <= 6d+147))) then
        tmp = c + (x * y)
    else
        tmp = c + (0.0625d0 * (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -5.2e+77) || !((x * y) <= 6e+147)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (0.0625 * (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -5.2e+77) or not ((x * y) <= 6e+147):
		tmp = c + (x * y)
	else:
		tmp = c + (0.0625 * (z * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -5.2e+77) || !(Float64(x * y) <= 6e+147))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -5.2e+77) || ~(((x * y) <= 6e+147)))
		tmp = c + (x * y);
	else
		tmp = c + (0.0625 * (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -5.2e+77], N[Not[LessEqual[N[(x * y), $MachinePrecision], 6e+147]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -5.2000000000000004e77 or 5.99999999999999987e147 < (*.f64 x 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. Add Preprocessing

   3. Taylor expanded in x around inf 78.3%

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

   if -5.2000000000000004e77 < (*.f64 x y) < 5.99999999999999987e147

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 56.8%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.2 \cdot 10^{+77} \lor \neg \left(x \cdot y \leq 6 \cdot 10^{+147}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

3. Final simplification 97.6%

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

Alternative 12: 49.3% accurate, 3.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

3. Taylor expanded in x around inf 45.2%

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

4. Final simplification 45.2%

   \[\leadsto c + x \cdot y \]
5. Add Preprocessing

Alternative 13: 22.9% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

3. Taylor expanded in c around inf 15.9%

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

4. Final simplification 15.9%

   \[\leadsto c \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024040 
(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))