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

Percentage Accurate: 99.9% → 99.9%

Time: 10.6s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(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 + cos(y)) - (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(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 + cos(y)) - (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(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 + cos(y)) - (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 2: 98.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y\\ t_1 := z \cdot \sin y\\ t_2 := t\_0 - t\_1\\ \mathbf{if}\;t\_2 \leq -1000000000000:\\ \;\;\;\;\mathsf{fma}\left(\sin y, -z, x\right)\\ \mathbf{elif}\;t\_2 \leq 0.99:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (cos y))) (t_1 (* z (sin y))) (t_2 (- t_0 t_1)))
   (if (<= t_2 -1000000000000.0)
     (fma (sin y) (- z) x)
     (if (<= t_2 0.99) t_0 (- (+ x 1.0) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double t_1 = z * sin(y);
	double t_2 = t_0 - t_1;
	double tmp;
	if (t_2 <= -1000000000000.0) {
		tmp = fma(sin(y), -z, x);
	} else if (t_2 <= 0.99) {
		tmp = t_0;
	} else {
		tmp = (x + 1.0) - t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	t_1 = Float64(z * sin(y))
	t_2 = Float64(t_0 - t_1)
	tmp = 0.0
	if (t_2 <= -1000000000000.0)
		tmp = fma(sin(y), Float64(-z), x);
	elseif (t_2 <= 0.99)
		tmp = t_0;
	else
		tmp = Float64(Float64(x + 1.0) - t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -1000000000000.0], N[(N[Sin[y], $MachinePrecision] * (-z) + x), $MachinePrecision], If[LessEqual[t$95$2, 0.99], t$95$0, N[(N[(x + 1.0), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -1e12

   1. Initial program 99.9%

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

      1. lift-cos.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-sin.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. lower-/.f64 N/A

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

      8. clear-num N/A

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

      9. flip-- N/A

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

      10. lift--.f64 N/A

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

      11. lower-/.f64 99.7

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

      12. lift--.f64 N/A

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

      13. lift-+.f64 N/A

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

      14. associate--l+ N/A

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-sin.f64 99.6

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

   7. Applied rewrites 99.6%

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

      1. *-rgt-identity N/A

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

      2. lift-sin.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. /-rgt-identity N/A

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

      5. sub-neg N/A

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{x \cdot 1 - \frac{z \cdot \sin y}{1}}}} \]

      6. *-rgt-identity N/A

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{x} - \frac{z \cdot \sin y}{1}}} \]

      7. /-rgt-identity N/A

         \[\leadsto \frac{1}{\frac{1}{x - \color{blue}{z \cdot \sin y}}} \]

      8. unsub-neg N/A

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

      9. lift-neg.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. remove-double-div 99.8

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

      12. lift-+.f64 N/A

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

      13. +-commutative N/A

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

      14. lift-neg.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-fma.f64 N/A

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

      19. lower-neg.f64 99.8

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

   9. Applied rewrites 99.8%

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

   if -1e12 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.98999999999999999

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-cos.f64 97.8

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

   5. Applied rewrites 97.8%

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

   if 0.98999999999999999 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 99.8

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

   5. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\left(x + 1\right)} - z \cdot \sin y \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + \cos y\right) - z \cdot \sin y \leq -1000000000000:\\ \;\;\;\;\mathsf{fma}\left(\sin y, -z, x\right)\\ \mathbf{elif}\;\left(x + \cos y\right) - z \cdot \sin y \leq 0.99:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y\\ t_1 := t\_0 - z \cdot \sin y\\ t_2 := \mathsf{fma}\left(\sin y, -z, x\right)\\ \mathbf{if}\;t\_1 \leq -1000000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+14}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (cos y)))
        (t_1 (- t_0 (* z (sin y))))
        (t_2 (fma (sin y) (- z) x)))
   (if (<= t_1 -1000000000000.0) t_2 (if (<= t_1 5e+14) t_0 t_2))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double t_1 = t_0 - (z * sin(y));
	double t_2 = fma(sin(y), -z, x);
	double tmp;
	if (t_1 <= -1000000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 5e+14) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	t_1 = Float64(t_0 - Float64(z * sin(y)))
	t_2 = fma(sin(y), Float64(-z), x)
	tmp = 0.0
	if (t_1 <= -1000000000000.0)
		tmp = t_2;
	elseif (t_1 <= 5e+14)
		tmp = t_0;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Sin[y], $MachinePrecision] * (-z) + x), $MachinePrecision]}, If[LessEqual[t$95$1, -1000000000000.0], t$95$2, If[LessEqual[t$95$1, 5e+14], t$95$0, t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -1e12 or 5e14 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

