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

Percentage Accurate: 97.9% → 98.6%

Time: 7.7s

Alternatives: 12

Speedup: 0.5×

• Unsound rule application detected in e-graph. Results may not be sound.

• 32.9% 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: 98.6% accurate, 0.1× speedup

Math

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

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (- (+ (/ (* t z) 16.0) (* x y)) (/ (* b a) 4.0)) INFINITY)
   (+ (fma x y (/ z (/ 16.0 t))) (- c (/ a (/ 4.0 b))))
   (+ c (* x y))))

C

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

Julia

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

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(N[(N[(N[(t * z), $MachinePrecision] / 16.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision], Infinity], 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], 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 99.7%

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

      1. associate-+l- 99.7%

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

      2. sub-neg 99.7%

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

      3. neg-mul-1 99.7%

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

      4. metadata-eval 99.7%

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

      5. metadata-eval 99.7%

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

      6. cancel-sign-sub-inv 99.7%

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

      7. fma-def 99.7%

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

      8. associate-/l* 99.6%

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

      9. metadata-eval 99.6%

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

      10. *-lft-identity 99.6%

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

      11. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   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 x around inf 57.7%

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

4. Final simplification 98.7%

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

Alternative 2: 98.9% accurate, 0.1× speedup

Math

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

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (fma t (/ z 16.0) (fma x y (- c (* b (/ a 4.0))))))

C

assert(z < t);
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

z, t = sort([z, t])
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

NOTE: z and t should be sorted in increasing order before calling this function.
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 97.7%

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

   7. fma-neg 98.1%

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

   8. neg-sub0 98.1%

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

   9. associate-+l- 98.1%

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

   10. neg-sub0 98.1%

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

   11. +-commutative 98.1%

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

   12. unsub-neg 98.1%

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

   13. *-commutative 98.1%

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

   14. associate-*r/ 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 3: 98.6% accurate, 0.5× speedup

Math

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

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(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

assert(z < t);
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

assert z < t;
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

[z, t] = sort([z, t])
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

z, t = sort([z, t])
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

z, t = num2cell(sort([z, t])){:}
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

NOTE: z and t should be sorted in increasing order before calling this function.
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 99.7%

