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

Percentage Accurate: 97.7% → 98.8%

Time: 8.3s

Alternatives: 15

Speedup: 0.5×

• 32.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.8% 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 98.4%

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

   7. fma-neg 99.6%

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

   8. neg-sub0 99.6%

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

   9. associate-+l- 99.6%

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

   10. neg-sub0 99.6%

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

   11. +-commutative 99.6%

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

   12. unsub-neg 99.6%

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

   13. *-commutative 99.6%

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

   14. associate-*r/ 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 98.7% accurate, 0.1× speedup

Math

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

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 (fma b (* a -0.25) c)))))

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, fma(b, (a * -0.25), c));
	}
	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, fma(b, Float64(a * -0.25), c));
	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[(b * N[(a * -0.25), $MachinePrecision] + c), $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 z around 0 42.9%

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

      1. +-commutative 42.9%

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

      2. *-commutative 42.9%

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

      3. *-commutative 42.9%

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

      4. *-commutative 42.9%

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

      5. associate-*r* 42.9%

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

      6. associate-+r- 42.9%

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

      7. *-commutative 42.9%

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

      8. fma-def 85.7%

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

      9. sub-neg 85.7%

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

      10. +-commutative 85.7%

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

      11. distribute-rgt-neg-in 85.7%

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

      12. fma-def 85.7%

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

      13. distribute-rgt-neg-in 85.7%

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

      14. metadata-eval 85.7%

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

   4. Simplified 85.7%

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

4. Final simplification 99.6%

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

Alternative 3: 98.1% 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 97.7%

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

   8. associate-/l* 97.6%

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

   9. metadata-eval 97.6%

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

   10. *-lft-identity 97.6%

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

   11. associate-/l* 97.6%

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

3. Simplified 97.6%

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

4. Final simplification 97.6%

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

Alternative 4: 98.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in a around inf 58.7%

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

      1. *-commutative 58.7%

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

   4. Simplified 58.7%

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

4. Final simplification 98.9%

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

Alternative 5: 62.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot -0.25\\ \mathbf{if}\;b \cdot a \leq -8 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 7.3 \cdot 10^{-38}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 3.1 \cdot 10^{+272}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) -0.25)))
   (if (<= (* b a) -8e+140)
     t_1
     (if (<= (* b a) 7.3e-38)
       (+ c (* x y))
       (if (<= (* b a) 3.1e+272) (+ c (* t (* z 0.0625))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -8e+140) {
		tmp = t_1;
	} else if ((b * a) <= 7.3e-38) {
		tmp = c + (x * y);
	} else if ((b * a) <= 3.1e+272) {
		tmp = c + (t * (z * 0.0625));
	} 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 = (b * a) * (-0.25d0)
    if ((b * a) <= (-8d+140)) then
        tmp = t_1
    else if ((b * a) <= 7.3d-38) then
        tmp = c + (x * y)
    else if ((b * a) <= 3.1d+272) then
        tmp = c + (t * (z * 0.0625d0))
    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 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -8e+140) {
		tmp = t_1;
	} else if ((b * a) <= 7.3e-38) {
		tmp = c + (x * y);
	} else if ((b * a) <= 3.1e+272) {
		tmp = c + (t * (z * 0.0625));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * -0.25
	tmp = 0
	if (b * a) <= -8e+140:
		tmp = t_1
	elif (b * a) <= 7.3e-38:
		tmp = c + (x * y)
	elif (b * a) <= 3.1e+272:
		tmp = c + (t * (z * 0.0625))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b * a) * -0.25)
	tmp = 0.0
	if (Float64(b * a) <= -8e+140)
		tmp = t_1;
	elseif (Float64(b * a) <= 7.3e-38)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(b * a) <= 3.1e+272)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b * a) * -0.25;
	tmp = 0.0;
	if ((b * a) <= -8e+140)
		tmp = t_1;
	elseif ((b * a) <= 7.3e-38)
		tmp = c + (x * y);
	elseif ((b * a) <= 3.1e+272)
		tmp = c + (t * (z * 0.0625));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -8e+140], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 7.3e-38], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 3.1e+272], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -8.00000000000000047e140 or 3.09999999999999972e272 < (*.f64 a b)

