Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C

Percentage Accurate: 99.9% → 99.9%

Time: 9.2s

Alternatives: 8

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x + \sin y\right) + z \cdot \cos y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (+ x (sin y)) (* z (cos y))))

C

double code(double x, double y, double z) {
	return (x + sin(y)) + (z * cos(y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + sin(y)) + (z * cos(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.sin(y)) + (z * Math.cos(y));
}

Python

def code(x, y, z):
	return (x + math.sin(y)) + (z * math.cos(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + sin(y)) + Float64(z * cos(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + sin(y)) + (z * cos(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + \sin y\right) + z \cdot \cos y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (+ x (sin y)) (* z (cos y))))

C

double code(double x, double y, double z) {
	return (x + sin(y)) + (z * cos(y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + sin(y)) + (z * cos(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.sin(y)) + (z * Math.cos(y));
}

Python

def code(x, y, z):
	return (x + math.sin(y)) + (z * math.cos(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + sin(y)) + Float64(z * cos(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + sin(y)) + (z * cos(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\cos y, z, x + \sin y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (cos y) z (+ x (sin y))))

C

double code(double x, double y, double z) {
	return fma(cos(y), z, (x + sin(y)));
}

Julia

function code(x, y, z)
	return fma(cos(y), z, Float64(x + sin(y)))
end

Wolfram

code[x_, y_, z_] := N[(N[Cos[y], $MachinePrecision] * z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. lift-sin.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. lift-cos.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. +-commutative N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

   8. lower-fma.f64 99.9

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

4. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x + \sin y\right)} \]
5. Add Preprocessing

Alternative 2: 79.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z + \left(x + \sin y\right)\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+28}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t\_0 \leq -0.005:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-12}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+18}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* (cos y) z) (+ x (sin y)))))
   (if (<= t_0 -2e+28)
     (+ z x)
     (if (<= t_0 -0.005)
       (sin y)
       (if (<= t_0 5e-12)
         (+ y (+ z x))
         (if (<= t_0 2e+18) (sin y) (+ z x)))))))

C

double code(double x, double y, double z) {
	double t_0 = (cos(y) * z) + (x + sin(y));
	double tmp;
	if (t_0 <= -2e+28) {
		tmp = z + x;
	} else if (t_0 <= -0.005) {
		tmp = sin(y);
	} else if (t_0 <= 5e-12) {
		tmp = y + (z + x);
	} else if (t_0 <= 2e+18) {
		tmp = sin(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (cos(y) * z) + (x + sin(y))
    if (t_0 <= (-2d+28)) then
        tmp = z + x
    else if (t_0 <= (-0.005d0)) then
        tmp = sin(y)
    else if (t_0 <= 5d-12) then
        tmp = y + (z + x)
    else if (t_0 <= 2d+18) then
        tmp = sin(y)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (Math.cos(y) * z) + (x + Math.sin(y));
	double tmp;
	if (t_0 <= -2e+28) {
		tmp = z + x;
	} else if (t_0 <= -0.005) {
		tmp = Math.sin(y);
	} else if (t_0 <= 5e-12) {
		tmp = y + (z + x);
	} else if (t_0 <= 2e+18) {
		tmp = Math.sin(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (math.cos(y) * z) + (x + math.sin(y))
	tmp = 0
	if t_0 <= -2e+28:
		tmp = z + x
	elif t_0 <= -0.005:
		tmp = math.sin(y)
	elif t_0 <= 5e-12:
		tmp = y + (z + x)
	elif t_0 <= 2e+18:
		tmp = math.sin(y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(cos(y) * z) + Float64(x + sin(y)))
	tmp = 0.0
	if (t_0 <= -2e+28)
		tmp = Float64(z + x);
	elseif (t_0 <= -0.005)
		tmp = sin(y);
	elseif (t_0 <= 5e-12)
		tmp = Float64(y + Float64(z + x));
	elseif (t_0 <= 2e+18)
		tmp = sin(y);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (cos(y) * z) + (x + sin(y));
	tmp = 0.0;
	if (t_0 <= -2e+28)
		tmp = z + x;
	elseif (t_0 <= -0.005)
		tmp = sin(y);
	elseif (t_0 <= 5e-12)
		tmp = y + (z + x);
	elseif (t_0 <= 2e+18)
		tmp = sin(y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision] + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+28], N[(z + x), $MachinePrecision], If[LessEqual[t$95$0, -0.005], N[Sin[y], $MachinePrecision], If[LessEqual[t$95$0, 5e-12], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e+18], N[Sin[y], $MachinePrecision], N[(z + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -1.99999999999999992e28 or 2e18 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 80.9

