Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1

Percentage Accurate: 92.5% → 96.2%

Time: 8.6s

Alternatives: 10

Speedup: 1.0×

• 32.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot z\right) + \left(a \cdot t + \left(z \cdot y + x\right)\right)\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, b, t\right), a, z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* b (* a z)) (+ (* a t) (+ (* z y) x)))))
   (if (<= t_1 2e+306) t_1 (fma (fma z b t) a (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * (a * z)) + ((a * t) + ((z * y) + x));
	double tmp;
	if (t_1 <= 2e+306) {
		tmp = t_1;
	} else {
		tmp = fma(fma(z, b, t), a, (z * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * Float64(a * z)) + Float64(Float64(a * t) + Float64(Float64(z * y) + x)))
	tmp = 0.0
	if (t_1 <= 2e+306)
		tmp = t_1;
	else
		tmp = fma(fma(z, b, t), a, Float64(z * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * N[(a * z), $MachinePrecision]), $MachinePrecision] + N[(N[(a * t), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+306], t$95$1, N[(N[(z * b + t), $MachinePrecision] * a + N[(z * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b)) < 2.00000000000000003e306

   1. Initial program 98.6%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   if 2.00000000000000003e306 < (+.f64 (+.f64 (+.f64 x (*.f64 y z)) (*.f64 t a)) (*.f64 (*.f64 a z) b))

   1. Initial program 74.4%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. distribute-lft-in N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 96.0

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

   5. Applied rewrites 96.0%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot \left(a \cdot z\right) + \left(a \cdot t + \left(z \cdot y + x\right)\right) \leq 2 \cdot 10^{+306}:\\ \;\;\;\;b \cdot \left(a \cdot z\right) + \left(a \cdot t + \left(z \cdot y + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, b, t\right), a, z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(z, b, t\right), a, z \cdot y\right)\\ \mathbf{if}\;a \leq -6.1 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(y, z, \mathsf{fma}\left(t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma (fma z b t) a (* z y))))
   (if (<= a -6.1e+35) t_1 (if (<= a 3e+14) (fma y z (fma t a x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(fma(z, b, t), a, (z * y));
	double tmp;
	if (a <= -6.1e+35) {
		tmp = t_1;
	} else if (a <= 3e+14) {
		tmp = fma(y, z, fma(t, a, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(fma(z, b, t), a, Float64(z * y))
	tmp = 0.0
	if (a <= -6.1e+35)
		tmp = t_1;
	elseif (a <= 3e+14)
		tmp = fma(y, z, fma(t, a, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * b + t), $MachinePrecision] * a + N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.1e+35], t$95$1, If[LessEqual[a, 3e+14], N[(y * z + N[(t * a + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.09999999999999977e35 or 3e14 < a

   1. Initial program 86.6%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. distribute-lft-in N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 92.4

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

   5. Applied rewrites 92.4%

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

   if -6.09999999999999977e35 < a < 3e14

   1. Initial program 99.9%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 83.8

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

   5. Applied rewrites 83.8%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.1 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, b, t\right), a, z \cdot y\right)\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(y, z, \mathsf{fma}\left(t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, b, t\right), a, z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.3 \cdot 10^{+188}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a, z, \mathsf{fma}\left(a, t, \mathsf{fma}\left(z, y, x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, b, t\right), a, z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1.3e+188)
   (fma (* b a) z (fma a t (fma z y x)))
   (fma (fma z b t) a (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.3e+188) {
		tmp = fma((b * a), z, fma(a, t, fma(z, y, x)));
	} else {
		tmp = fma(fma(z, b, t), a, (z * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1.3e+188)
		tmp = fma(Float64(b * a), z, fma(a, t, fma(z, y, x)));
	else
		tmp = fma(fma(z, b, t), a, Float64(z * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1.3e+188], N[(N[(b * a), $MachinePrecision] * z + N[(a * t + N[(z * y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * b + t), $MachinePrecision] * a + N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.29999999999999994e188

   1. Initial program 94.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. associate-*r* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 97.0

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 97.4

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

      14. lift-+.f64 N/A

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

      15. +-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-fma.f64 97.4

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

   4. Applied rewrites 97.4%

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

   if 1.29999999999999994e188 < a

   1. Initial program 91.8%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. distribute-lft-in N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 99.9

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

   5. Applied rewrites 99.9%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.3 \cdot 10^{+188}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot a, z, \mathsf{fma}\left(a, t, \mathsf{fma}\left(z, y, x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, b, t\right), a, z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{fma}\left(b, a, y\right) \cdot z\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(y, z, \mathsf{fma}\left(t, a, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, b, t\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6e+49)
   (* (fma b a y) z)
   (if (<= b 2.2e+80) (fma y z (fma t a x)) (* (fma z b t) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6e+49) {
		tmp = fma(b, a, y) * z;
	} else if (b <= 2.2e+80) {
		tmp = fma(y, z, fma(t, a, x));
	} else {
		tmp = fma(z, b, t) * a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6e+49)
		tmp = Float64(fma(b, a, y) * z);
	elseif (b <= 2.2e+80)
		tmp = fma(y, z, fma(t, a, x));
	else
		tmp = Float64(fma(z, b, t) * a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6e+49], N[(N[(b * a + y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[b, 2.2e+80], N[(y * z + N[(t * a + x), $MachinePrecision]), $MachinePrecision], N[(N[(z * b + t), $MachinePrecision] * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.0000000000000005e49

