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

Percentage Accurate: 97.9% → 99.0%

Time: 15.5s

Alternatives: 14

Speedup: 1.0×

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

• 33.8% 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: 99.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. associate-+l- 97.3%

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

   2. +-commutative 97.3%

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

   3. associate--l+ 97.3%

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

   4. associate-*l/ 97.3%

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

   5. *-commutative 97.3%

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

   6. fma-def 98.0%

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

   7. fma-neg 98.8%

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

   8. neg-sub0 98.8%

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

   9. associate-+l- 98.8%

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

   10. neg-sub0 98.8%

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

   11. +-commutative 98.8%

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

   12. unsub-neg 98.8%

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

   13. *-commutative 98.8%

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

   14. associate-*r/ 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 2: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in a around 0 14.3%

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

   3. Taylor expanded in c around 0 14.3%

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

      1. fma-def 57.1%

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

   5. Applied egg-rr 57.1%

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

4. Final simplification 98.8%

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

Alternative 3: 98.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. associate-+l- 97.3%

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

   2. sub-neg 97.3%

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

   3. neg-mul-1 97.3%

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

   4. metadata-eval 97.3%

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

   5. metadata-eval 97.3%

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

   6. cancel-sign-sub-inv 97.3%

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

   7. fma-def 98.4%

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

   8. associate-/l* 98.4%

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

   9. metadata-eval 98.4%

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

   10. *-lft-identity 98.4%

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

   11. associate-/l* 98.3%

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

3. Simplified 98.3%

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

4. Final simplification 98.3%

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

Alternative 4: 65.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + z \cdot \left(t \cdot 0.0625\right)\\ t_2 := c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+159}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-68}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+149}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* z (* t 0.0625)))) (t_2 (+ c (* b (* a -0.25)))))
   (if (<= (* b a) -5e+159)
     t_2
     (if (<= (* b a) -1e-21)
       t_1
       (if (<= (* b a) -2e-68)
         (+ c (* x y))
         (if (<= (* b a) 1e-150)
           t_1
           (if (<= (* b a) 2e+149) (+ (* 0.0625 (* t z)) (* x y)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (z * (t * 0.0625));
	double t_2 = c + (b * (a * -0.25));
	double tmp;
	if ((b * a) <= -5e+159) {
		tmp = t_2;
	} else if ((b * a) <= -1e-21) {
		tmp = t_1;
	} else if ((b * a) <= -2e-68) {
		tmp = c + (x * y);
	} else if ((b * a) <= 1e-150) {
		tmp = t_1;
	} else if ((b * a) <= 2e+149) {
		tmp = (0.0625 * (t * z)) + (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (z * (t * 0.0625d0))
    t_2 = c + (b * (a * (-0.25d0)))
    if ((b * a) <= (-5d+159)) then
        tmp = t_2
    else if ((b * a) <= (-1d-21)) then
        tmp = t_1
    else if ((b * a) <= (-2d-68)) then
        tmp = c + (x * y)
    else if ((b * a) <= 1d-150) then
        tmp = t_1
    else if ((b * a) <= 2d+149) then
        tmp = (0.0625d0 * (t * z)) + (x * y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (z * (t * 0.0625));
	double t_2 = c + (b * (a * -0.25));
	double tmp;
	if ((b * a) <= -5e+159) {
		tmp = t_2;
	} else if ((b * a) <= -1e-21) {
		tmp = t_1;
	} else if ((b * a) <= -2e-68) {
		tmp = c + (x * y);
	} else if ((b * a) <= 1e-150) {
		tmp = t_1;
	} else if ((b * a) <= 2e+149) {
		tmp = (0.0625 * (t * z)) + (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (z * (t * 0.0625))
	t_2 = c + (b * (a * -0.25))
	tmp = 0
	if (b * a) <= -5e+159:
		tmp = t_2
	elif (b * a) <= -1e-21:
		tmp = t_1
	elif (b * a) <= -2e-68:
		tmp = c + (x * y)
	elif (b * a) <= 1e-150:
		tmp = t_1
	elif (b * a) <= 2e+149:
		tmp = (0.0625 * (t * z)) + (x * y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(z * Float64(t * 0.0625)))
	t_2 = Float64(c + Float64(b * Float64(a * -0.25)))
	tmp = 0.0
	if (Float64(b * a) <= -5e+159)
		tmp = t_2;
	elseif (Float64(b * a) <= -1e-21)
		tmp = t_1;
	elseif (Float64(b * a) <= -2e-68)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(b * a) <= 1e-150)
		tmp = t_1;
	elseif (Float64(b * a) <= 2e+149)
		tmp = Float64(Float64(0.0625 * Float64(t * z)) + Float64(x * y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (z * (t * 0.0625));
	t_2 = c + (b * (a * -0.25));
	tmp = 0.0;
	if ((b * a) <= -5e+159)
		tmp = t_2;
	elseif ((b * a) <= -1e-21)
		tmp = t_1;
	elseif ((b * a) <= -2e-68)
		tmp = c + (x * y);
	elseif ((b * a) <= 1e-150)
		tmp = t_1;
	elseif ((b * a) <= 2e+149)
		tmp = (0.0625 * (t * z)) + (x * y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -5e+159], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -1e-21], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -2e-68], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 1e-150], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 2e+149], N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -5.00000000000000003e159 or 2.0000000000000001e149 < (*.f64 a b)