   1. Initial program 89.6%

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

   2. Taylor expanded in z around 0 86.0%

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

      1. +-commutative 86.0%

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

      2. *-commutative 86.0%

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

      3. *-commutative 86.0%

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

      4. *-commutative 86.0%

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

      5. associate-*r* 86.0%

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

      6. associate-+r- 86.0%

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

      7. *-commutative 86.0%

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

      8. fma-def 92.2%

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

      9. sub-neg 92.2%

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

      10. +-commutative 92.2%

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

      11. distribute-rgt-neg-in 92.2%

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

      12. fma-def 92.2%

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

      13. distribute-rgt-neg-in 92.2%

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

      14. metadata-eval 92.2%

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

   4. Simplified 92.2%

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

   5. Taylor expanded in b around inf 84.2%

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

   if -8.00000000000000047e140 < (*.f64 a b) < 7.3000000000000001e-38

   1. Initial program 98.7%

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

   2. Taylor expanded in x around inf 67.6%

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

   if 7.3000000000000001e-38 < (*.f64 a b) < 3.09999999999999972e272

   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 60.7%

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

      1. *-commutative 60.7%

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

      2. associate-*r* 60.7%

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

      3. *-commutative 60.7%

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

   4. Simplified 60.7%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -8 \cdot 10^{+140}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq 7.3 \cdot 10^{-38}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 3.1 \cdot 10^{+272}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 6: 85.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot -0.25\\ \mathbf{if}\;b \cdot a \leq -5.2 \cdot 10^{+84}:\\ \;\;\;\;x \cdot y + t_1\\ \mathbf{elif}\;b \cdot a \leq 5.3 \cdot 10^{+272}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) -0.25)))
   (if (<= (* b a) -5.2e+84)
     (+ (* x y) t_1)
     (if (<= (* b a) 5.3e+272) (+ c (+ (* x y) (* 0.0625 (* t z)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -5.2e+84) {
		tmp = (x * y) + t_1;
	} else if ((b * a) <= 5.3e+272) {
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	} 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 = (b * a) * (-0.25d0)
    if ((b * a) <= (-5.2d+84)) then
        tmp = (x * y) + t_1
    else if ((b * a) <= 5.3d+272) then
        tmp = c + ((x * y) + (0.0625d0 * (t * z)))
    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 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -5.2e+84) {
		tmp = (x * y) + t_1;
	} else if ((b * a) <= 5.3e+272) {
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * -0.25
	tmp = 0
	if (b * a) <= -5.2e+84:
		tmp = (x * y) + t_1
	elif (b * a) <= 5.3e+272:
		tmp = c + ((x * y) + (0.0625 * (t * z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b * a) * -0.25)
	tmp = 0.0
	if (Float64(b * a) <= -5.2e+84)
		tmp = Float64(Float64(x * y) + t_1);
	elseif (Float64(b * a) <= 5.3e+272)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(t * z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b * a) * -0.25;
	tmp = 0.0;
	if ((b * a) <= -5.2e+84)
		tmp = (x * y) + t_1;
	elseif ((b * a) <= 5.3e+272)
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -5.2e+84], N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 5.3e+272], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.2000000000000002e84

   1. Initial program 90.2%

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

   2. Taylor expanded in z around 0 83.6%

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

      1. +-commutative 83.6%

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

      2. *-commutative 83.6%

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

      3. *-commutative 83.6%

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

      4. *-commutative 83.6%

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

      5. associate-*r* 83.6%

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

      6. associate-+r- 83.6%

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

      7. *-commutative 83.6%

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

      8. fma-def 88.5%

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

      9. sub-neg 88.5%

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

      10. +-commutative 88.5%

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

      11. distribute-rgt-neg-in 88.5%

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

      12. fma-def 88.5%

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

      13. distribute-rgt-neg-in 88.5%

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

      14. metadata-eval 88.5%

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

   4. Simplified 88.5%

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

   5. Taylor expanded in c around 0 81.2%

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

   if -5.2000000000000002e84 < (*.f64 a b) < 5.30000000000000011e272

   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 89.4%

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

   if 5.30000000000000011e272 < (*.f64 a b)