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

   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 x around inf 57.7%

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

4. Final simplification 98.5%

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

Alternative 4: 60.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{-225}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+64}:\\ \;\;\;\;c + t_2\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+101} \lor \neg \left(b \leq 2.05 \cdot 10^{+113}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + t_2\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25)))) (t_2 (* 0.0625 (* t z))))
   (if (<= b -1.45e-5)
     t_1
     (if (<= b 1.26e-225)
       (+ c (* x y))
       (if (<= b 2.6e+64)
         (+ c t_2)
         (if (or (<= b 1.02e+101) (not (<= b 2.05e+113)))
           t_1
           (+ (* x y) t_2)))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double t_2 = 0.0625 * (t * z);
	double tmp;
	if (b <= -1.45e-5) {
		tmp = t_1;
	} else if (b <= 1.26e-225) {
		tmp = c + (x * y);
	} else if (b <= 2.6e+64) {
		tmp = c + t_2;
	} else if ((b <= 1.02e+101) || !(b <= 2.05e+113)) {
		tmp = t_1;
	} else {
		tmp = (x * y) + t_2;
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
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 + (a * (b * (-0.25d0)))
    t_2 = 0.0625d0 * (t * z)
    if (b <= (-1.45d-5)) then
        tmp = t_1
    else if (b <= 1.26d-225) then
        tmp = c + (x * y)
    else if (b <= 2.6d+64) then
        tmp = c + t_2
    else if ((b <= 1.02d+101) .or. (.not. (b <= 2.05d+113))) then
        tmp = t_1
    else
        tmp = (x * y) + t_2
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double t_2 = 0.0625 * (t * z);
	double tmp;
	if (b <= -1.45e-5) {
		tmp = t_1;
	} else if (b <= 1.26e-225) {
		tmp = c + (x * y);
	} else if (b <= 2.6e+64) {
		tmp = c + t_2;
	} else if ((b <= 1.02e+101) || !(b <= 2.05e+113)) {
		tmp = t_1;
	} else {
		tmp = (x * y) + t_2;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	t_2 = 0.0625 * (t * z)
	tmp = 0
	if b <= -1.45e-5:
		tmp = t_1
	elif b <= 1.26e-225:
		tmp = c + (x * y)
	elif b <= 2.6e+64:
		tmp = c + t_2
	elif (b <= 1.02e+101) or not (b <= 2.05e+113):
		tmp = t_1
	else:
		tmp = (x * y) + t_2
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_2 = Float64(0.0625 * Float64(t * z))
	tmp = 0.0
	if (b <= -1.45e-5)
		tmp = t_1;
	elseif (b <= 1.26e-225)
		tmp = Float64(c + Float64(x * y));
	elseif (b <= 2.6e+64)
		tmp = Float64(c + t_2);
	elseif ((b <= 1.02e+101) || !(b <= 2.05e+113))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * y) + t_2);
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (a * (b * -0.25));
	t_2 = 0.0625 * (t * z);
	tmp = 0.0;
	if (b <= -1.45e-5)
		tmp = t_1;
	elseif (b <= 1.26e-225)
		tmp = c + (x * y);
	elseif (b <= 2.6e+64)
		tmp = c + t_2;
	elseif ((b <= 1.02e+101) || ~((b <= 2.05e+113)))
		tmp = t_1;
	else
		tmp = (x * y) + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.45e-5], t$95$1, If[LessEqual[b, 1.26e-225], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e+64], N[(c + t$95$2), $MachinePrecision], If[Or[LessEqual[b, 1.02e+101], N[Not[LessEqual[b, 2.05e+113]], $MachinePrecision]], t$95$1, N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.45e-5 or 2.59999999999999997e64 < b < 1.02000000000000002e101 or 2.04999999999999996e113 < b

   1. Initial program 93.6%

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

   2. Taylor expanded in a around inf 64.6%

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

      1. *-commutative 64.6%

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

      2. associate-*l* 65.3%

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

   4. Simplified 65.3%

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

   if -1.45e-5 < b < 1.2599999999999999e-225

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 64.9%

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

   if 1.2599999999999999e-225 < b < 2.59999999999999997e64

   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 z around inf 65.0%

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

   if 1.02000000000000002e101 < b < 2.04999999999999996e113

   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 a around 0 100.0%

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

   3. Taylor expanded in c around 0 100.0%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{-5}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{-225}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+64}:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+101} \lor \neg \left(b \leq 2.05 \cdot 10^{+113}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\\ \end{array} \]