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

      1. lift-cos.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-sin.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. lower-/.f64 N/A

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

      8. clear-num N/A

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

      9. flip-- N/A

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

      10. lift--.f64 N/A

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

      11. lower-/.f64 99.7

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

      12. lift--.f64 N/A

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

      13. lift-+.f64 N/A

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

      14. associate--l+ N/A

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-sin.f64 99.7

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

   7. Applied rewrites 99.7%

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

      1. *-rgt-identity N/A

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

      2. lift-sin.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. /-rgt-identity N/A

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

      5. sub-neg N/A

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{x \cdot 1 - \frac{z \cdot \sin y}{1}}}} \]

      6. *-rgt-identity N/A

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{x} - \frac{z \cdot \sin y}{1}}} \]

      7. /-rgt-identity N/A

         \[\leadsto \frac{1}{\frac{1}{x - \color{blue}{z \cdot \sin y}}} \]

      8. unsub-neg N/A

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

      9. lift-neg.f64 N/A

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

      10. lift-+.f64 N/A

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

      11. remove-double-div 99.9

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

      12. lift-+.f64 N/A

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

      13. +-commutative N/A

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

      14. lift-neg.f64 N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

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

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

      18. lower-fma.f64 N/A

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

      19. lower-neg.f64 99.9

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

   9. Applied rewrites 99.9%

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

   if -1e12 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 5e14

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-cos.f64 96.8

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

   5. Applied rewrites 96.8%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + \cos y\right) - z \cdot \sin y \leq -1000000000000:\\ \;\;\;\;\mathsf{fma}\left(\sin y, -z, x\right)\\ \mathbf{elif}\;\left(x + \cos y\right) - z \cdot \sin y \leq 5 \cdot 10^{+14}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\sin y, -z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + \cos y\right) - z \cdot \sin y\\ t_1 := x - \mathsf{fma}\left(y, z, -1\right)\\ \mathbf{if}\;t\_0 \leq -10000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0.99:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ x (cos y)) (* z (sin y)))) (t_1 (- x (fma y z -1.0))))
   (if (<= t_0 -10000000.0) t_1 (if (<= t_0 0.99) (cos y) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (x + cos(y)) - (z * sin(y));
	double t_1 = x - fma(y, z, -1.0);
	double tmp;
	if (t_0 <= -10000000.0) {
		tmp = t_1;
	} else if (t_0 <= 0.99) {
		tmp = cos(y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
	t_1 = Float64(x - fma(y, z, -1.0))
	tmp = 0.0
	if (t_0 <= -10000000.0)
		tmp = t_1;
	elseif (t_0 <= 0.99)
		tmp = cos(y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x - N[(y * z + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -10000000.0], t$95$1, If[LessEqual[t$95$0, 0.99], N[Cos[y], $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -1e7 or 0.98999999999999999 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

      5. lower--.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 75.5

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(y, z, -1\right)} \]