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 92.9%

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

      1. +-commutative 92.9%

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

      2. *-commutative 92.9%

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

      3. *-commutative 92.9%

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

      4. *-commutative 92.9%

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

      5. associate-*r* 92.9%

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

      6. associate-+r- 92.9%

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

      7. *-commutative 92.9%

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

      8. fma-def 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. fma-def 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in b around inf 100.0%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5.2 \cdot 10^{+84}:\\ \;\;\;\;x \cdot y + \left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq 5.3 \cdot 10^{+272}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 7: 86.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;b \cdot a \leq -3 \cdot 10^{+141}:\\ \;\;\;\;t_1 - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 8 \cdot 10^{+272}:\\ \;\;\;\;c + \left(x \cdot y + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* t z))))
   (if (<= (* b a) -3e+141)
     (- t_1 (* (* b a) 0.25))
     (if (<= (* b a) 8e+272) (+ c (+ (* x y) t_1)) (* (* b a) -0.25)))))

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 ((b * a) <= -3e+141) {
		tmp = t_1 - ((b * a) * 0.25);
	} else if ((b * a) <= 8e+272) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (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) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (t * z)
    if ((b * a) <= (-3d+141)) then
        tmp = t_1 - ((b * a) * 0.25d0)
    else if ((b * a) <= 8d+272) then
        tmp = c + ((x * y) + t_1)
    else
        tmp = (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 t_1 = 0.0625 * (t * z);
	double tmp;
	if ((b * a) <= -3e+141) {
		tmp = t_1 - ((b * a) * 0.25);
	} else if ((b * a) <= 8e+272) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (b * a) * -0.25;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (t * z)
	tmp = 0
	if (b * a) <= -3e+141:
		tmp = t_1 - ((b * a) * 0.25)
	elif (b * a) <= 8e+272:
		tmp = c + ((x * y) + t_1)
	else:
		tmp = (b * a) * -0.25
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(t * z))
	tmp = 0.0
	if (Float64(b * a) <= -3e+141)
		tmp = Float64(t_1 - Float64(Float64(b * a) * 0.25));
	elseif (Float64(b * a) <= 8e+272)
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	else
		tmp = Float64(Float64(b * a) * -0.25);
	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 ((b * a) <= -3e+141)
		tmp = t_1 - ((b * a) * 0.25);
	elseif ((b * a) <= 8e+272)
		tmp = c + ((x * y) + t_1);
	else
		tmp = (b * a) * -0.25;
	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[N[(b * a), $MachinePrecision], -3e+141], N[(t$95$1 - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 8e+272], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.9999999999999999e141

   1. Initial program 88.2%

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

   2. Taylor expanded in x around 0 88.5%

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

   3. Taylor expanded in c around 0 85.8%

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

   if -2.9999999999999999e141 < (*.f64 a b) < 8.0000000000000005e272

   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 88.8%

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

   if 8.0000000000000005e272 < (*.f64 a b)