Alternative 5: 39.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25\right)\\ t_2 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;t \leq -2.55 \cdot 10^{-54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-307}:\\ \;\;\;\;c\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-214}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+85}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (* a -0.25))) (t_2 (* 0.0625 (* t z))))
   (if (<= t -2.55e-54)
     t_2
     (if (<= t 2e-307)
       c
       (if (<= t 4.5e-263)
         t_1
         (if (<= t 7e-214)
           (* x y)
           (if (<= t 1.9e-20) t_1 (if (<= t 5.8e+85) c t_2))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (a * -0.25);
	double t_2 = 0.0625 * (t * z);
	double tmp;
	if (t <= -2.55e-54) {
		tmp = t_2;
	} else if (t <= 2e-307) {
		tmp = c;
	} else if (t <= 4.5e-263) {
		tmp = t_1;
	} else if (t <= 7e-214) {
		tmp = x * y;
	} else if (t <= 1.9e-20) {
		tmp = t_1;
	} else if (t <= 5.8e+85) {
		tmp = c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
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 = b * (a * (-0.25d0))
    t_2 = 0.0625d0 * (t * z)
    if (t <= (-2.55d-54)) then
        tmp = t_2
    else if (t <= 2d-307) then
        tmp = c
    else if (t <= 4.5d-263) then
        tmp = t_1
    else if (t <= 7d-214) then
        tmp = x * y
    else if (t <= 1.9d-20) then
        tmp = t_1
    else if (t <= 5.8d+85) then
        tmp = c
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert z < t;
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 t_2 = 0.0625 * (t * z);
	double tmp;
	if (t <= -2.55e-54) {
		tmp = t_2;
	} else if (t <= 2e-307) {
		tmp = c;
	} else if (t <= 4.5e-263) {
		tmp = t_1;
	} else if (t <= 7e-214) {
		tmp = x * y;
	} else if (t <= 1.9e-20) {
		tmp = t_1;
	} else if (t <= 5.8e+85) {
		tmp = c;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	t_1 = b * (a * -0.25)
	t_2 = 0.0625 * (t * z)
	tmp = 0
	if t <= -2.55e-54:
		tmp = t_2
	elif t <= 2e-307:
		tmp = c
	elif t <= 4.5e-263:
		tmp = t_1
	elif t <= 7e-214:
		tmp = x * y
	elif t <= 1.9e-20:
		tmp = t_1
	elif t <= 5.8e+85:
		tmp = c
	else:
		tmp = t_2
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(a * -0.25))
	t_2 = Float64(0.0625 * Float64(t * z))
	tmp = 0.0
	if (t <= -2.55e-54)
		tmp = t_2;
	elseif (t <= 2e-307)
		tmp = c;
	elseif (t <= 4.5e-263)
		tmp = t_1;
	elseif (t <= 7e-214)
		tmp = Float64(x * y);
	elseif (t <= 1.9e-20)
		tmp = t_1;
	elseif (t <= 5.8e+85)
		tmp = c;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b * (a * -0.25);
	t_2 = 0.0625 * (t * z);
	tmp = 0.0;
	if (t <= -2.55e-54)
		tmp = t_2;
	elseif (t <= 2e-307)
		tmp = c;
	elseif (t <= 4.5e-263)
		tmp = t_1;
	elseif (t <= 7e-214)
		tmp = x * y;
	elseif (t <= 1.9e-20)
		tmp = t_1;
	elseif (t <= 5.8e+85)
		tmp = c;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.55e-54], t$95$2, If[LessEqual[t, 2e-307], c, If[LessEqual[t, 4.5e-263], t$95$1, If[LessEqual[t, 7e-214], N[(x * y), $MachinePrecision], If[LessEqual[t, 1.9e-20], t$95$1, If[LessEqual[t, 5.8e+85], c, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.55000000000000005e-54 or 5.79999999999999995e85 < t

   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 x around 0 81.5%

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

      1. +-commutative 81.5%

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

      2. *-commutative 81.5%

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

      3. *-commutative 81.5%

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

      4. associate-*r* 81.5%

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

      5. *-commutative 81.5%

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

      6. *-commutative 81.5%

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

      7. associate-*r* 81.5%

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

      8. associate--l+ 81.5%

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

      9. associate-*r* 81.5%

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

      10. *-commutative 81.5%

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

      11. *-commutative 81.5%

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

      12. sub-neg 81.5%

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

      13. +-commutative 81.5%

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

      14. distribute-rgt-neg-in 81.5%

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

      15. fma-def 81.5%

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

      16. distribute-rgt-neg-in 81.5%

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

      17. metadata-eval 81.5%

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

   4. Simplified 81.5%

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

   5. Taylor expanded in t around inf 48.6%

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

   if -2.55000000000000005e-54 < t < 1.99999999999999982e-307 or 1.8999999999999999e-20 < t < 5.79999999999999995e85

   1. Initial program 99.0%

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

   2. Taylor expanded in c around inf 35.6%

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

   if 1.99999999999999982e-307 < t < 4.4999999999999997e-263 or 7e-214 < t < 1.8999999999999999e-20

