Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3

Percentage Accurate: 97.7% → 100.0%

Time: 7.0s

Alternatives: 5

Speedup: 1.7×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot y + z \cdot \left(1 - y\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - 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 * y) + (z * (1.0d0 - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot y + z \cdot \left(1 - y\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - 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 * y) + (z * (1.0d0 - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Julia

function code(x, y, z)
	return fma(y, Float64(x - z), z)
end

Wolfram

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

Derivation

1. Initial program 95.7%

   \[x \cdot y + z \cdot \left(1 - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

   1. distribute-rgt-out-- N/A

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

   2. unsub-neg N/A

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

   3. *-lft-identity N/A

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

   4. mul-1-neg N/A

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

   5. +-commutative N/A

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

   6. associate-+l+ N/A

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

   7. *-commutative N/A

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

   8. mul-1-neg N/A

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

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

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

   10. mul-1-neg N/A

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

   11. distribute-lft-in N/A

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

   12. +-commutative N/A

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

   13. remove-double-neg N/A

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

   14. mul-1-neg N/A

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

   15. mul-1-neg N/A

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

   16. distribute-neg-in N/A

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

   17. lower-fma.f64 N/A

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

5. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, x - z, z\right)} \]
6. Add Preprocessing

Alternative 2: 99.1% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x z))))
   (if (<= y -1.0) t_0 (if (<= y 1.0) (fma y x z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 1.0) {
		tmp = fma(y, x, z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 91.4%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-in N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. unsub-neg N/A

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

      12. lower--.f64 97.6

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

   5. Applied rewrites 97.6%

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

   if -1 < y < 1

   1. Initial program 99.9%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-neg N/A

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

      8. distribute-lft-in N/A

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

      9. *-rgt-identity N/A

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

      10. associate-+l+ N/A

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

      11. lower-+.f64 N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-neg.f64 100.0

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

   4. Applied rewrites 100.0%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 97.6

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

   7. Applied rewrites 97.6%

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

      1. lift-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 97.6

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

   9. Applied rewrites 97.6%

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

Alternative 3: 76.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -y \cdot z\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{+232}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* y z))))
   (if (<= y -2.15e+232) t_0 (if (<= y 1.5e+29) (fma y x z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -(y * z);
	double tmp;
	if (y <= -2.15e+232) {
		tmp = t_0;
	} else if (y <= 1.5e+29) {
		tmp = fma(y, x, z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(-Float64(y * z))
	tmp = 0.0
	if (y <= -2.15e+232)
		tmp = t_0;
	elseif (y <= 1.5e+29)
		tmp = fma(y, x, z);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = (-N[(y * z), $MachinePrecision])}, If[LessEqual[y, -2.15e+232], t$95$0, If[LessEqual[y, 1.5e+29], N[(y * x + z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1500000000000001e232 or 1.5e29 < y

   1. Initial program 88.9%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. remove-double-neg N/A

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

      3. mul-1-neg N/A

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

      4. mul-1-neg N/A

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

      5. distribute-neg-in N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. unsub-neg N/A

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

      12. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 59.5

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

   8. Applied rewrites 59.5%

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

   if -2.1500000000000001e232 < y < 1.5e29

   1. Initial program 98.8%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. sub-neg N/A

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

      8. distribute-lft-in N/A

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

      9. *-rgt-identity N/A

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

      10. associate-+l+ N/A

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

      11. lower-+.f64 N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-neg.f64 98.8

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

   4. Applied rewrites 98.8%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 87.3

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

   7. Applied rewrites 87.3%

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

      1. lift-*.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lower-fma.f64 87.4

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

   9. Applied rewrites 87.4%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+232}:\\ \;\;\;\;-y \cdot z\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;-y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.6% accurate, 2.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.7%

   \[x \cdot y + z \cdot \left(1 - y\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. +-commutative N/A

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

   5. lift-*.f64 N/A

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

   6. lift--.f64 N/A

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

   7. sub-neg N/A

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

   8. distribute-lft-in N/A

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

   9. *-rgt-identity N/A

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

   10. associate-+l+ N/A

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

   11. lower-+.f64 N/A

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

   12. lower-fma.f64 N/A

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

   13. lower-neg.f64 97.2

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

4. Applied rewrites 97.2%

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

5. Taylor expanded in z around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 74.9

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

7. Applied rewrites 74.9%

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

   1. lift-*.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-*.f64 N/A

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

   4. lower-fma.f64 74.9

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

9. Applied rewrites 74.9%

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

Alternative 5: 41.8% accurate, 2.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return y * 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 = y * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

   \[x \cdot y + z \cdot \left(1 - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 39.4

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

5. Applied rewrites 39.4%

   \[\leadsto \color{blue}{y \cdot x} \]
6. Add Preprocessing

Developer Target 1: 100.0% accurate, 1.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return z - ((z - x) * 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 = z - ((z - x) * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024216 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- z (* (- z x) y)))

  (+ (* x y) (* z (- 1.0 y))))