   1. Initial program 92.8%

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

   2. Taylor expanded in a around inf 85.9%

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

      1. *-commutative 85.9%

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

      2. *-commutative 85.9%

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

      3. associate-*r* 85.9%

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

   4. Simplified 85.9%

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

   if -5.00000000000000003e159 < (*.f64 a b) < -9.99999999999999908e-22 or -2.00000000000000013e-68 < (*.f64 a b) < 1.00000000000000001e-150

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 71.1%

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

      1. *-commutative 71.1%

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

      2. associate-*r* 71.1%

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

      3. *-commutative 71.1%

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

      4. associate-*l* 71.1%

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

   4. Simplified 71.1%

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

   if -9.99999999999999908e-22 < (*.f64 a b) < -2.00000000000000013e-68

   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 84.2%

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

   if 1.00000000000000001e-150 < (*.f64 a b) < 2.0000000000000001e149

   1. Initial program 98.1%

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

   2. Taylor expanded in a around 0 83.1%

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

   3. Taylor expanded in c around 0 73.8%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+159}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-21}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-68}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 10^{-150}:\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+149}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 5: 86.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+159} \lor \neg \left(b \cdot a \leq 2 \cdot 10^{+149}\right):\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -5e+159) (not (<= (* b a) 2e+149)))
   (+ c (* b (* a -0.25)))
   (+ c (+ (* 0.0625 (* t z)) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -5e+159) || !((b * a) <= 2e+149)) {
		tmp = c + (b * (a * -0.25));
	} else {
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((b * a) <= (-5d+159)) .or. (.not. ((b * a) <= 2d+149))) then
        tmp = c + (b * (a * (-0.25d0)))
    else
        tmp = c + ((0.0625d0 * (t * z)) + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -5e+159) || !((b * a) <= 2e+149)) {
		tmp = c + (b * (a * -0.25));
	} else {
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((b * a) <= -5e+159) or not ((b * a) <= 2e+149):
		tmp = c + (b * (a * -0.25))
	else:
		tmp = c + ((0.0625 * (t * z)) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(b * a) <= -5e+159) || !(Float64(b * a) <= 2e+149))
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	else
		tmp = Float64(c + Float64(Float64(0.0625 * Float64(t * z)) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((b * a) <= -5e+159) || ~(((b * a) <= 2e+149)))
		tmp = c + (b * (a * -0.25));
	else
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -5e+159], N[Not[LessEqual[N[(b * a), $MachinePrecision], 2e+149]], $MachinePrecision]], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.00000000000000003e159 or 2.0000000000000001e149 < (*.f64 a b)