   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 x around 0 81.4%

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

      1. +-commutative 81.4%

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

      2. *-commutative 81.4%

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

      3. *-commutative 81.4%

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

      4. associate-*r* 81.4%

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

      5. *-commutative 81.4%

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

      6. *-commutative 81.4%

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

      7. associate-*r* 81.4%

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

      8. associate--l+ 81.4%

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

      9. associate-*r* 81.4%

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

      10. *-commutative 81.4%

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

      11. *-commutative 81.4%

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

      12. sub-neg 81.4%

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

      13. +-commutative 81.4%

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

      14. distribute-rgt-neg-in 81.4%

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

      15. fma-def 81.4%

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

      16. distribute-rgt-neg-in 81.4%

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

      17. metadata-eval 81.4%

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

   4. Simplified 81.4%

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

   5. Taylor expanded in b around inf 51.1%

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

      1. *-commutative 51.1%

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

      2. *-commutative 51.1%

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

      3. associate-*r* 51.1%

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

      4. *-commutative 51.1%

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

   7. Simplified 51.1%

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

   if 4.4999999999999997e-263 < t < 7e-214

   1. Initial program 70.0%

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

   2. Taylor expanded in x around inf 71.0%

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

   3. Taylor expanded in y around inf 61.4%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{-54}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-307}:\\ \;\;\;\;c\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-263}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-214}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+85}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \end{array} \]

Alternative 6: 77.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+221} \lor \neg \left(a \leq 1.6 \cdot 10^{+19}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -3.5e+221) (not (<= a 1.6e+19)))
   (+ c (* a (* b -0.25)))
   (+ c (+ (* x y) (* 0.0625 (* t z))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -3.5e+221) || !(a <= 1.6e+19)) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
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 <= (-3.5d+221)) .or. (.not. (a <= 1.6d+19))) then
        tmp = c + (a * (b * (-0.25d0)))
    else
        tmp = c + ((x * y) + (0.0625d0 * (t * z)))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -3.5e+221) || !(a <= 1.6e+19)) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -3.5e+221) or not (a <= 1.6e+19):
		tmp = c + (a * (b * -0.25))
	else:
		tmp = c + ((x * y) + (0.0625 * (t * z)))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -3.5e+221) || !(a <= 1.6e+19))
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(t * z))));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -3.5e+221) || ~((a <= 1.6e+19)))
		tmp = c + (a * (b * -0.25));
	else
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -3.5e+221], N[Not[LessEqual[a, 1.6e+19]], $MachinePrecision]], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.5000000000000002e221 or 1.6e19 < a

   1. Initial program 93.5%

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

   2. Taylor expanded in a around inf 66.0%

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

      1. *-commutative 66.0%

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

      2. associate-*l* 67.1%

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

   4. Simplified 67.1%

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

   if -3.5000000000000002e221 < a < 1.6e19

   1. Initial program 98.3%

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

   2. Taylor expanded in a around 0 86.4%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+221} \lor \neg \left(a \leq 1.6 \cdot 10^{+19}\right):\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\right)\\ \end{array} \]