   5. Applied rewrites 75.5%

      \[\leadsto \color{blue}{x - \mathsf{fma}\left(y, z, -1\right)} \]

   if -1e7 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.98999999999999999

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-cos.f64 97.7

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

   5. Applied rewrites 97.7%

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

   6. Taylor expanded in x around 0

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

      1. lower-cos.f64 93.5

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

   8. Applied rewrites 93.5%

      \[\leadsto \color{blue}{\cos y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 81.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+224}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+155}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) (- z))))
   (if (<= z -1.35e+224) t_0 (if (<= z 1.1e+155) (+ x (cos y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * -z;
	double tmp;
	if (z <= -1.35e+224) {
		tmp = t_0;
	} else if (z <= 1.1e+155) {
		tmp = x + cos(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 = sin(y) * -z
    if (z <= (-1.35d+224)) then
        tmp = t_0
    else if (z <= 1.1d+155) then
        tmp = x + cos(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.sin(y) * -z;
	double tmp;
	if (z <= -1.35e+224) {
		tmp = t_0;
	} else if (z <= 1.1e+155) {
		tmp = x + Math.cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * -z
	tmp = 0
	if z <= -1.35e+224:
		tmp = t_0
	elif z <= 1.1e+155:
		tmp = x + math.cos(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * Float64(-z))
	tmp = 0.0
	if (z <= -1.35e+224)
		tmp = t_0;
	elseif (z <= 1.1e+155)
		tmp = Float64(x + cos(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * -z;
	tmp = 0.0;
	if (z <= -1.35e+224)
		tmp = t_0;
	elseif (z <= 1.1e+155)
		tmp = x + cos(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[z, -1.35e+224], t$95$0, If[LessEqual[z, 1.1e+155], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3499999999999999e224 or 1.1000000000000001e155 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \sin y\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \sin y\right)} \]

      2. lower-neg.f64 N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \sin y\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{z \cdot \sin y}\right) \]

      4. lower-sin.f64 78.1

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

   5. Applied rewrites 78.1%

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

   if -1.3499999999999999e224 < z < 1.1000000000000001e155

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-cos.f64 87.3

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

   5. Applied rewrites 87.3%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+224}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+155}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{+50}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.0305:\\ \;\;\;\;\mathsf{fma}\left(y, y \cdot -0.5 - z, x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (cos y))))
   (if (<= y -2.25e+50)
     t_0
     (if (<= y 0.0305) (fma y (- (* y -0.5) z) (+ x 1.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double tmp;
	if (y <= -2.25e+50) {
		tmp = t_0;
	} else if (y <= 0.0305) {
		tmp = fma(y, ((y * -0.5) - z), (x + 1.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	tmp = 0.0
	if (y <= -2.25e+50)
		tmp = t_0;
	elseif (y <= 0.0305)
		tmp = fma(y, Float64(Float64(y * -0.5) - z), Float64(x + 1.0));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.25e+50], t$95$0, If[LessEqual[y, 0.0305], N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision] + N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lower-cos.f64 64.7

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

   5. Applied rewrites 64.7%

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

   if -2.25000000000000007e50 < y < 0.030499999999999999

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(\frac{-1}{2} \cdot y - z\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(1 + x\right) + y \cdot \left(\frac{-1}{2} \cdot y - z\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot \left(\frac{-1}{2} \cdot y - z\right) + \left(1 + x\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{-1}{2} \cdot y - z, 1 + x\right)} \]

      4. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{-1}{2} \cdot y - z}, 1 + x\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{y \cdot \frac{-1}{2}} - z, 1 + x\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{y \cdot \frac{-1}{2}} - z, 1 + x\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, y \cdot \frac{-1}{2} - z, \color{blue}{x + 1}\right) \]

      8. lower-+.f64 98.0

         \[\leadsto \mathsf{fma}\left(y, y \cdot -0.5 - z, \color{blue}{x + 1}\right) \]

   5. Applied rewrites 98.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, y \cdot -0.5 - z, x + 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+50}:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;y \leq 0.0305:\\ \;\;\;\;\mathsf{fma}\left(y, y \cdot -0.5 - z, x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.4% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+17}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(y, y \cdot -0.5 - z, x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.2e+17)
   (+ x 1.0)
   (if (<= y 4.4e+15) (fma y (- (* y -0.5) z) (+ x 1.0)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.2e+17) {
		tmp = x + 1.0;
	} else if (y <= 4.4e+15) {
		tmp = fma(y, ((y * -0.5) - z), (x + 1.0));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.2e+17)
		tmp = Float64(x + 1.0);
	elseif (y <= 4.4e+15)
		tmp = fma(y, Float64(Float64(y * -0.5) - z), Float64(x + 1.0));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.2e+17], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 4.4e+15], N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision] + N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2e17 or 4.4e15 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{x + 1} \]