   1. Initial program 92.8%

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

   2. Taylor expanded in a around inf 85.9%

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

      1. *-commutative 85.9%

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

      2. *-commutative 85.9%

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

      3. associate-*r* 85.9%

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

   4. Simplified 85.9%

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

   if -5.00000000000000003e159 < (*.f64 a b) < 2.0000000000000001e149

   1. Initial program 98.9%

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

   2. Taylor expanded in a around 0 90.1%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+159} \lor \neg \left(b \cdot a \leq 2 \cdot 10^{+149}\right):\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \end{array} \]

Alternative 6: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+159} \lor \neg \left(b \cdot a \leq 2 \cdot 10^{+130}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -5e+159) (not (<= (* b a) 2e+130)))
   (- (+ c (* x y)) (* (* b a) 0.25))
   (+ c (+ (* 0.0625 (* t z)) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -5e+159) || !((b * a) <= 2e+130)) {
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	} else {
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((b * a) <= (-5d+159)) .or. (.not. ((b * a) <= 2d+130))) then
        tmp = (c + (x * y)) - ((b * a) * 0.25d0)
    else
        tmp = c + ((0.0625d0 * (t * z)) + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -5e+159) || !((b * a) <= 2e+130)) {
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	} else {
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((b * a) <= -5e+159) or not ((b * a) <= 2e+130):
		tmp = (c + (x * y)) - ((b * a) * 0.25)
	else:
		tmp = c + ((0.0625 * (t * z)) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(b * a) <= -5e+159) || !(Float64(b * a) <= 2e+130))
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(b * a) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(0.0625 * Float64(t * z)) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((b * a) <= -5e+159) || ~(((b * a) <= 2e+130)))
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	else
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -5e+159], N[Not[LessEqual[N[(b * a), $MachinePrecision], 2e+130]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.00000000000000003e159 or 2.0000000000000001e130 < (*.f64 a b)

   1. Initial program 93.0%

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

      1. associate-+l- 93.0%

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

      2. sub-neg 93.0%

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

      3. neg-mul-1 93.0%

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

      4. metadata-eval 93.0%

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

      5. metadata-eval 93.0%

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

      6. cancel-sign-sub-inv 93.0%

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

      7. fma-def 94.4%

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

      8. associate-/l* 94.4%

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

      9. metadata-eval 94.4%

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

      10. *-lft-identity 94.4%

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

      11. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in z around 0 87.6%

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

   if -5.00000000000000003e159 < (*.f64 a b) < 2.0000000000000001e130

   1. Initial program 98.9%

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

   2. Taylor expanded in a around 0 90.6%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+159} \lor \neg \left(b \cdot a \leq 2 \cdot 10^{+130}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \end{array} \]

Alternative 7: 39.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-301}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+29}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* t z))))
   (if (<= y -7e+36)
     (* x y)
     (if (<= y -3.1e-58)
       t_1
       (if (<= y -1.7e-301)
         c
         (if (<= y 1.8e-20)
           t_1
           (if (<= y 4.2e+29) c (if (<= y 4.8e+149) t_1 (* x y)))))))))