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 92.9%

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

      1. +-commutative 92.9%

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

      2. *-commutative 92.9%

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

      3. *-commutative 92.9%

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

      4. *-commutative 92.9%

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

      5. associate-*r* 92.9%

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

      6. associate-+r- 92.9%

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

      7. *-commutative 92.9%

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

      8. fma-def 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. fma-def 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in b around inf 100.0%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -3 \cdot 10^{+141}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 8 \cdot 10^{+272}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 8: 36.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+150}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+45}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+18}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-205}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-37}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* t z))))
   (if (<= x -3.1e+150)
     (* x y)
     (if (<= x -6.2e+45)
       (* (* b a) -0.25)
       (if (<= x -1.05e+18)
         c
         (if (<= x -8e-134)
           t_1
           (if (<= x -4.5e-205)
             c
             (if (<= x -5.4e-252) t_1 (if (<= x 3.9e-37) c (* 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 (x <= -3.1e+150) {
		tmp = x * y;
	} else if (x <= -6.2e+45) {
		tmp = (b * a) * -0.25;
	} else if (x <= -1.05e+18) {
		tmp = c;
	} else if (x <= -8e-134) {
		tmp = t_1;
	} else if (x <= -4.5e-205) {
		tmp = c;
	} else if (x <= -5.4e-252) {
		tmp = t_1;
	} else if (x <= 3.9e-37) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (t * z)
    if (x <= (-3.1d+150)) then
        tmp = x * y
    else if (x <= (-6.2d+45)) then
        tmp = (b * a) * (-0.25d0)
    else if (x <= (-1.05d+18)) then
        tmp = c
    else if (x <= (-8d-134)) then
        tmp = t_1
    else if (x <= (-4.5d-205)) then
        tmp = c
    else if (x <= (-5.4d-252)) then
        tmp = t_1
    else if (x <= 3.9d-37) then
        tmp = c
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (t * z);
	double tmp;
	if (x <= -3.1e+150) {
		tmp = x * y;
	} else if (x <= -6.2e+45) {
		tmp = (b * a) * -0.25;
	} else if (x <= -1.05e+18) {
		tmp = c;
	} else if (x <= -8e-134) {
		tmp = t_1;
	} else if (x <= -4.5e-205) {
		tmp = c;
	} else if (x <= -5.4e-252) {
		tmp = t_1;
	} else if (x <= 3.9e-37) {
		tmp = c;
	} 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 x <= -3.1e+150:
		tmp = x * y
	elif x <= -6.2e+45:
		tmp = (b * a) * -0.25
	elif x <= -1.05e+18:
		tmp = c
	elif x <= -8e-134:
		tmp = t_1
	elif x <= -4.5e-205:
		tmp = c
	elif x <= -5.4e-252:
		tmp = t_1
	elif x <= 3.9e-37:
		tmp = c
	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 (x <= -3.1e+150)
		tmp = Float64(x * y);
	elseif (x <= -6.2e+45)
		tmp = Float64(Float64(b * a) * -0.25);
	elseif (x <= -1.05e+18)
		tmp = c;
	elseif (x <= -8e-134)
		tmp = t_1;
	elseif (x <= -4.5e-205)
		tmp = c;
	elseif (x <= -5.4e-252)
		tmp = t_1;
	elseif (x <= 3.9e-37)
		tmp = c;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (t * z);
	tmp = 0.0;
	if (x <= -3.1e+150)
		tmp = x * y;
	elseif (x <= -6.2e+45)
		tmp = (b * a) * -0.25;
	elseif (x <= -1.05e+18)
		tmp = c;
	elseif (x <= -8e-134)
		tmp = t_1;
	elseif (x <= -4.5e-205)
		tmp = c;
	elseif (x <= -5.4e-252)
		tmp = t_1;
	elseif (x <= 3.9e-37)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.1e+150], N[(x * y), $MachinePrecision], If[LessEqual[x, -6.2e+45], N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision], If[LessEqual[x, -1.05e+18], c, If[LessEqual[x, -8e-134], t$95$1, If[LessEqual[x, -4.5e-205], c, If[LessEqual[x, -5.4e-252], t$95$1, If[LessEqual[x, 3.9e-37], c, N[(x * y), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.10000000000000014e150 or 3.8999999999999999e-37 < x

   1. Initial program 94.6%

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

   2. Taylor expanded in z around 0 77.3%

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

      1. +-commutative 77.3%

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

      2. *-commutative 77.3%

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

      3. *-commutative 77.3%

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

      4. *-commutative 77.3%

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

      5. associate-*r* 77.3%

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

      6. associate-+r- 77.3%

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

      7. *-commutative 77.3%

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

      8. fma-def 79.9%

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

      9. sub-neg 79.9%

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

      10. +-commutative 79.9%

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

      11. distribute-rgt-neg-in 79.9%

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

      12. fma-def 79.9%

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

      13. distribute-rgt-neg-in 79.9%

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

      14. metadata-eval 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in y around inf 45.9%

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

   if -3.10000000000000014e150 < x < -6.19999999999999975e45

   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 0 79.1%

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

      1. +-commutative 79.1%

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

      2. *-commutative 79.1%

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

      3. *-commutative 79.1%

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

      4. *-commutative 79.1%

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

      5. associate-*r* 79.1%

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

      6. associate-+r- 79.1%

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

      7. *-commutative 79.1%

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

      8. fma-def 79.1%

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

      9. sub-neg 79.1%

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

      10. +-commutative 79.1%

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

      11. distribute-rgt-neg-in 79.1%

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

      12. fma-def 79.1%

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

      13. distribute-rgt-neg-in 79.1%

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

      14. metadata-eval 79.1%

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

   4. Simplified 79.1%

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

   5. Taylor expanded in b around inf 19.5%

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

   if -6.19999999999999975e45 < x < -1.05e18 or -8.00000000000000032e-134 < x < -4.49999999999999956e-205 or -5.39999999999999962e-252 < x < 3.8999999999999999e-37