Alternative 7: 54.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -7.3 \cdot 10^{+252} \lor \neg \left(a \leq -4.1 \cdot 10^{+249}\right) \land \left(a \leq -3.5 \cdot 10^{+221} \lor \neg \left(a \leq 1.5 \cdot 10^{+19}\right)\right):\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -7.3e+252)
         (and (not (<= a -4.1e+249))
              (or (<= a -3.5e+221) (not (<= a 1.5e+19)))))
   (* b (* a -0.25))
   (+ c (* x y))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -7.3e+252) || (!(a <= -4.1e+249) && ((a <= -3.5e+221) || !(a <= 1.5e+19)))) {
		tmp = b * (a * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
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 <= (-7.3d+252)) .or. (.not. (a <= (-4.1d+249))) .and. (a <= (-3.5d+221)) .or. (.not. (a <= 1.5d+19))) then
        tmp = b * (a * (-0.25d0))
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -7.3e+252) || (!(a <= -4.1e+249) && ((a <= -3.5e+221) || !(a <= 1.5e+19)))) {
		tmp = b * (a * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -7.3e+252) or (not (a <= -4.1e+249) and ((a <= -3.5e+221) or not (a <= 1.5e+19))):
		tmp = b * (a * -0.25)
	else:
		tmp = c + (x * y)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -7.3e+252) || (!(a <= -4.1e+249) && ((a <= -3.5e+221) || !(a <= 1.5e+19))))
		tmp = Float64(b * Float64(a * -0.25));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -7.3e+252) || (~((a <= -4.1e+249)) && ((a <= -3.5e+221) || ~((a <= 1.5e+19)))))
		tmp = b * (a * -0.25);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -7.3e+252], And[N[Not[LessEqual[a, -4.1e+249]], $MachinePrecision], Or[LessEqual[a, -3.5e+221], N[Not[LessEqual[a, 1.5e+19]], $MachinePrecision]]]], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.2999999999999997e252 or -4.0999999999999997e249 < a < -3.5000000000000002e221 or 1.5e19 < a

   1. Initial program 93.4%

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

   2. Taylor expanded in x around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. *-commutative 80.1%

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

      3. *-commutative 80.1%

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

      4. associate-*r* 80.1%

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

      5. *-commutative 80.1%

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

      6. *-commutative 80.1%

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

      7. associate-*r* 81.2%

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

      8. associate--l+ 81.2%

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

      9. associate-*r* 81.2%

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

      10. *-commutative 81.2%

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

      11. *-commutative 81.2%

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

      12. sub-neg 81.2%

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

      13. +-commutative 81.2%

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

      14. distribute-rgt-neg-in 81.2%

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

      15. fma-def 81.3%

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

      16. distribute-rgt-neg-in 81.3%

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

      17. metadata-eval 81.3%

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

   4. Simplified 81.3%

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

   5. Taylor expanded in b around inf 55.9%

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

      1. *-commutative 55.9%

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

      2. *-commutative 55.9%

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

      3. associate-*r* 57.0%

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

      4. *-commutative 57.0%

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

   7. Simplified 57.0%

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

   if -7.2999999999999997e252 < a < -4.0999999999999997e249 or -3.5000000000000002e221 < a < 1.5e19

   1. Initial program 98.4%

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

   2. Taylor expanded in x around inf 57.6%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.3 \cdot 10^{+252} \lor \neg \left(a \leq -4.1 \cdot 10^{+249}\right) \land \left(a \leq -3.5 \cdot 10^{+221} \lor \neg \left(a \leq 1.5 \cdot 10^{+19}\right)\right):\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 8: 60.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;b \leq -1.14 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{-223}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+63}:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25)))))
   (if (<= b -1.14e-7)
     t_1
     (if (<= b 1.36e-223)
       (+ c (* x y))
       (if (<= b 2.8e+63) (+ c (* 0.0625 (* t z))) t_1)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double tmp;
	if (b <= -1.14e-7) {
		tmp = t_1;
	} else if (b <= 1.36e-223) {
		tmp = c + (x * y);
	} else if (b <= 2.8e+63) {
		tmp = c + (0.0625 * (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
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 = c + (a * (b * (-0.25d0)))
    if (b <= (-1.14d-7)) then
        tmp = t_1
    else if (b <= 1.36d-223) then
        tmp = c + (x * y)
    else if (b <= 2.8d+63) then
        tmp = c + (0.0625d0 * (t * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double tmp;
	if (b <= -1.14e-7) {
		tmp = t_1;
	} else if (b <= 1.36e-223) {
		tmp = c + (x * y);
	} else if (b <= 2.8e+63) {
		tmp = c + (0.0625 * (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	tmp = 0
	if b <= -1.14e-7:
		tmp = t_1
	elif b <= 1.36e-223:
		tmp = c + (x * y)
	elif b <= 2.8e+63:
		tmp = c + (0.0625 * (t * z))
	else:
		tmp = t_1
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(a * Float64(b * -0.25)))
	tmp = 0.0
	if (b <= -1.14e-7)
		tmp = t_1;
	elseif (b <= 1.36e-223)
		tmp = Float64(c + Float64(x * y));
	elseif (b <= 2.8e+63)
		tmp = Float64(c + Float64(0.0625 * Float64(t * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (a * (b * -0.25));
	tmp = 0.0;
	if (b <= -1.14e-7)
		tmp = t_1;
	elseif (b <= 1.36e-223)
		tmp = c + (x * y);
	elseif (b <= 2.8e+63)
		tmp = c + (0.0625 * (t * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.14e-7], t$95$1, If[LessEqual[b, 1.36e-223], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e+63], N[(c + N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.14000000000000002e-7 or 2.79999999999999987e63 < b

