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

Percentage Accurate: 97.8% → 100.0%

Time: 5.6s

Alternatives: 7

Speedup: 1.7×

• 21.3% 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: 97.8% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. *-commutative N/A

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

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

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

   5. *-lft-identity N/A

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

   6. associate-+l- N/A

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

   7. *-commutative N/A

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

   8. distribute-lft-out-- N/A

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

   9. unsub-neg N/A

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

   10. mul-1-neg N/A

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

   11. sub-neg N/A

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

   12. mul-1-neg N/A

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

   13. +-commutative N/A

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

   14. mul-1-neg N/A

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

   15. *-commutative N/A

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

   16. distribute-lft-neg-in N/A

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

   17. lower-fma.f64 N/A

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

   18. +-commutative N/A

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

   19. distribute-neg-in N/A

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

   20. mul-1-neg N/A

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

   21. remove-double-neg N/A

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

   22. unsub-neg N/A

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

   23. lower--.f64 100.0

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

5. Applied rewrites 100.0%

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

Alternative 2: 60.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(-z\right) \cdot y\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+226}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -10000000:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1 \cdot z\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+137}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- z) y)))
   (if (<= y -8.2e+226)
     t_0
     (if (<= y -10000000.0)
       (* y x)
       (if (<= y 1.0) (* 1.0 z) (if (<= y 9.5e+137) t_0 (* y x)))))))

C

double code(double x, double y, double z) {
	double t_0 = -z * y;
	double tmp;
	if (y <= -8.2e+226) {
		tmp = t_0;
	} else if (y <= -10000000.0) {
		tmp = y * x;
	} else if (y <= 1.0) {
		tmp = 1.0 * z;
	} else if (y <= 9.5e+137) {
		tmp = t_0;
	} else {
		tmp = y * 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 = -z * y
    if (y <= (-8.2d+226)) then
        tmp = t_0
    else if (y <= (-10000000.0d0)) then
        tmp = y * x
    else if (y <= 1.0d0) then
        tmp = 1.0d0 * z
    else if (y <= 9.5d+137) then
        tmp = t_0
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -z * y;
	double tmp;
	if (y <= -8.2e+226) {
		tmp = t_0;
	} else if (y <= -10000000.0) {
		tmp = y * x;
	} else if (y <= 1.0) {
		tmp = 1.0 * z;
	} else if (y <= 9.5e+137) {
		tmp = t_0;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -z * y
	tmp = 0
	if y <= -8.2e+226:
		tmp = t_0
	elif y <= -10000000.0:
		tmp = y * x
	elif y <= 1.0:
		tmp = 1.0 * z
	elif y <= 9.5e+137:
		tmp = t_0
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-z) * y)
	tmp = 0.0
	if (y <= -8.2e+226)
		tmp = t_0;
	elseif (y <= -10000000.0)
		tmp = Float64(y * x);
	elseif (y <= 1.0)
		tmp = Float64(1.0 * z);
	elseif (y <= 9.5e+137)
		tmp = t_0;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -z * y;
	tmp = 0.0;
	if (y <= -8.2e+226)
		tmp = t_0;
	elseif (y <= -10000000.0)
		tmp = y * x;
	elseif (y <= 1.0)
		tmp = 1.0 * z;
	elseif (y <= 9.5e+137)
		tmp = t_0;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-z) * y), $MachinePrecision]}, If[LessEqual[y, -8.2e+226], t$95$0, If[LessEqual[y, -10000000.0], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.0], N[(1.0 * z), $MachinePrecision], If[LessEqual[y, 9.5e+137], t$95$0, N[(y * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.19999999999999971e226 or 1 < y < 9.50000000000000031e137

   1. Initial program 95.2%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   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

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-in N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. unsub-neg N/A

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

      13. lower--.f64 95.8

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

   5. Applied rewrites 95.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 72.2%

      \[\leadsto \left(-z\right) \cdot y \]

   if -8.19999999999999971e226 < y < -1e7 or 9.50000000000000031e137 < y

   1. Initial program 96.2%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 62.9

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

   5. Applied rewrites 62.9%

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

   if -1e7 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 74.4

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

   5. Applied rewrites 74.4%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 71.5%

      \[\leadsto 1 \cdot z \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - z\right) \cdot y\\ \mathbf{if}\;y \leq -10000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1350000:\\ \;\;\;\;\mathsf{fma}\left(-z, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- x z) y)))
   (if (<= y -10000000.0) t_0 (if (<= y 1350000.0) (fma (- z) y z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x - z) * y;
	double tmp;
	if (y <= -10000000.0) {
		tmp = t_0;
	} else if (y <= 1350000.0) {
		tmp = fma(-z, y, z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - z) * y)
	tmp = 0.0
	if (y <= -10000000.0)
		tmp = t_0;
	elseif (y <= 1350000.0)
		tmp = fma(Float64(-z), y, z);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -10000000.0], t$95$0, If[LessEqual[y, 1350000.0], N[((-z) * y + z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1e7 or 1.35e6 < y

   1. Initial program 95.8%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   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

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-in N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. unsub-neg N/A