   1. Initial program 100.0%

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

   2. Taylor expanded in c around inf 42.9%

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

   if -1.05e18 < x < -8.00000000000000032e-134 or -4.49999999999999956e-205 < x < -5.39999999999999962e-252

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0 85.2%

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

   3. Taylor expanded in t around inf 37.0%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+150}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{+45}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+18}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-134}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-205}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-252}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-37}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 9: 35.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot -0.25\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+150}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.82 \cdot 10^{+37}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-18}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-36}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) -0.25)))
   (if (<= x -3.1e+150)
     (* x y)
     (if (<= x -1.35e+42)
       t_1
       (if (<= x -1.82e+37)
         (* x y)
         (if (<= x -4e-18)
           c
           (if (<= x -5.8e-182) t_1 (if (<= x 2.55e-36) c (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * -0.25;
	double tmp;
	if (x <= -3.1e+150) {
		tmp = x * y;
	} else if (x <= -1.35e+42) {
		tmp = t_1;
	} else if (x <= -1.82e+37) {
		tmp = x * y;
	} else if (x <= -4e-18) {
		tmp = c;
	} else if (x <= -5.8e-182) {
		tmp = t_1;
	} else if (x <= 2.55e-36) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * a) * (-0.25d0)
    if (x <= (-3.1d+150)) then
        tmp = x * y
    else if (x <= (-1.35d+42)) then
        tmp = t_1
    else if (x <= (-1.82d+37)) then
        tmp = x * y
    else if (x <= (-4d-18)) then
        tmp = c
    else if (x <= (-5.8d-182)) then
        tmp = t_1
    else if (x <= 2.55d-36) then
        tmp = c
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * -0.25;
	double tmp;
	if (x <= -3.1e+150) {
		tmp = x * y;
	} else if (x <= -1.35e+42) {
		tmp = t_1;
	} else if (x <= -1.82e+37) {
		tmp = x * y;
	} else if (x <= -4e-18) {
		tmp = c;
	} else if (x <= -5.8e-182) {
		tmp = t_1;
	} else if (x <= 2.55e-36) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * -0.25
	tmp = 0
	if x <= -3.1e+150:
		tmp = x * y
	elif x <= -1.35e+42:
		tmp = t_1
	elif x <= -1.82e+37:
		tmp = x * y
	elif x <= -4e-18:
		tmp = c
	elif x <= -5.8e-182:
		tmp = t_1
	elif x <= 2.55e-36:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b * a) * -0.25)
	tmp = 0.0
	if (x <= -3.1e+150)
		tmp = Float64(x * y);
	elseif (x <= -1.35e+42)
		tmp = t_1;
	elseif (x <= -1.82e+37)
		tmp = Float64(x * y);
	elseif (x <= -4e-18)
		tmp = c;
	elseif (x <= -5.8e-182)
		tmp = t_1;
	elseif (x <= 2.55e-36)
		tmp = c;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b * a) * -0.25;
	tmp = 0.0;
	if (x <= -3.1e+150)
		tmp = x * y;
	elseif (x <= -1.35e+42)
		tmp = t_1;
	elseif (x <= -1.82e+37)
		tmp = x * y;
	elseif (x <= -4e-18)
		tmp = c;
	elseif (x <= -5.8e-182)
		tmp = t_1;
	elseif (x <= 2.55e-36)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[x, -3.1e+150], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.35e+42], t$95$1, If[LessEqual[x, -1.82e+37], N[(x * y), $MachinePrecision], If[LessEqual[x, -4e-18], c, If[LessEqual[x, -5.8e-182], t$95$1, If[LessEqual[x, 2.55e-36], c, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.10000000000000014e150 or -1.35e42 < x < -1.81999999999999998e37 or 2.54999999999999987e-36 < x