   1. Initial program 94.5%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 77.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, y\right)} \cdot z \]

   5. Applied rewrites 77.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, y\right) \cdot z} \]

   if -6.0000000000000005e49 < b < 2.20000000000000003e80

   1. Initial program 93.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 91.6

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

   5. Applied rewrites 91.6%

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

   if 2.20000000000000003e80 < b

   1. Initial program 95.8%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 72.2

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

   5. Applied rewrites 72.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, b, t\right) \cdot a} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 75.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(z, b, t\right) \cdot a\\ \mathbf{if}\;a \leq -210000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.1 \cdot 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (fma z b t) a)))
   (if (<= a -210000.0) t_1 (if (<= a 7.1e+28) (fma y z x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(z, b, t) * a;
	double tmp;
	if (a <= -210000.0) {
		tmp = t_1;
	} else if (a <= 7.1e+28) {
		tmp = fma(y, z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(z, b, t) * a)
	tmp = 0.0
	if (a <= -210000.0)
		tmp = t_1;
	elseif (a <= 7.1e+28)
		tmp = fma(y, z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * b + t), $MachinePrecision] * a), $MachinePrecision]}, If[LessEqual[a, -210000.0], t$95$1, If[LessEqual[a, 7.1e+28], N[(y * z + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.1e5 or 7.0999999999999999e28 < a

   1. Initial program 87.6%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 79.0

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

   5. Applied rewrites 79.0%

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

   if -2.1e5 < a < 7.0999999999999999e28

   1. Initial program 99.9%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + y \cdot z} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-fma.f64 78.2

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

   5. Applied rewrites 78.2%

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

Alternative 6: 73.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(b, a, y\right) \cdot z\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.75 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (fma b a y) z)))
   (if (<= z -1.2e-53) t_1 (if (<= z 4.75e-7) (fma t a x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(b, a, y) * z;
	double tmp;
	if (z <= -1.2e-53) {
		tmp = t_1;
	} else if (z <= 4.75e-7) {
		tmp = fma(t, a, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(b, a, y) * z)
	tmp = 0.0
	if (z <= -1.2e-53)
		tmp = t_1;
	elseif (z <= 4.75e-7)
		tmp = fma(t, a, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * a + y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -1.2e-53], t$95$1, If[LessEqual[z, 4.75e-7], N[(t * a + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.20000000000000004e-53 or 4.75e-7 < z

   1. Initial program 89.2%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 73.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, y\right)} \cdot z \]

   5. Applied rewrites 73.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b, a, y\right) \cdot z} \]

   if -1.20000000000000004e-53 < z < 4.75e-7

   1. Initial program 100.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + a \cdot t} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot t + x} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{t \cdot a} + x \]

      3. lower-fma.f64 73.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, a, x\right)} \]

   5. Applied rewrites 73.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, a, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 61.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+207}:\\ \;\;\;\;\mathsf{fma}\left(t, a, x\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-30}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.8e+207) (fma t a x) (if (<= t 6e-30) (fma y z x) (fma t a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.8e+207) {
		tmp = fma(t, a, x);
	} else if (t <= 6e-30) {
		tmp = fma(y, z, x);
	} else {
		tmp = fma(t, a, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.8e+207)
		tmp = fma(t, a, x);
	elseif (t <= 6e-30)
		tmp = fma(y, z, x);
	else
		tmp = fma(t, a, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.8e+207], N[(t * a + x), $MachinePrecision], If[LessEqual[t, 6e-30], N[(y * z + x), $MachinePrecision], N[(t * a + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.8000000000000002e207 or 5.9999999999999998e-30 < t

   1. Initial program 92.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + a \cdot t} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot t + x} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{t \cdot a} + x \]

      3. lower-fma.f64 76.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, a, x\right)} \]

   5. Applied rewrites 76.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, a, x\right)} \]

   if -4.8000000000000002e207 < t < 5.9999999999999998e-30

   1. Initial program 94.6%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + y \cdot z} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-fma.f64 63.4

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

   5. Applied rewrites 63.4%

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

Alternative 8: 57.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+71}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+140}:\\ \;\;\;\;\mathsf{fma}\left(t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.3e+71) (* z y) (if (<= y 6.5e+140) (fma t a x) (* z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.3e+71) {
		tmp = z * y;
	} else if (y <= 6.5e+140) {
		tmp = fma(t, a, x);
	} else {
		tmp = z * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.3e+71)
		tmp = Float64(z * y);
	elseif (y <= 6.5e+140)
		tmp = fma(t, a, x);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.3e+71], N[(z * y), $MachinePrecision], If[LessEqual[y, 6.5e+140], N[(t * a + x), $MachinePrecision], N[(z * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3000000000000002e71 or 6.4999999999999999e140 < y