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

      13. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if -1e7 < y < 1.35e6

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.0

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

   5. Applied rewrites 75.0%

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

   7. Applied rewrites 75.0%

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

Alternative 4: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - z\right) \cdot y\\ \mathbf{if}\;y \leq -10000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1350000:\\ \;\;\;\;\left(1 - y\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- x z) y)))
   (if (<= y -10000000.0) t_0 (if (<= y 1350000.0) (* (- 1.0 y) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x - z) * y;
	double tmp;
	if (y <= -10000000.0) {
		tmp = t_0;
	} else if (y <= 1350000.0) {
		tmp = (1.0 - y) * z;
	} 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 - z) * y
    if (y <= (-10000000.0d0)) then
        tmp = t_0
    else if (y <= 1350000.0d0) then
        tmp = (1.0d0 - y) * z
    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 - z) * y;
	double tmp;
	if (y <= -10000000.0) {
		tmp = t_0;
	} else if (y <= 1350000.0) {
		tmp = (1.0 - y) * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x - z) * y
	tmp = 0
	if y <= -10000000.0:
		tmp = t_0
	elif y <= 1350000.0:
		tmp = (1.0 - y) * z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x - z) * y)
	tmp = 0.0
	if (y <= -10000000.0)
		tmp = t_0;
	elseif (y <= 1350000.0)
		tmp = Float64(Float64(1.0 - y) * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x - z) * y;
	tmp = 0.0;
	if (y <= -10000000.0)
		tmp = t_0;
	elseif (y <= 1350000.0)
		tmp = (1.0 - y) * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x - z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -10000000.0], t$95$0, If[LessEqual[y, 1350000.0], N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1e7 or 1.35e6 < y

   1. Initial program 95.8%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   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

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

      2. +-commutative N/A

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

      3. remove-double-neg N/A

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

      4. mul-1-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-neg-in N/A

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

      7. lower-*.f64 N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. unsub-neg N/A

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

      13. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   if -1e7 < y < 1.35e6

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 75.0

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

   5. Applied rewrites 75.0%

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

Alternative 5: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{-86}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-145}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)))
   (if (<= z -5.5e-86) t_0 (if (<= z 1.12e-145) (* y x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (z <= -5.5e-86) {
		tmp = t_0;
	} else if (z <= 1.12e-145) {
		tmp = y * 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 = (1.0d0 - y) * z
    if (z <= (-5.5d-86)) then
        tmp = t_0
    else if (z <= 1.12d-145) then
        tmp = y * 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 = (1.0 - y) * z;
	double tmp;
	if (z <= -5.5e-86) {
		tmp = t_0;
	} else if (z <= 1.12e-145) {
		tmp = y * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - y) * z
	tmp = 0
	if z <= -5.5e-86:
		tmp = t_0
	elif z <= 1.12e-145:
		tmp = y * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (z <= -5.5e-86)
		tmp = t_0;
	elseif (z <= 1.12e-145)
		tmp = Float64(y * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - y) * z;
	tmp = 0.0;
	if (z <= -5.5e-86)
		tmp = t_0;
	elseif (z <= 1.12e-145)
		tmp = y * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -5.5e-86], t$95$0, If[LessEqual[z, 1.12e-145], N[(y * x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5e-86 or 1.12000000000000001e-145 < z

   1. Initial program 97.2%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 80.6

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

   5. Applied rewrites 80.6%

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

   if -5.5e-86 < z < 1.12000000000000001e-145

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 74.7

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

   5. Applied rewrites 74.7%

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

Alternative 6: 60.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -10000000:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-63}:\\ \;\;\;\;1 \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -10000000.0) (* y x) (if (<= y 1.35e-63) (* 1.0 z) (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -10000000.0) {
		tmp = y * x;
	} else if (y <= 1.35e-63) {
		tmp = 1.0 * z;
	} else {
		tmp = y * 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) :: tmp
    if (y <= (-10000000.0d0)) then
        tmp = y * x
    else if (y <= 1.35d-63) then
        tmp = 1.0d0 * z
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -10000000.0) {
		tmp = y * x;
	} else if (y <= 1.35e-63) {
		tmp = 1.0 * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -10000000.0:
		tmp = y * x
	elif y <= 1.35e-63:
		tmp = 1.0 * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -10000000.0)
		tmp = Float64(y * x);
	elseif (y <= 1.35e-63)
		tmp = Float64(1.0 * z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -10000000.0)
		tmp = y * x;
	elseif (y <= 1.35e-63)
		tmp = 1.0 * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -10000000.0], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.35e-63], N[(1.0 * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1e7 or 1.3500000000000001e-63 < y

   1. Initial program 96.2%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 50.9

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

   5. Applied rewrites 50.9%

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

   if -1e7 < y < 1.3500000000000001e-63

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 76.7

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

   5. Applied rewrites 76.7%

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

   6. Taylor expanded in y around 0

      \[\leadsto 1 \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 74.8%

      \[\leadsto 1 \cdot z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 42.2% 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 98.0%

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

3. Taylor expanded in z around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 38.6

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

5. Applied rewrites 38.6%

   \[\leadsto \color{blue}{y \cdot x} \]
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 2024254 
(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))))