C

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 (y <= -7e+36) {
		tmp = x * y;
	} else if (y <= -3.1e-58) {
		tmp = t_1;
	} else if (y <= -1.7e-301) {
		tmp = c;
	} else if (y <= 1.8e-20) {
		tmp = t_1;
	} else if (y <= 4.2e+29) {
		tmp = c;
	} else if (y <= 4.8e+149) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (t * z)
    if (y <= (-7d+36)) then
        tmp = x * y
    else if (y <= (-3.1d-58)) then
        tmp = t_1
    else if (y <= (-1.7d-301)) then
        tmp = c
    else if (y <= 1.8d-20) then
        tmp = t_1
    else if (y <= 4.2d+29) then
        tmp = c
    else if (y <= 4.8d+149) then
        tmp = t_1
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (t * z);
	double tmp;
	if (y <= -7e+36) {
		tmp = x * y;
	} else if (y <= -3.1e-58) {
		tmp = t_1;
	} else if (y <= -1.7e-301) {
		tmp = c;
	} else if (y <= 1.8e-20) {
		tmp = t_1;
	} else if (y <= 4.2e+29) {
		tmp = c;
	} else if (y <= 4.8e+149) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (t * z)
	tmp = 0
	if y <= -7e+36:
		tmp = x * y
	elif y <= -3.1e-58:
		tmp = t_1
	elif y <= -1.7e-301:
		tmp = c
	elif y <= 1.8e-20:
		tmp = t_1
	elif y <= 4.2e+29:
		tmp = c
	elif y <= 4.8e+149:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(t * z))
	tmp = 0.0
	if (y <= -7e+36)
		tmp = Float64(x * y);
	elseif (y <= -3.1e-58)
		tmp = t_1;
	elseif (y <= -1.7e-301)
		tmp = c;
	elseif (y <= 1.8e-20)
		tmp = t_1;
	elseif (y <= 4.2e+29)
		tmp = c;
	elseif (y <= 4.8e+149)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (t * z);
	tmp = 0.0;
	if (y <= -7e+36)
		tmp = x * y;
	elseif (y <= -3.1e-58)
		tmp = t_1;
	elseif (y <= -1.7e-301)
		tmp = c;
	elseif (y <= 1.8e-20)
		tmp = t_1;
	elseif (y <= 4.2e+29)
		tmp = c;
	elseif (y <= 4.8e+149)
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+36], N[(x * y), $MachinePrecision], If[LessEqual[y, -3.1e-58], t$95$1, If[LessEqual[y, -1.7e-301], c, If[LessEqual[y, 1.8e-20], t$95$1, If[LessEqual[y, 4.2e+29], c, If[LessEqual[y, 4.8e+149], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.9999999999999996e36 or 4.80000000000000024e149 < y

   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 a around 0 75.0%

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

   3. Taylor expanded in c around 0 63.4%

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

   4. Taylor expanded in y around inf 45.0%

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

   if -6.9999999999999996e36 < y < -3.0999999999999999e-58 or -1.7000000000000001e-301 < y < 1.79999999999999987e-20 or 4.2000000000000003e29 < y < 4.80000000000000024e149

   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 a around 0 71.9%

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

   3. Taylor expanded in c around 0 50.9%

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

   4. Taylor expanded in y around 0 39.0%

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

   if -3.0999999999999999e-58 < y < -1.7000000000000001e-301 or 1.79999999999999987e-20 < y < 4.2000000000000003e29

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. cancel-sign-sub-inv 100.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 99.9%

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

      9. metadata-eval 99.9%

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

      10. *-lft-identity 99.9%

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

      11. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in c around inf 37.9%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+36}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-58}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-301}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-20}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+29}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+149}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 8: 39.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+35}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-196}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+28}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* t z))))
   (if (<= y -1.85e+35)
     (* x y)
     (if (<= y -7e-69)
       t_1
       (if (<= y -1.6e-196)
         (* b (* a -0.25))
         (if (<= y 1.05e-19)
           t_1
           (if (<= y 4.5e+28) c (if (<= y 5e+149) t_1 (* x y)))))))))