   1. Initial program 94.5%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot z} \]
   4. Step-by-step derivation

      1. lower-*.f64 63.6

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

   5. Applied rewrites 63.6%

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

   if -2.3000000000000002e71 < y < 6.4999999999999999e140

   1. Initial program 93.6%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + a \cdot t} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{a \cdot t + x} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{t \cdot a} + x \]

      3. lower-fma.f64 59.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(t, a, x\right)} \]

   5. Applied rewrites 59.8%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+71}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+140}:\\ \;\;\;\;\mathsf{fma}\left(t, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 36.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+207}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-30}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4.8e+207) (* a t) (if (<= t 6e-30) (* z y) (* a t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.8e+207) {
		tmp = a * t;
	} else if (t <= 6e-30) {
		tmp = z * y;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (t <= (-4.8d+207)) then
        tmp = a * t
    else if (t <= 6d-30) then
        tmp = z * y
    else
        tmp = a * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4.8e+207) {
		tmp = a * t;
	} else if (t <= 6e-30) {
		tmp = z * y;
	} else {
		tmp = a * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4.8e+207:
		tmp = a * t
	elif t <= 6e-30:
		tmp = z * y
	else:
		tmp = a * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4.8e+207)
		tmp = Float64(a * t);
	elseif (t <= 6e-30)
		tmp = Float64(z * y);
	else
		tmp = Float64(a * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4.8e+207)
		tmp = a * t;
	elseif (t <= 6e-30)
		tmp = z * y;
	else
		tmp = a * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4.8e+207], N[(a * t), $MachinePrecision], If[LessEqual[t, 6e-30], N[(z * y), $MachinePrecision], N[(a * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.8000000000000002e207 or 5.9999999999999998e-30 < t

   1. Initial program 92.0%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{a \cdot t} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{t \cdot a} \]

      2. lower-*.f64 61.1

         \[\leadsto \color{blue}{t \cdot a} \]

   5. Applied rewrites 61.1%

      \[\leadsto \color{blue}{t \cdot a} \]

   if -4.8000000000000002e207 < t < 5.9999999999999998e-30

   1. Initial program 94.6%

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot z} \]
   4. Step-by-step derivation

      1. lower-*.f64 34.1

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

   5. Applied rewrites 34.1%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+207}:\\ \;\;\;\;a \cdot t\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-30}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;a \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 27.4% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ a \cdot t \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = a * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a * t), $MachinePrecision]

Derivation

1. Initial program 93.8%

   \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \]
2. Add Preprocessing

3. Taylor expanded in t around inf

   \[\leadsto \color{blue}{a \cdot t} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{t \cdot a} \]

   2. lower-*.f64 25.2

      \[\leadsto \color{blue}{t \cdot a} \]

5. Applied rewrites 25.2%

   \[\leadsto \color{blue}{t \cdot a} \]

6. Final simplification 25.2%

   \[\leadsto a \cdot t \]
7. Add Preprocessing

Developer Target 1: 97.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{if}\;z < -11820553527347888000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* z (+ (* b a) y)) (+ x (* t a)))))
   (if (< z -11820553527347888000.0)
     t_1
     (if (< z 4.7589743188364287e-122)
       (+ (* (+ (* b z) t) a) (+ (* z y) x))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = (z * ((b * a) + y)) + (x + (t * a))
    if (z < (-11820553527347888000.0d0)) then
        tmp = t_1
    else if (z < 4.7589743188364287d-122) then
        tmp = (((b * z) + t) * a) + ((z * y) + x)
    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 t_1 = (z * ((b * a) + y)) + (x + (t * a));
	double tmp;
	if (z < -11820553527347888000.0) {
		tmp = t_1;
	} else if (z < 4.7589743188364287e-122) {
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((b * a) + y)) + (x + (t * a))
	tmp = 0
	if z < -11820553527347888000.0:
		tmp = t_1
	elif z < 4.7589743188364287e-122:
		tmp = (((b * z) + t) * a) + ((z * y) + x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(b * a) + y)) + Float64(x + Float64(t * a)))
	tmp = 0.0
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = Float64(Float64(Float64(Float64(b * z) + t) * a) + Float64(Float64(z * y) + x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((b * a) + y)) + (x + (t * a));
	tmp = 0.0;
	if (z < -11820553527347888000.0)
		tmp = t_1;
	elseif (z < 4.7589743188364287e-122)
		tmp = (((b * z) + t) * a) + ((z * y) + x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(N[(b * a), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + N[(x + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -11820553527347888000.0], t$95$1, If[Less[z, 4.7589743188364287e-122], N[(N[(N[(N[(b * z), $MachinePrecision] + t), $MachinePrecision] * a), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024235 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -11820553527347888000) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 47589743188364287/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a))))))

  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))