   1. Initial program 93.7%

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

   2. Taylor expanded in a around inf 63.6%

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

      1. *-commutative 63.6%

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

      2. associate-*l* 64.3%

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

   4. Simplified 64.3%

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

   if -1.14000000000000002e-7 < b < 1.35999999999999997e-223

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 64.9%

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

   if 1.35999999999999997e-223 < b < 2.79999999999999987e63

   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 z around inf 65.0%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.14 \cdot 10^{-7}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{-223}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+63}:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]

Alternative 9: 39.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;t \leq -9 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-44}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+86}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* t z))))
   (if (<= t -9e-48)
     t_1
     (if (<= t 2.3e-44) (* x y) (if (<= t 2.9e+86) c t_1)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (t * z);
	double tmp;
	if (t <= -9e-48) {
		tmp = t_1;
	} else if (t <= 2.3e-44) {
		tmp = x * y;
	} else if (t <= 2.9e+86) {
		tmp = c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
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 * (t * z)
    if (t <= (-9d-48)) then
        tmp = t_1
    else if (t <= 2.3d-44) then
        tmp = x * y
    else if (t <= 2.9d+86) then
        tmp = c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (t * z);
	double tmp;
	if (t <= -9e-48) {
		tmp = t_1;
	} else if (t <= 2.3e-44) {
		tmp = x * y;
	} else if (t <= 2.9e+86) {
		tmp = c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (t * z)
	tmp = 0
	if t <= -9e-48:
		tmp = t_1
	elif t <= 2.3e-44:
		tmp = x * y
	elif t <= 2.9e+86:
		tmp = c
	else:
		tmp = t_1
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(t * z))
	tmp = 0.0
	if (t <= -9e-48)
		tmp = t_1;
	elseif (t <= 2.3e-44)
		tmp = Float64(x * y);
	elseif (t <= 2.9e+86)
		tmp = c;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (t * z);
	tmp = 0.0;
	if (t <= -9e-48)
		tmp = t_1;
	elseif (t <= 2.3e-44)
		tmp = x * y;
	elseif (t <= 2.9e+86)
		tmp = c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e-48], t$95$1, If[LessEqual[t, 2.3e-44], N[(x * y), $MachinePrecision], If[LessEqual[t, 2.9e+86], c, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.99999999999999977e-48 or 2.8999999999999999e86 < t