C

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 (y <= -1.85e+35) {
		tmp = x * y;
	} else if (y <= -7e-69) {
		tmp = t_1;
	} else if (y <= -1.6e-196) {
		tmp = b * (a * -0.25);
	} else if (y <= 1.05e-19) {
		tmp = t_1;
	} else if (y <= 4.5e+28) {
		tmp = c;
	} else if (y <= 5e+149) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (t * z)
    if (y <= (-1.85d+35)) then
        tmp = x * y
    else if (y <= (-7d-69)) then
        tmp = t_1
    else if (y <= (-1.6d-196)) then
        tmp = b * (a * (-0.25d0))
    else if (y <= 1.05d-19) then
        tmp = t_1
    else if (y <= 4.5d+28) then
        tmp = c
    else if (y <= 5d+149) then
        tmp = t_1
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (t * z);
	double tmp;
	if (y <= -1.85e+35) {
		tmp = x * y;
	} else if (y <= -7e-69) {
		tmp = t_1;
	} else if (y <= -1.6e-196) {
		tmp = b * (a * -0.25);
	} else if (y <= 1.05e-19) {
		tmp = t_1;
	} else if (y <= 4.5e+28) {
		tmp = c;
	} else if (y <= 5e+149) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (t * z)
	tmp = 0
	if y <= -1.85e+35:
		tmp = x * y
	elif y <= -7e-69:
		tmp = t_1
	elif y <= -1.6e-196:
		tmp = b * (a * -0.25)
	elif y <= 1.05e-19:
		tmp = t_1
	elif y <= 4.5e+28:
		tmp = c
	elif y <= 5e+149:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(t * z))
	tmp = 0.0
	if (y <= -1.85e+35)
		tmp = Float64(x * y);
	elseif (y <= -7e-69)
		tmp = t_1;
	elseif (y <= -1.6e-196)
		tmp = Float64(b * Float64(a * -0.25));
	elseif (y <= 1.05e-19)
		tmp = t_1;
	elseif (y <= 4.5e+28)
		tmp = c;
	elseif (y <= 5e+149)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (t * z);
	tmp = 0.0;
	if (y <= -1.85e+35)
		tmp = x * y;
	elseif (y <= -7e-69)
		tmp = t_1;
	elseif (y <= -1.6e-196)
		tmp = b * (a * -0.25);
	elseif (y <= 1.05e-19)
		tmp = t_1;
	elseif (y <= 4.5e+28)
		tmp = c;
	elseif (y <= 5e+149)
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e+35], N[(x * y), $MachinePrecision], If[LessEqual[y, -7e-69], t$95$1, If[LessEqual[y, -1.6e-196], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-19], t$95$1, If[LessEqual[y, 4.5e+28], c, If[LessEqual[y, 5e+149], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.85e35 or 4.9999999999999999e149 < y

   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 a around 0 75.2%

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

   3. Taylor expanded in c around 0 63.8%

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

   4. Taylor expanded in y around inf 44.6%

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

   if -1.85e35 < y < -7.0000000000000003e-69 or -1.6e-196 < y < 1.0499999999999999e-19 or 4.4999999999999997e28 < y < 4.9999999999999999e149

   1. Initial program 99.2%

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

   2. Taylor expanded in a around 0 73.9%

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

   3. Taylor expanded in c around 0 47.0%

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

   4. Taylor expanded in y around 0 37.6%

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

   if -7.0000000000000003e-69 < y < -1.6e-196

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. cancel-sign-sub-inv 100.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 100.0%

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

      9. metadata-eval 100.0%

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

      10. *-lft-identity 100.0%

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

      11. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 73.7%

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

   5. Taylor expanded in c around 0 52.2%

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

   6. Taylor expanded in y around 0 40.4%

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

      1. associate-*r* 40.4%

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

   8. Simplified 40.4%

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

   if 1.0499999999999999e-19 < y < 4.4999999999999997e28

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. cancel-sign-sub-inv 100.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 99.8%