   1. Initial program 94.8%

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

   2. Taylor expanded in z around 0 77.8%

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

      1. +-commutative 77.8%

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

      2. *-commutative 77.8%

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

      3. *-commutative 77.8%

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

      4. *-commutative 77.8%

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

      5. associate-*r* 77.8%

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

      6. associate-+r- 77.8%

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

      7. *-commutative 77.8%

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

      8. fma-def 80.5%

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

      9. sub-neg 80.5%

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

      10. +-commutative 80.5%

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

      11. distribute-rgt-neg-in 80.5%

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

      12. fma-def 80.5%

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

      13. distribute-rgt-neg-in 80.5%

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

      14. metadata-eval 80.5%

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

   4. Simplified 80.5%

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

   5. Taylor expanded in y around inf 46.5%

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

   if -3.10000000000000014e150 < x < -1.35e42 or -4.0000000000000003e-18 < x < -5.79999999999999974e-182

   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 z around 0 71.3%

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

      1. +-commutative 71.3%

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

      2. *-commutative 71.3%

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

      3. *-commutative 71.3%

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

      4. *-commutative 71.3%

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

      5. associate-*r* 71.3%

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

      6. associate-+r- 71.3%

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

      7. *-commutative 71.3%

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

      8. fma-def 71.3%

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

      9. sub-neg 71.3%

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

      10. +-commutative 71.3%

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

      11. distribute-rgt-neg-in 71.3%

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

      12. fma-def 71.3%

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

      13. distribute-rgt-neg-in 71.3%

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

      14. metadata-eval 71.3%

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

   4. Simplified 71.3%

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

   5. Taylor expanded in b around inf 33.1%

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

   if -1.81999999999999998e37 < x < -4.0000000000000003e-18 or -5.79999999999999974e-182 < x < 2.54999999999999987e-36

   1. Initial program 100.0%

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

   2. Taylor expanded in c around inf 44.0%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+150}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{+42}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;x \leq -1.82 \cdot 10^{+37}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-18}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-182}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-36}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 10: 65.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1.55 \cdot 10^{+119} \lor \neg \left(b \cdot a \leq 1.15 \cdot 10^{+64}\right):\\ \;\;\;\;c + \left(b \cdot a\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -1.55e+119) (not (<= (* b a) 1.15e+64)))
   (+ c (* (* b a) -0.25))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -1.55e+119) || !((b * a) <= 1.15e+64)) {
		tmp = c + ((b * a) * -0.25);
	} else {
		tmp = c + (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) <= (-1.55d+119)) .or. (.not. ((b * a) <= 1.15d+64))) then
        tmp = c + ((b * a) * (-0.25d0))
    else
        tmp = c + (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) <= -1.55e+119) || !((b * a) <= 1.15e+64)) {
		tmp = c + ((b * a) * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((b * a) <= -1.55e+119) or not ((b * a) <= 1.15e+64):
		tmp = c + ((b * a) * -0.25)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(b * a) <= -1.55e+119) || !(Float64(b * a) <= 1.15e+64))
		tmp = Float64(c + Float64(Float64(b * a) * -0.25));
	else
		tmp = Float64(c + 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) <= -1.55e+119) || ~(((b * a) <= 1.15e+64)))
		tmp = c + ((b * a) * -0.25);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -1.55e+119], N[Not[LessEqual[N[(b * a), $MachinePrecision], 1.15e+64]], $MachinePrecision]], N[(c + N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.54999999999999998e119 or 1.15e64 < (*.f64 a 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 73.0%

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

      1. *-commutative 73.0%

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

   4. Simplified 73.0%

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

   if -1.54999999999999998e119 < (*.f64 a b) < 1.15e64

   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 x around inf 67.3%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1.55 \cdot 10^{+119} \lor \neg \left(b \cdot a \leq 1.15 \cdot 10^{+64}\right):\\ \;\;\;\;c + \left(b \cdot a\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 11: 84.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+83} \lor \neg \left(z \leq 5.6 \cdot 10^{-64}\right):\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -4.1e+83) (not (<= z 5.6e-64)))
   (+ c (+ (* x y) (* 0.0625 (* t z))))
   (- (+ c (* x y)) (* (* b a) 0.25))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -4.1e+83) || !(z <= 5.6e-64)) {
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	} else {
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-4.1d+83)) .or. (.not. (z <= 5.6d-64))) then
        tmp = c + ((x * y) + (0.0625d0 * (t * z)))
    else
        tmp = (c + (x * y)) - ((b * a) * 0.25d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -4.1e+83) || !(z <= 5.6e-64)) {
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	} else {
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -4.1e+83) or not (z <= 5.6e-64):
		tmp = c + ((x * y) + (0.0625 * (t * z)))
	else:
		tmp = (c + (x * y)) - ((b * a) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -4.1e+83) || !(z <= 5.6e-64))
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(t * z))));
	else
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(b * a) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -4.1e+83) || ~((z <= 5.6e-64)))
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	else
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -4.1e+83], N[Not[LessEqual[z, 5.6e-64]], $MachinePrecision]], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1000000000000001e83 or 5.60000000000000008e-64 < z