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

   5. Applied rewrites 80.9%

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

   if -1.99999999999999992e28 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < -0.0050000000000000001 or 4.9999999999999997e-12 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 2e18

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-sin.f64 94.1

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

   5. Applied rewrites 94.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\sin y} \]
   7. Step-by-step derivation

      1. lower-sin.f64 86.2

         \[\leadsto \color{blue}{\sin y} \]

   8. Applied rewrites 86.2%

      \[\leadsto \color{blue}{\sin y} \]

   if -0.0050000000000000001 < (+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y))) < 4.9999999999999997e-12

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 100.0

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

   5. Applied rewrites 100.0%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos y \cdot z + \left(x + \sin y\right) \leq -2 \cdot 10^{+28}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;\cos y \cdot z + \left(x + \sin y\right) \leq -0.005:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;\cos y \cdot z + \left(x + \sin y\right) \leq 5 \cdot 10^{-12}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{elif}\;\cos y \cdot z + \left(x + \sin y\right) \leq 2 \cdot 10^{+18}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(\frac{\cos y \cdot z}{x} + 1\right)\\ \mathbf{if}\;x \leq -14500000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(z, \cos y, \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (/ (* (cos y) z) x) 1.0))))
   (if (<= x -14500000.0)
     t_0
     (if (<= x 2.8e-23) (fma z (cos y) (sin y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (((cos(y) * z) / x) + 1.0);
	double tmp;
	if (x <= -14500000.0) {
		tmp = t_0;
	} else if (x <= 2.8e-23) {
		tmp = fma(z, cos(y), sin(y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(Float64(cos(y) * z) / x) + 1.0))
	tmp = 0.0
	if (x <= -14500000.0)
		tmp = t_0;
	elseif (x <= 2.8e-23)
		tmp = fma(z, cos(y), sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision] / x), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -14500000.0], t$95$0, If[LessEqual[x, 2.8e-23], N[(z * N[Cos[y], $MachinePrecision] + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.45e7 or 2.7999999999999997e-23 < x

   1. Initial program 99.9%

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

      1. lift-sin.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-cos.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(x \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)\right)} \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{x \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)\right)} \]

      5. sub-neg N/A

         \[\leadsto x \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} + \left(\mathsf{neg}\left(1\right)\right)\right)}\right) \]

      6. metadata-eval N/A

         \[\leadsto x \cdot \left(-1 \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} + \color{blue}{-1}\right)\right) \]

      7. distribute-lft-in N/A

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x}\right) + -1 \cdot -1\right)} \]

      8. neg-mul-1 N/A

         \[\leadsto x \cdot \left(\color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x}\right)\right)} + -1 \cdot -1\right) \]

      9. mul-1-neg N/A

         \[\leadsto x \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{\sin y + z \cdot \cos y}{x}\right)\right)}\right)\right) + -1 \cdot -1\right) \]

      10. remove-double-neg N/A

          \[\leadsto x \cdot \left(\color{blue}{\frac{\sin y + z \cdot \cos y}{x}} + -1 \cdot -1\right) \]

      11. metadata-eval N/A

          \[\leadsto x \cdot \left(\frac{\sin y + z \cdot \cos y}{x} + \color{blue}{1}\right) \]

      12. lower-+.f64 N/A

          \[\leadsto x \cdot \color{blue}{\left(\frac{\sin y + z \cdot \cos y}{x} + 1\right)} \]

   7. Applied rewrites 99.9%

      \[\leadsto \color{blue}{x \cdot \left(\frac{\mathsf{fma}\left(z, \cos y, \sin y\right)}{x} + 1\right)} \]

   8. Taylor expanded in z around inf

      \[\leadsto x \cdot \left(\color{blue}{\frac{z \cdot \cos y}{x}} + 1\right) \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x \cdot \left(\color{blue}{\frac{z \cdot \cos y}{x}} + 1\right) \]

      2. lower-*.f64 N/A

         \[\leadsto x \cdot \left(\frac{\color{blue}{z \cdot \cos y}}{x} + 1\right) \]

      3. lower-cos.f64 99.1

         \[\leadsto x \cdot \left(\frac{z \cdot \color{blue}{\cos y}}{x} + 1\right) \]