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

      9. metadata-eval 99.8%

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

      10. *-lft-identity 99.8%

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

      11. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in c around inf 57.2%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+35}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-69}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-196}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-19}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+28}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+149}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 9: 53.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + b \cdot \left(a \cdot -0.25\right)\\ t_2 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{+164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-50}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-236}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* b (* a -0.25)))) (t_2 (* 0.0625 (* t z))))
   (if (<= z -2.45e+164)
     t_2
     (if (<= z -3.4e-50)
       (+ c (* x y))
       (if (<= z -2e-206)
         t_1
         (if (<= z -1.3e-236) (* x y) (if (<= z 7e+15) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double t_2 = 0.0625 * (t * z);
	double tmp;
	if (z <= -2.45e+164) {
		tmp = t_2;
	} else if (z <= -3.4e-50) {
		tmp = c + (x * y);
	} else if (z <= -2e-206) {
		tmp = t_1;
	} else if (z <= -1.3e-236) {
		tmp = x * y;
	} else if (z <= 7e+15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (b * (a * (-0.25d0)))
    t_2 = 0.0625d0 * (t * z)
    if (z <= (-2.45d+164)) then
        tmp = t_2
    else if (z <= (-3.4d-50)) then
        tmp = c + (x * y)
    else if (z <= (-2d-206)) then
        tmp = t_1
    else if (z <= (-1.3d-236)) then
        tmp = x * y
    else if (z <= 7d+15) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double t_2 = 0.0625 * (t * z);
	double tmp;
	if (z <= -2.45e+164) {
		tmp = t_2;
	} else if (z <= -3.4e-50) {
		tmp = c + (x * y);
	} else if (z <= -2e-206) {
		tmp = t_1;
	} else if (z <= -1.3e-236) {
		tmp = x * y;
	} else if (z <= 7e+15) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (b * (a * -0.25))
	t_2 = 0.0625 * (t * z)
	tmp = 0
	if z <= -2.45e+164:
		tmp = t_2
	elif z <= -3.4e-50:
		tmp = c + (x * y)
	elif z <= -2e-206:
		tmp = t_1
	elif z <= -1.3e-236:
		tmp = x * y
	elif z <= 7e+15:
		tmp = t_1
	else:
		tmp = t_2
	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(0.0625 * Float64(t * z))
	tmp = 0.0
	if (z <= -2.45e+164)
		tmp = t_2;
	elseif (z <= -3.4e-50)
		tmp = Float64(c + Float64(x * y));
	elseif (z <= -2e-206)
		tmp = t_1;
	elseif (z <= -1.3e-236)
		tmp = Float64(x * y);
	elseif (z <= 7e+15)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (b * (a * -0.25));
	t_2 = 0.0625 * (t * z);
	tmp = 0.0;
	if (z <= -2.45e+164)
		tmp = t_2;
	elseif (z <= -3.4e-50)
		tmp = c + (x * y);
	elseif (z <= -2e-206)
		tmp = t_1;
	elseif (z <= -1.3e-236)
		tmp = x * y;
	elseif (z <= 7e+15)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.45e+164], t$95$2, If[LessEqual[z, -3.4e-50], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e-206], t$95$1, If[LessEqual[z, -1.3e-236], N[(x * y), $MachinePrecision], If[LessEqual[z, 7e+15], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.4499999999999999e164 or 7e15 < z

   1. Initial program 96.2%

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

   2. Taylor expanded in a around 0 78.6%

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

   3. Taylor expanded in c around 0 64.0%

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

   4. Taylor expanded in y around 0 56.3%

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

   if -2.4499999999999999e164 < z < -3.40000000000000014e-50

   1. Initial program 97.7%

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

   2. Taylor expanded in x around inf 61.7%

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

   if -3.40000000000000014e-50 < z < -2.00000000000000006e-206 or -1.3e-236 < z < 7e15

   1. Initial program 98.1%

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

   2. Taylor expanded in a around inf 62.4%

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

      1. *-commutative 62.4%

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

      2. *-commutative 62.4%

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

      3. associate-*r* 62.4%

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

   4. Simplified 62.4%

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

   if -2.00000000000000006e-206 < z < -1.3e-236

   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 52.2%

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

   3. Taylor expanded in c around 0 50.9%

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

   4. Taylor expanded in y around inf 26.4%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+164}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-50}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-206}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-236}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+15}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \end{array} \]