   1. Initial program 95.4%

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

   2. Taylor expanded in a around 0 83.9%

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

   if -4.1000000000000001e83 < z < 5.60000000000000008e-64

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 91.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+83} \lor \neg \left(z \leq 5.6 \cdot 10^{-64}\right):\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 12: 66.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot -0.25\\ \mathbf{if}\;b \cdot a \leq -3.6 \cdot 10^{+63}:\\ \;\;\;\;x \cdot y + t_1\\ \mathbf{elif}\;b \cdot a \leq 1.15 \cdot 10^{+64}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) -0.25)))
   (if (<= (* b a) -3.6e+63)
     (+ (* x y) t_1)
     (if (<= (* b a) 1.15e+64) (+ c (* x y)) (+ c t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -3.6e+63) {
		tmp = (x * y) + t_1;
	} else if ((b * a) <= 1.15e+64) {
		tmp = c + (x * y);
	} else {
		tmp = c + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b * a) * (-0.25d0)
    if ((b * a) <= (-3.6d+63)) then
        tmp = (x * y) + t_1
    else if ((b * a) <= 1.15d+64) then
        tmp = c + (x * y)
    else
        tmp = c + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -3.6e+63) {
		tmp = (x * y) + t_1;
	} else if ((b * a) <= 1.15e+64) {
		tmp = c + (x * y);
	} else {
		tmp = c + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * -0.25
	tmp = 0
	if (b * a) <= -3.6e+63:
		tmp = (x * y) + t_1
	elif (b * a) <= 1.15e+64:
		tmp = c + (x * y)
	else:
		tmp = c + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b * a) * -0.25)
	tmp = 0.0
	if (Float64(b * a) <= -3.6e+63)
		tmp = Float64(Float64(x * y) + t_1);
	elseif (Float64(b * a) <= 1.15e+64)
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b * a) * -0.25;
	tmp = 0.0;
	if ((b * a) <= -3.6e+63)
		tmp = (x * y) + t_1;
	elseif ((b * a) <= 1.15e+64)
		tmp = c + (x * y);
	else
		tmp = c + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -3.6e+63], N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 1.15e+64], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -3.59999999999999999e63

   1. Initial program 91.1%

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

   2. Taylor expanded in z around 0 80.6%

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

      1. +-commutative 80.6%

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

      2. *-commutative 80.6%

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

      3. *-commutative 80.6%

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

      4. *-commutative 80.6%

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

      5. associate-*r* 80.6%

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

      6. associate-+r- 80.6%

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

      7. *-commutative 80.6%

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

      8. fma-def 85.0%

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

      9. sub-neg 85.0%

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

      10. +-commutative 85.0%

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

      11. distribute-rgt-neg-in 85.0%

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

      12. fma-def 85.1%

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

      13. distribute-rgt-neg-in 85.1%

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

      14. metadata-eval 85.1%

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

   4. Simplified 85.1%

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

   5. Taylor expanded in c around 0 77.4%

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

   if -3.59999999999999999e63 < (*.f64 a b) < 1.15e64

   1. Initial program 98.8%

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

   2. Taylor expanded in x around inf 68.1%

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

   if 1.15e64 < (*.f64 a b)