      2. lower-+.f64 43.8

         \[\leadsto \color{blue}{x + 1} \]

   5. Applied rewrites 43.8%

      \[\leadsto \color{blue}{x + 1} \]

   if -8.2e17 < y < 4.4e15

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(\frac{-1}{2} \cdot y - z\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(1 + x\right) + y \cdot \left(\frac{-1}{2} \cdot y - z\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot \left(\frac{-1}{2} \cdot y - z\right) + \left(1 + x\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{-1}{2} \cdot y - z, 1 + x\right)} \]

      4. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{-1}{2} \cdot y - z}, 1 + x\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{y \cdot \frac{-1}{2}} - z, 1 + x\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{y \cdot \frac{-1}{2}} - z, 1 + x\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, y \cdot \frac{-1}{2} - z, \color{blue}{x + 1}\right) \]

      8. lower-+.f64 98.6

         \[\leadsto \mathsf{fma}\left(y, y \cdot -0.5 - z, \color{blue}{x + 1}\right) \]

   5. Applied rewrites 98.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, y \cdot -0.5 - z, x + 1\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 70.2% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+20}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+67}:\\ \;\;\;\;x - \mathsf{fma}\left(y, z, -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.75e+20)
   (+ x 1.0)
   (if (<= y 2.65e+67) (- x (fma y z -1.0)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.75e+20) {
		tmp = x + 1.0;
	} else if (y <= 2.65e+67) {
		tmp = x - fma(y, z, -1.0);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.75e+20)
		tmp = Float64(x + 1.0);
	elseif (y <= 2.65e+67)
		tmp = Float64(x - fma(y, z, -1.0));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.75e+20], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 2.65e+67], N[(x - N[(y * z + -1.0), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.75e20 or 2.65e67 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{x + 1} \]

      2. lower-+.f64 42.1

         \[\leadsto \color{blue}{x + 1} \]

   5. Applied rewrites 42.1%

      \[\leadsto \color{blue}{x + 1} \]

   if -2.75e20 < y < 2.65e67

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

      5. lower--.f64 N/A

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. lower-fma.f64 95.6

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(y, z, -1\right)} \]

   5. Applied rewrites 95.6%

      \[\leadsto \color{blue}{x - \mathsf{fma}\left(y, z, -1\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 67.4% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-9}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 0.48:\\ \;\;\;\;\mathsf{fma}\left(z, -y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.2e-9) (+ x 1.0) (if (<= x 0.48) (fma z (- y) 1.0) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.2e-9) {
		tmp = x + 1.0;
	} else if (x <= 0.48) {
		tmp = fma(z, -y, 1.0);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.2e-9)
		tmp = Float64(x + 1.0);
	elseif (x <= 0.48)
		tmp = fma(z, Float64(-y), 1.0);
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.2e-9], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 0.48], N[(z * (-y) + 1.0), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.2000000000000006e-9 or 0.47999999999999998 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{x + 1} \]

      2. lower-+.f64 88.6

         \[\leadsto \color{blue}{x + 1} \]

   5. Applied rewrites 88.6%

      \[\leadsto \color{blue}{x + 1} \]

   if -8.2000000000000006e-9 < x < 0.47999999999999998

   1. Initial program 99.9%

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

      1. lift-cos.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-sin.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. flip-- N/A

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

      6. clear-num N/A

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

      7. lower-/.f64 N/A

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

      8. clear-num N/A

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

      9. flip-- N/A

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

      10. lift--.f64 N/A

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

      11. lower-/.f64 99.7

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

      12. lift--.f64 N/A

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

      13. lift-+.f64 N/A

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

      14. associate--l+ N/A

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. lower-+.f64 N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 52.2