   1. Initial program 97.4%

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

   2. Taylor expanded in x around 0 82.2%

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

      1. +-commutative 82.2%

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

      2. *-commutative 82.2%

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

      3. *-commutative 82.2%

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

      4. associate-*r* 82.2%

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

      5. *-commutative 82.2%

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

      6. *-commutative 82.2%

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

      7. associate-*r* 82.2%

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

      8. associate--l+ 82.2%

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

      9. associate-*r* 82.2%

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

      10. *-commutative 82.2%

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

      11. *-commutative 82.2%

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

      12. sub-neg 82.2%

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

      13. +-commutative 82.2%

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

      14. distribute-rgt-neg-in 82.2%

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

      15. fma-def 82.2%

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

      16. distribute-rgt-neg-in 82.2%

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

      17. metadata-eval 82.2%

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

   4. Simplified 82.2%

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

   5. Taylor expanded in t around inf 49.0%

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

   if -8.99999999999999977e-48 < t < 2.29999999999999998e-44

   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 x around inf 61.1%

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

   3. Taylor expanded in y around inf 33.0%

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

   if 2.29999999999999998e-44 < t < 2.8999999999999999e86

   1. Initial program 93.3%

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

   2. Taylor expanded in c around inf 31.5%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{-48}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-44}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+86}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \end{array} \]

Alternative 10: 59.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+26} \lor \neg \left(y \leq 4 \cdot 10^{+52}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= y -1.42e+26) (not (<= y 4e+52)))
   (+ c (* x y))
   (+ c (* 0.0625 (* t z)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y <= -1.42e+26) || !(y <= 4e+52)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (0.0625 * (t * z));
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
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 <= (-1.42d+26)) .or. (.not. (y <= 4d+52))) then
        tmp = c + (x * y)
    else
        tmp = c + (0.0625d0 * (t * z))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y <= -1.42e+26) || !(y <= 4e+52)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (0.0625 * (t * z));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (y <= -1.42e+26) or not (y <= 4e+52):
		tmp = c + (x * y)
	else:
		tmp = c + (0.0625 * (t * z))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((y <= -1.42e+26) || !(y <= 4e+52))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(0.0625 * Float64(t * z)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((y <= -1.42e+26) || ~((y <= 4e+52)))
		tmp = c + (x * y);
	else
		tmp = c + (0.0625 * (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[y, -1.42e+26], N[Not[LessEqual[y, 4e+52]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.42e26 or 4e52 < y

   1. Initial program 95.1%

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

   2. Taylor expanded in x around inf 65.7%

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

   if -1.42e26 < y < 4e52

   1. Initial program 98.5%

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

   2. Taylor expanded in z around inf 61.9%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+26} \lor \neg \left(y \leq 4 \cdot 10^{+52}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \end{array} \]

Alternative 11: 36.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq -1.02 \cdot 10^{+127}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{-29}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -1.02e+127) c (if (<= c 6.6e-29) (* x y) c)))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -1.02e+127) {
		tmp = c;
	} else if (c <= 6.6e-29) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
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 (c <= (-1.02d+127)) then
        tmp = c
    else if (c <= 6.6d-29) then
        tmp = x * y
    else
        tmp = c
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -1.02e+127) {
		tmp = c;
	} else if (c <= 6.6e-29) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -1.02e+127:
		tmp = c
	elif c <= 6.6e-29:
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -1.02e+127)
		tmp = c;
	elseif (c <= 6.6e-29)
		tmp = Float64(x * y);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -1.02e+127)
		tmp = c;
	elseif (c <= 6.6e-29)
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -1.02e+127], c, If[LessEqual[c, 6.6e-29], N[(x * y), $MachinePrecision], c]]

Derivation

1. Split input into 2 regimes

2. if c < -1.02e127 or 6.60000000000000055e-29 < c

   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 c around inf 48.7%

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

   if -1.02e127 < c < 6.60000000000000055e-29

   1. Initial program 98.0%

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

   2. Taylor expanded in x around inf 40.6%

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

   3. Taylor expanded in y around inf 35.2%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.02 \cdot 10^{+127}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{-29}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 12: 23.0% accurate, 17.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ c \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 c)

C

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

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
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

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

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b, c):
	return c

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b, c)
	return c
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp = code(x, y, z, t, a, b, c)
	tmp = c;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
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 25.8%

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

3. Final simplification 25.8%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023174 
(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))