   10. Applied rewrites 99.1%

       \[\leadsto x \cdot \left(\color{blue}{\frac{z \cdot \cos y}{x}} + 1\right) \]

   if -1.45e7 < x < 2.7999999999999997e-23

   1. Initial program 99.8%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-cos.f64 N/A

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

      4. lower-sin.f64 95.3

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

   5. Applied rewrites 95.3%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -14500000:\\ \;\;\;\;x \cdot \left(\frac{\cos y \cdot z}{x} + 1\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-23}:\\ \;\;\;\;\mathsf{fma}\left(z, \cos y, \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{\cos y \cdot z}{x} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ t_1 := x \cdot \left(\frac{t\_0}{x} + 1\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+67}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-20}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)) (t_1 (* x (+ (/ t_0 x) 1.0))))
   (if (<= z -8.5e+67)
     t_0
     (if (<= z -1.45e-25)
       t_1
       (if (<= z 3.2e-20) (+ x (sin y)) (if (<= z 6.8e+152) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double t_1 = x * ((t_0 / x) + 1.0);
	double tmp;
	if (z <= -8.5e+67) {
		tmp = t_0;
	} else if (z <= -1.45e-25) {
		tmp = t_1;
	} else if (z <= 3.2e-20) {
		tmp = x + sin(y);
	} else if (z <= 6.8e+152) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = cos(y) * z
    t_1 = x * ((t_0 / x) + 1.0d0)
    if (z <= (-8.5d+67)) then
        tmp = t_0
    else if (z <= (-1.45d-25)) then
        tmp = t_1
    else if (z <= 3.2d-20) then
        tmp = x + sin(y)
    else if (z <= 6.8d+152) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cos(y) * z;
	double t_1 = x * ((t_0 / x) + 1.0);
	double tmp;
	if (z <= -8.5e+67) {
		tmp = t_0;
	} else if (z <= -1.45e-25) {
		tmp = t_1;
	} else if (z <= 3.2e-20) {
		tmp = x + Math.sin(y);
	} else if (z <= 6.8e+152) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cos(y) * z
	t_1 = x * ((t_0 / x) + 1.0)
	tmp = 0
	if z <= -8.5e+67:
		tmp = t_0
	elif z <= -1.45e-25:
		tmp = t_1
	elif z <= 3.2e-20:
		tmp = x + math.sin(y)
	elif z <= 6.8e+152:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * z)
	t_1 = Float64(x * Float64(Float64(t_0 / x) + 1.0))
	tmp = 0.0
	if (z <= -8.5e+67)
		tmp = t_0;
	elseif (z <= -1.45e-25)
		tmp = t_1;
	elseif (z <= 3.2e-20)
		tmp = Float64(x + sin(y));
	elseif (z <= 6.8e+152)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cos(y) * z;
	t_1 = x * ((t_0 / x) + 1.0);
	tmp = 0.0;
	if (z <= -8.5e+67)
		tmp = t_0;
	elseif (z <= -1.45e-25)
		tmp = t_1;
	elseif (z <= 3.2e-20)
		tmp = x + sin(y);
	elseif (z <= 6.8e+152)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(N[(t$95$0 / x), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+67], t$95$0, If[LessEqual[z, -1.45e-25], t$95$1, If[LessEqual[z, 3.2e-20], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+152], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.50000000000000038e67 or 6.80000000000000041e152 < z

   1. Initial program 99.8%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-cos.f64 83.6

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

   5. Applied rewrites 83.6%

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

   if -8.50000000000000038e67 < z < -1.45e-25 or 3.1999999999999997e-20 < z < 6.80000000000000041e152

   1. Initial program 99.8%

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

      1. lift-sin.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-cos.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(x \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)\right)} \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{x \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)\right)\right)} \]

      3. mul-1-neg N/A

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)\right)} \]

      5. sub-neg N/A

         \[\leadsto x \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} + \left(\mathsf{neg}\left(1\right)\right)\right)}\right) \]

      6. metadata-eval N/A

         \[\leadsto x \cdot \left(-1 \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} + \color{blue}{-1}\right)\right) \]

      7. distribute-lft-in N/A

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x}\right) + -1 \cdot -1\right)} \]

      8. neg-mul-1 N/A

         \[\leadsto x \cdot \left(\color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x}\right)\right)} + -1 \cdot -1\right) \]

      9. mul-1-neg N/A

         \[\leadsto x \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{\sin y + z \cdot \cos y}{x}\right)\right)}\right)\right) + -1 \cdot -1\right) \]

      10. remove-double-neg N/A

          \[\leadsto x \cdot \left(\color{blue}{\frac{\sin y + z \cdot \cos y}{x}} + -1 \cdot -1\right) \]

      11. metadata-eval N/A

          \[\leadsto x \cdot \left(\frac{\sin y + z \cdot \cos y}{x} + \color{blue}{1}\right) \]