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

   7. Applied rewrites 52.2%

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

   8. Taylor expanded in x around 0

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

      1. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{1 + \left(\mathsf{neg}\left(y\right)\right) \cdot z} \]

      2. lft-mult-inverse N/A

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

      3. mul-1-neg N/A

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

      4. distribute-rgt-in N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. rgt-mult-inverse N/A

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

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, -1 \cdot y, 1\right)} \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(z, \color{blue}{\mathsf{neg}\left(y\right)}, 1\right) \]

      10. lower-neg.f64 51.7

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{-y}, 1\right) \]

   10. Applied rewrites 51.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(z, -y, 1\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 62.4% accurate, 15.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.8 \cdot 10^{+206}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 1.8e+206) (+ x 1.0) (* y (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.8e+206) {
		tmp = x + 1.0;
	} else {
		tmp = y * -z;
	}
	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) :: tmp
    if (z <= 1.8d+206) then
        tmp = x + 1.0d0
    else
        tmp = y * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.8e+206) {
		tmp = x + 1.0;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.8e+206:
		tmp = x + 1.0
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.8e+206)
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.8e+206)
		tmp = x + 1.0;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.8e+206], N[(x + 1.0), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.80000000000000014e206

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{x + 1} \]

      2. lower-+.f64 70.3

         \[\leadsto \color{blue}{x + 1} \]

   5. Applied rewrites 70.3%

      \[\leadsto \color{blue}{x + 1} \]

   if 1.80000000000000014e206 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)\right)} \]
   4. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto 1 + \color{blue}{\left(y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right) + x\right)} \]

      3. lower-fma.f64 N/A

         \[\leadsto 1 + \color{blue}{\mathsf{fma}\left(y, y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z, x\right)} \]

      4. sub-neg N/A

         \[\leadsto 1 + \mathsf{fma}\left(y, \color{blue}{y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) + \left(\mathsf{neg}\left(z\right)\right)}, x\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto 1 + \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, \frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}, \mathsf{neg}\left(z\right)\right)}, x\right) \]

      6. sub-neg N/A

         \[\leadsto 1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\frac{1}{6} \cdot \left(y \cdot z\right) + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right)}, \mathsf{neg}\left(z\right)\right), x\right) \]

      7. associate-*r* N/A

         \[\leadsto 1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\left(\frac{1}{6} \cdot y\right) \cdot z} + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right), \mathsf{neg}\left(z\right)\right), x\right) \]

      8. *-commutative N/A

         \[\leadsto 1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\left(y \cdot \frac{1}{6}\right)} \cdot z + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right), \mathsf{neg}\left(z\right)\right), x\right) \]

      9. associate-*l* N/A

         \[\leadsto 1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{y \cdot \left(\frac{1}{6} \cdot z\right)} + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right), \mathsf{neg}\left(z\right)\right), x\right) \]

      10. metadata-eval N/A

          \[\leadsto 1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, y \cdot \left(\frac{1}{6} \cdot z\right) + \color{blue}{\frac{-1}{2}}, \mathsf{neg}\left(z\right)\right), x\right) \]

      11. lower-fma.f64 N/A

          \[\leadsto 1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(y, \frac{1}{6} \cdot z, \frac{-1}{2}\right)}, \mathsf{neg}\left(z\right)\right), x\right) \]

      12. *-commutative N/A

          \[\leadsto 1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{z \cdot \frac{1}{6}}, \frac{-1}{2}\right), \mathsf{neg}\left(z\right)\right), x\right) \]

      13. lower-*.f64 N/A

          \[\leadsto 1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \color{blue}{z \cdot \frac{1}{6}}, \frac{-1}{2}\right), \mathsf{neg}\left(z\right)\right), x\right) \]

      14. lower-neg.f64 58.6

          \[\leadsto 1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z \cdot 0.16666666666666666, -0.5\right), \color{blue}{-z}\right), x\right) \]