   1. Initial program 97.6%

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

   2. Taylor expanded in a around inf 69.4%

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

      1. *-commutative 69.4%

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

   4. Simplified 69.4%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -3.6 \cdot 10^{+63}:\\ \;\;\;\;x \cdot y + \left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq 1.15 \cdot 10^{+64}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + \left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 13: 62.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1.6 \cdot 10^{+141} \lor \neg \left(b \cdot a \leq 3.1 \cdot 10^{+272}\right):\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -1.6e+141) (not (<= (* b a) 3.1e+272)))
   (* (* b a) -0.25)
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -1.6e+141) || !((b * a) <= 3.1e+272)) {
		tmp = (b * a) * -0.25;
	} else {
		tmp = c + (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) <= (-1.6d+141)) .or. (.not. ((b * a) <= 3.1d+272))) then
        tmp = (b * a) * (-0.25d0)
    else
        tmp = c + (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) <= -1.6e+141) || !((b * a) <= 3.1e+272)) {
		tmp = (b * a) * -0.25;
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((b * a) <= -1.6e+141) or not ((b * a) <= 3.1e+272):
		tmp = (b * a) * -0.25
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(b * a) <= -1.6e+141) || !(Float64(b * a) <= 3.1e+272))
		tmp = Float64(Float64(b * a) * -0.25);
	else
		tmp = Float64(c + 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) <= -1.6e+141) || ~(((b * a) <= 3.1e+272)))
		tmp = (b * a) * -0.25;
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -1.6e+141], N[Not[LessEqual[N[(b * a), $MachinePrecision], 3.1e+272]], $MachinePrecision]], N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.60000000000000009e141 or 3.09999999999999972e272 < (*.f64 a b)

   1. Initial program 89.6%

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

   2. Taylor expanded in z around 0 86.0%

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

      1. +-commutative 86.0%

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

      2. *-commutative 86.0%

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

      3. *-commutative 86.0%

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

      4. *-commutative 86.0%

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

      5. associate-*r* 86.0%

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

      6. associate-+r- 86.0%

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

      7. *-commutative 86.0%

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

      8. fma-def 92.2%

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

      9. sub-neg 92.2%

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

      10. +-commutative 92.2%

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

      11. distribute-rgt-neg-in 92.2%

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

      12. fma-def 92.2%

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

      13. distribute-rgt-neg-in 92.2%

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

      14. metadata-eval 92.2%

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

   4. Simplified 92.2%

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

   5. Taylor expanded in b around inf 84.2%

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

   if -1.60000000000000009e141 < (*.f64 a b) < 3.09999999999999972e272

   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 x around inf 63.5%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1.6 \cdot 10^{+141} \lor \neg \left(b \cdot a \leq 3.1 \cdot 10^{+272}\right):\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 14: 37.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+37}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 10^{-36}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -1.95e+37) (* x y) (if (<= x 1e-36) c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -1.95e+37) {
		tmp = x * y;
	} else if (x <= 1e-36) {
		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 (x <= (-1.95d+37)) then
        tmp = x * y
    else if (x <= 1d-36) 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 (x <= -1.95e+37) {
		tmp = x * y;
	} else if (x <= 1e-36) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -1.95e+37:
		tmp = x * y
	elif x <= 1e-36:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -1.95e+37)
		tmp = Float64(x * y);
	elseif (x <= 1e-36)
		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 (x <= -1.95e+37)
		tmp = x * y;
	elseif (x <= 1e-36)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -1.95e+37], N[(x * y), $MachinePrecision], If[LessEqual[x, 1e-36], c, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9499999999999999e37 or 9.9999999999999994e-37 < x

   1. Initial program 95.7%

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

   2. Taylor expanded in z around 0 78.2%

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

      1. +-commutative 78.2%

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

      2. *-commutative 78.2%

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

      3. *-commutative 78.2%

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

      4. *-commutative 78.2%

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

      5. associate-*r* 78.2%

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

      6. associate-+r- 78.2%

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

      7. *-commutative 78.2%

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

      8. fma-def 80.4%

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

      9. sub-neg 80.4%

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

      10. +-commutative 80.4%

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

      11. distribute-rgt-neg-in 80.4%

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

      12. fma-def 80.4%

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

      13. distribute-rgt-neg-in 80.4%

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

      14. metadata-eval 80.4%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in y around inf 45.9%

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

   if -1.9499999999999999e37 < x < 9.9999999999999994e-37

   1. Initial program 99.1%

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

   2. Taylor expanded in c around inf 33.8%

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

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+37}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 10^{-36}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 15: 22.2% 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. Taylor expanded in c around inf 27.1%

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

3. Final simplification 27.1%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023228 
(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))