      12. lower-+.f64 N/A

          \[\leadsto x \cdot \color{blue}{\left(\frac{\sin y + z \cdot \cos y}{x} + 1\right)} \]

   7. Applied rewrites 94.3%

      \[\leadsto \color{blue}{x \cdot \left(\frac{\mathsf{fma}\left(z, \cos y, \sin y\right)}{x} + 1\right)} \]

   8. Taylor expanded in z around inf

      \[\leadsto x \cdot \left(\color{blue}{\frac{z \cdot \cos y}{x}} + 1\right) \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x \cdot \left(\color{blue}{\frac{z \cdot \cos y}{x}} + 1\right) \]

      2. lower-*.f64 N/A

         \[\leadsto x \cdot \left(\frac{\color{blue}{z \cdot \cos y}}{x} + 1\right) \]

      3. lower-cos.f64 90.8

         \[\leadsto x \cdot \left(\frac{z \cdot \color{blue}{\cos y}}{x} + 1\right) \]

   10. Applied rewrites 90.8%

       \[\leadsto x \cdot \left(\color{blue}{\frac{z \cdot \cos y}{x}} + 1\right) \]

   if -1.45e-25 < z < 3.1999999999999997e-20

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{\sin y + x} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\sin y + x} \]

      3. lower-sin.f64 93.6

         \[\leadsto \color{blue}{\sin y} + x \]

   5. Applied rewrites 93.6%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+67}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(\frac{\cos y \cdot z}{x} + 1\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-20}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \left(\frac{\cos y \cdot z}{x} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot z\\ \mathbf{if}\;z \leq -9 \cdot 10^{+230}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-25}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 3.85 \cdot 10^{+65}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) z)))
   (if (<= z -9e+230)
     t_0
     (if (<= z -1.6e-25) (+ z x) (if (<= z 3.85e+65) (+ x (sin y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * z;
	double tmp;
	if (z <= -9e+230) {
		tmp = t_0;
	} else if (z <= -1.6e-25) {
		tmp = z + x;
	} else if (z <= 3.85e+65) {
		tmp = x + sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = cos(y) * z
    if (z <= (-9d+230)) then
        tmp = t_0
    else if (z <= (-1.6d-25)) then
        tmp = z + x
    else if (z <= 3.85d+65) then
        tmp = x + sin(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cos(y) * z;
	double tmp;
	if (z <= -9e+230) {
		tmp = t_0;
	} else if (z <= -1.6e-25) {
		tmp = z + x;
	} else if (z <= 3.85e+65) {
		tmp = x + Math.sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cos(y) * z
	tmp = 0
	if z <= -9e+230:
		tmp = t_0
	elif z <= -1.6e-25:
		tmp = z + x
	elif z <= 3.85e+65:
		tmp = x + math.sin(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * z)
	tmp = 0.0
	if (z <= -9e+230)
		tmp = t_0;
	elseif (z <= -1.6e-25)
		tmp = Float64(z + x);
	elseif (z <= 3.85e+65)
		tmp = Float64(x + sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cos(y) * z;
	tmp = 0.0;
	if (z <= -9e+230)
		tmp = t_0;
	elseif (z <= -1.6e-25)
		tmp = z + x;
	elseif (z <= 3.85e+65)
		tmp = x + sin(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -9e+230], t$95$0, If[LessEqual[z, -1.6e-25], N[(z + x), $MachinePrecision], If[LessEqual[z, 3.85e+65], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999998e230 or 3.85000000000000019e65 < z

   1. Initial program 99.8%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-cos.f64 87.0

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

   5. Applied rewrites 87.0%

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

   if -8.9999999999999998e230 < z < -1.6000000000000001e-25

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 77.1

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

   5. Applied rewrites 77.1%

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

   if -1.6000000000000001e-25 < z < 3.85000000000000019e65

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{\sin y + x} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\sin y + x} \]

      3. lower-sin.f64 90.5

         \[\leadsto \color{blue}{\sin y} + x \]