   5. Applied rewrites 58.6%

      \[\leadsto \color{blue}{1 + \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, z \cdot 0.16666666666666666, -0.5\right), -z\right), x\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(\frac{1}{6} \cdot {y}^{2} - 1\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot \left(\frac{1}{6} \cdot {y}^{2} - 1\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot \left(\frac{1}{6} \cdot {y}^{2} - 1\right) \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{z \cdot \left(y \cdot \left(\frac{1}{6} \cdot {y}^{2} - 1\right)\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto \color{blue}{z \cdot \left(y \cdot \left(\frac{1}{6} \cdot {y}^{2} - 1\right)\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto z \cdot \color{blue}{\left(y \cdot \left(\frac{1}{6} \cdot {y}^{2} - 1\right)\right)} \]

      6. sub-neg N/A

         \[\leadsto z \cdot \left(y \cdot \color{blue}{\left(\frac{1}{6} \cdot {y}^{2} + \left(\mathsf{neg}\left(1\right)\right)\right)}\right) \]

      7. *-commutative N/A

         \[\leadsto z \cdot \left(y \cdot \left(\color{blue}{{y}^{2} \cdot \frac{1}{6}} + \left(\mathsf{neg}\left(1\right)\right)\right)\right) \]

      8. unpow2 N/A

         \[\leadsto z \cdot \left(y \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot \frac{1}{6} + \left(\mathsf{neg}\left(1\right)\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto z \cdot \left(y \cdot \left(\color{blue}{y \cdot \left(y \cdot \frac{1}{6}\right)} + \left(\mathsf{neg}\left(1\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto z \cdot \left(y \cdot \left(y \cdot \color{blue}{\left(\frac{1}{6} \cdot y\right)} + \left(\mathsf{neg}\left(1\right)\right)\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto z \cdot \left(y \cdot \left(y \cdot \left(\frac{1}{6} \cdot y\right) + \color{blue}{-1}\right)\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto z \cdot \left(y \cdot \color{blue}{\mathsf{fma}\left(y, \frac{1}{6} \cdot y, -1\right)}\right) \]

      13. *-commutative N/A

          \[\leadsto z \cdot \left(y \cdot \mathsf{fma}\left(y, \color{blue}{y \cdot \frac{1}{6}}, -1\right)\right) \]

      14. lower-*.f64 40.0

          \[\leadsto z \cdot \left(y \cdot \mathsf{fma}\left(y, \color{blue}{y \cdot 0.16666666666666666}, -1\right)\right) \]

   8. Applied rewrites 40.0%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot \mathsf{fma}\left(y, y \cdot 0.16666666666666666, -1\right)\right)} \]

   9. Taylor expanded in y around 0

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot y\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto z \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \]

       2. lower-neg.f64 41.7

          \[\leadsto z \cdot \color{blue}{\left(-y\right)} \]

   11. Applied rewrites 41.7%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.8 \cdot 10^{+206}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.6% accurate, 53.0× speedup

Math

\[\begin{array}{l} \\ x + 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x 1.0))

C

double code(double x, double y, double z) {
	return x + 1.0;
}

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 + 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return x + 1.0;
}

Python

def code(x, y, z):
	return x + 1.0

Julia

function code(x, y, z)
	return Float64(x + 1.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + 1.0;
end

Wolfram

code[x_, y_, z_] := N[(x + 1.0), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

      \[\leadsto \color{blue}{x + 1} \]

   2. lower-+.f64 65.3

      \[\leadsto \color{blue}{x + 1} \]

5. Applied rewrites 65.3%

   \[\leadsto \color{blue}{x + 1} \]
6. Add Preprocessing

Alternative 12: 21.2% accurate, 212.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

      \[\leadsto \color{blue}{x + 1} \]

   2. lower-+.f64 65.3

      \[\leadsto \color{blue}{x + 1} \]

5. Applied rewrites 65.3%

   \[\leadsto \color{blue}{x + 1} \]

6. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1} \]
7. Step-by-step derivation

8. Applied rewrites 20.6%

   \[\leadsto \color{blue}{1} \]
9. Add Preprocessing

Reproduce

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