Alternative 10: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + ((((t * z) / 16.0) + (x * y)) - ((b * a) / 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 + ((((t * z) / 16.0d0) + (x * y)) - ((b * a) / 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 + ((((t * z) / 16.0) + (x * y)) - ((b * a) / 4.0));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

2. Final simplification 97.3%

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

Alternative 11: 50.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-173}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-39}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* t z))))
   (if (<= z -1.22e+166)
     t_1
     (if (<= z 1.2e-173)
       (+ c (* x y))
       (if (<= z 1.85e-39) (* b (* a -0.25)) t_1)))))

C

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 (z <= -1.22e+166) {
		tmp = t_1;
	} else if (z <= 1.2e-173) {
		tmp = c + (x * y);
	} else if (z <= 1.85e-39) {
		tmp = b * (a * -0.25);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (t * z)
    if (z <= (-1.22d+166)) then
        tmp = t_1
    else if (z <= 1.2d-173) then
        tmp = c + (x * y)
    else if (z <= 1.85d-39) then
        tmp = b * (a * (-0.25d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (t * z);
	double tmp;
	if (z <= -1.22e+166) {
		tmp = t_1;
	} else if (z <= 1.2e-173) {
		tmp = c + (x * y);
	} else if (z <= 1.85e-39) {
		tmp = b * (a * -0.25);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (t * z)
	tmp = 0
	if z <= -1.22e+166:
		tmp = t_1
	elif z <= 1.2e-173:
		tmp = c + (x * y)
	elif z <= 1.85e-39:
		tmp = b * (a * -0.25)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(t * z))
	tmp = 0.0
	if (z <= -1.22e+166)
		tmp = t_1;
	elseif (z <= 1.2e-173)
		tmp = Float64(c + Float64(x * y));
	elseif (z <= 1.85e-39)
		tmp = Float64(b * Float64(a * -0.25));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (t * z);
	tmp = 0.0;
	if (z <= -1.22e+166)
		tmp = t_1;
	elseif (z <= 1.2e-173)
		tmp = c + (x * y);
	elseif (z <= 1.85e-39)
		tmp = b * (a * -0.25);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.22e+166], t$95$1, If[LessEqual[z, 1.2e-173], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e-39], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.21999999999999993e166 or 1.85000000000000007e-39 < z

   1. Initial program 95.8%

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

   2. Taylor expanded in a around 0 77.8%

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

   3. Taylor expanded in c around 0 62.5%

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

   4. Taylor expanded in y around 0 51.6%

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

   if -1.21999999999999993e166 < z < 1.20000000000000008e-173

   1. Initial program 98.1%

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

   2. Taylor expanded in x around inf 59.6%

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

   if 1.20000000000000008e-173 < z < 1.85000000000000007e-39

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. sub-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. cancel-sign-sub-inv 100.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 100.0%

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

      9. metadata-eval 100.0%

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

      10. *-lft-identity 100.0%

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

      11. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 95.3%

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

   5. Taylor expanded in c around 0 75.2%

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

   6. Taylor expanded in y around 0 49.7%

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

      1. associate-*r* 49.7%

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

   8. Simplified 49.7%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+166}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-173}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-39}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \end{array} \]