   5. Applied rewrites 90.5%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+230}:\\ \;\;\;\;\cos y \cdot z\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-25}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 3.85 \cdot 10^{+65}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \sin y\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{+50}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.0305:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (sin y))))
   (if (<= y -2.25e+50) t_0 (if (<= y 0.0305) (+ y (+ z x)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + sin(y);
	double tmp;
	if (y <= -2.25e+50) {
		tmp = t_0;
	} else if (y <= 0.0305) {
		tmp = y + (z + x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + sin(y)
    if (y <= (-2.25d+50)) then
        tmp = t_0
    else if (y <= 0.0305d0) then
        tmp = y + (z + x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + Math.sin(y);
	double tmp;
	if (y <= -2.25e+50) {
		tmp = t_0;
	} else if (y <= 0.0305) {
		tmp = y + (z + x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + math.sin(y)
	tmp = 0
	if y <= -2.25e+50:
		tmp = t_0
	elif y <= 0.0305:
		tmp = y + (z + x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + sin(y))
	tmp = 0.0
	if (y <= -2.25e+50)
		tmp = t_0;
	elseif (y <= 0.0305)
		tmp = Float64(y + Float64(z + x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + sin(y);
	tmp = 0.0;
	if (y <= -2.25e+50)
		tmp = t_0;
	elseif (y <= 0.0305)
		tmp = y + (z + x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.25e+50], t$95$0, If[LessEqual[y, 0.0305], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.25000000000000007e50 or 0.030499999999999999 < y

   1. Initial program 99.8%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{\sin y + x} \]

      2. lower-+.f64 N/A

         \[\leadsto \color{blue}{\sin y + x} \]

      3. lower-sin.f64 64.8

         \[\leadsto \color{blue}{\sin y} + x \]

   5. Applied rewrites 64.8%

      \[\leadsto \color{blue}{\sin y + x} \]

   if -2.25000000000000007e50 < y < 0.030499999999999999

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+l+ N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 98.1

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

   5. Applied rewrites 98.1%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+50}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;y \leq 0.0305:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.4% accurate, 53.0× speedup

Math

\[\begin{array}{l} \\ z + x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ z x))

C

double code(double x, double y, double z) {
	return z + x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z + x
end function

Java

public static double code(double x, double y, double z) {
	return z + x;
}

Python

def code(x, y, z):
	return z + x

Julia

function code(x, y, z)
	return Float64(z + x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = z + x;
end

Wolfram

code[x_, y_, z_] := N[(z + x), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(x + \sin y\right) + z \cdot \cos y \]
2. Add Preprocessing

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. lower-+.f64 70.6

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

5. Applied rewrites 70.6%

   \[\leadsto \color{blue}{z + x} \]
6. Add Preprocessing

Alternative 8: 42.6% accurate, 212.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

   1. lift-sin.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. lift-cos.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. +-commutative N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

   8. lower-fma.f64 99.9

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

4. Applied rewrites 99.9%

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

5. Taylor expanded in x around -inf

   \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)\right)} \]
6. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(x \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)\right)} \]

   2. distribute-rgt-neg-in N/A

      \[\leadsto \color{blue}{x \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)\right)\right)} \]

   3. mul-1-neg N/A

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)\right)} \]

   4. lower-*.f64 N/A

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} - 1\right)\right)} \]

   5. sub-neg N/A

      \[\leadsto x \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} + \left(\mathsf{neg}\left(1\right)\right)\right)}\right) \]

   6. metadata-eval N/A

      \[\leadsto x \cdot \left(-1 \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x} + \color{blue}{-1}\right)\right) \]

   7. distribute-lft-in N/A

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x}\right) + -1 \cdot -1\right)} \]

   8. neg-mul-1 N/A

      \[\leadsto x \cdot \left(\color{blue}{\left(\mathsf{neg}\left(-1 \cdot \frac{\sin y + z \cdot \cos y}{x}\right)\right)} + -1 \cdot -1\right) \]

   9. mul-1-neg N/A

      \[\leadsto x \cdot \left(\left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{\sin y + z \cdot \cos y}{x}\right)\right)}\right)\right) + -1 \cdot -1\right) \]

   10. remove-double-neg N/A

       \[\leadsto x \cdot \left(\color{blue}{\frac{\sin y + z \cdot \cos y}{x}} + -1 \cdot -1\right) \]

   11. metadata-eval N/A

       \[\leadsto x \cdot \left(\frac{\sin y + z \cdot \cos y}{x} + \color{blue}{1}\right) \]

   12. lower-+.f64 N/A

       \[\leadsto x \cdot \color{blue}{\left(\frac{\sin y + z \cdot \cos y}{x} + 1\right)} \]

7. Applied rewrites 85.9%

   \[\leadsto \color{blue}{x \cdot \left(\frac{\mathsf{fma}\left(z, \cos y, \sin y\right)}{x} + 1\right)} \]

8. Taylor expanded in x around inf

   \[\leadsto x \cdot \color{blue}{1} \]
9. Step-by-step derivation

10. Applied rewrites 43.7%

    \[\leadsto x \cdot \color{blue}{1} \]
11. Step-by-step derivation

    1. *-rgt-identity 43.7

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

12. Applied rewrites 43.7%

    \[\leadsto \color{blue}{x} \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2024219 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))