Alternative 12: 58.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+144} \lor \neg \left(z \leq 1.02 \cdot 10^{-27}\right):\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.3e+144) (not (<= z 1.02e-27)))
   (+ c (* z (* t 0.0625)))
   (+ c (* b (* a -0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.3e+144) || !(z <= 1.02e-27)) {
		tmp = c + (z * (t * 0.0625));
	} else {
		tmp = c + (b * (a * -0.25));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-1.3d+144)) .or. (.not. (z <= 1.02d-27))) then
        tmp = c + (z * (t * 0.0625d0))
    else
        tmp = c + (b * (a * (-0.25d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.3e+144) || !(z <= 1.02e-27)) {
		tmp = c + (z * (t * 0.0625));
	} else {
		tmp = c + (b * (a * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.3e+144) or not (z <= 1.02e-27):
		tmp = c + (z * (t * 0.0625))
	else:
		tmp = c + (b * (a * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.3e+144) || !(z <= 1.02e-27))
		tmp = Float64(c + Float64(z * Float64(t * 0.0625)));
	else
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.3e+144) || ~((z <= 1.02e-27)))
		tmp = c + (z * (t * 0.0625));
	else
		tmp = c + (b * (a * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.3e+144], N[Not[LessEqual[z, 1.02e-27]], $MachinePrecision]], N[(c + N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2999999999999999e144 or 1.02000000000000002e-27 < z

   1. Initial program 95.8%

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

   2. Taylor expanded in z around inf 67.3%

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

      1. *-commutative 67.3%

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

      2. associate-*r* 67.3%

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

      3. *-commutative 67.3%

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

      4. associate-*l* 67.3%

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

   4. Simplified 67.3%

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

   if -1.2999999999999999e144 < z < 1.02000000000000002e-27

   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 a around inf 61.1%

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

      1. *-commutative 61.1%

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

      2. *-commutative 61.1%

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

      3. associate-*r* 61.1%

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

   4. Simplified 61.1%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+144} \lor \neg \left(z \leq 1.02 \cdot 10^{-27}\right):\\ \;\;\;\;c + z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 13: 36.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+39}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+96}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -4.2e+39) (* x y) (if (<= y 3.2e+96) c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -4.2e+39) {
		tmp = x * y;
	} else if (y <= 3.2e+96) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= (-4.2d+39)) then
        tmp = x * y
    else if (y <= 3.2d+96) then
        tmp = c
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -4.2e+39) {
		tmp = x * y;
	} else if (y <= 3.2e+96) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -4.2e+39:
		tmp = x * y
	elif y <= 3.2e+96:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -4.2e+39)
		tmp = Float64(x * y);
	elseif (y <= 3.2e+96)
		tmp = c;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -4.2e+39)
		tmp = x * y;
	elseif (y <= 3.2e+96)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -4.2e+39], N[(x * y), $MachinePrecision], If[LessEqual[y, 3.2e+96], c, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1999999999999997e39 or 3.20000000000000006e96 < y

   1. Initial program 93.9%

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

   2. Taylor expanded in a around 0 76.0%

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

   3. Taylor expanded in c around 0 66.2%

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

   4. Taylor expanded in y around inf 46.4%

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

   if -4.1999999999999997e39 < y < 3.20000000000000006e96

   1. Initial program 99.4%

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

      1. associate-+l- 99.4%

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

      2. sub-neg 99.4%

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

      3. neg-mul-1 99.4%

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

      4. metadata-eval 99.4%

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

      5. metadata-eval 99.4%

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

      6. cancel-sign-sub-inv 99.4%

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

      7. fma-def 99.4%

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

      8. associate-/l* 99.3%

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

      9. metadata-eval 99.3%

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

      10. *-lft-identity 99.3%

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

      11. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in c around inf 30.5%

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

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+39}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+96}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 14: 21.7% 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 97.3%

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

   1. associate-+l- 97.3%

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

   2. sub-neg 97.3%

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

   3. neg-mul-1 97.3%

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

   4. metadata-eval 97.3%

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

   5. metadata-eval 97.3%

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

   6. cancel-sign-sub-inv 97.3%

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

   7. fma-def 98.4%

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

   8. associate-/l* 98.4%

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

   9. metadata-eval 98.4%

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

   10. *-lft-identity 98.4%

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

   11. associate-/l* 98.3%

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

3. Simplified 98.3%

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

4. Taylor expanded in c around inf 23.5%

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

5. Final simplification 23.5%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023187 
(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))