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

Percentage Accurate: 97.9% → 100.0%

Time: 4.1s

Alternatives: 7

Speedup: 1.3×

• 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: 97.9% 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, 0.1× 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 98.0%

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

   1. +-commutative 98.0%

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

   2. sub-neg 98.0%

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

   3. distribute-rgt-in 98.0%

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

   4. *-lft-identity 98.0%

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

   5. associate-+l+ 98.0%

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

   6. +-commutative 98.0%

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

   7. *-commutative 98.0%

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

   8. neg-mul-1 98.0%

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

   9. associate-*r* 98.0%

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

   10. distribute-rgt-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. *-commutative 100.0%

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

   14. neg-mul-1 100.0%

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

   15. unsub-neg 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 60.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{+147}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+91}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-19}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+109} \lor \neg \left(y \leq 6.2 \cdot 10^{+199}\right) \land y \leq 2 \cdot 10^{+277}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- y))))
   (if (<= y -1e+147)
     t_0
     (if (<= y -3.2e+91)
       (* y x)
       (if (<= y -1.0)
         t_0
         (if (<= y 9.5e-19)
           z
           (if (or (<= y 6.4e+109) (and (not (<= y 6.2e+199)) (<= y 2e+277)))
             (* y x)
             t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -y;
	double tmp;
	if (y <= -1e+147) {
		tmp = t_0;
	} else if (y <= -3.2e+91) {
		tmp = y * x;
	} else if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 9.5e-19) {
		tmp = z;
	} else if ((y <= 6.4e+109) || (!(y <= 6.2e+199) && (y <= 2e+277))) {
		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 = z * -y
    if (y <= (-1d+147)) then
        tmp = t_0
    else if (y <= (-3.2d+91)) then
        tmp = y * x
    else if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 9.5d-19) then
        tmp = z
    else if ((y <= 6.4d+109) .or. (.not. (y <= 6.2d+199)) .and. (y <= 2d+277)) 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 = z * -y;
	double tmp;
	if (y <= -1e+147) {
		tmp = t_0;
	} else if (y <= -3.2e+91) {
		tmp = y * x;
	} else if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 9.5e-19) {
		tmp = z;
	} else if ((y <= 6.4e+109) || (!(y <= 6.2e+199) && (y <= 2e+277))) {
		tmp = y * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -y
	tmp = 0
	if y <= -1e+147:
		tmp = t_0
	elif y <= -3.2e+91:
		tmp = y * x
	elif y <= -1.0:
		tmp = t_0
	elif y <= 9.5e-19:
		tmp = z
	elif (y <= 6.4e+109) or (not (y <= 6.2e+199) and (y <= 2e+277)):
		tmp = y * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-y))
	tmp = 0.0
	if (y <= -1e+147)
		tmp = t_0;
	elseif (y <= -3.2e+91)
		tmp = Float64(y * x);
	elseif (y <= -1.0)
		tmp = t_0;
	elseif (y <= 9.5e-19)
		tmp = z;
	elseif ((y <= 6.4e+109) || (!(y <= 6.2e+199) && (y <= 2e+277)))
		tmp = Float64(y * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -y;
	tmp = 0.0;
	if (y <= -1e+147)
		tmp = t_0;
	elseif (y <= -3.2e+91)
		tmp = y * x;
	elseif (y <= -1.0)
		tmp = t_0;
	elseif (y <= 9.5e-19)
		tmp = z;
	elseif ((y <= 6.4e+109) || (~((y <= 6.2e+199)) && (y <= 2e+277)))
		tmp = y * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[y, -1e+147], t$95$0, If[LessEqual[y, -3.2e+91], N[(y * x), $MachinePrecision], If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 9.5e-19], z, If[Or[LessEqual[y, 6.4e+109], And[N[Not[LessEqual[y, 6.2e+199]], $MachinePrecision], LessEqual[y, 2e+277]]], N[(y * x), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.9999999999999998e146 or -3.19999999999999989e91 < y < -1 or 6.4000000000000002e109 < y < 6.19999999999999971e199 or 2.00000000000000001e277 < y

   1. Initial program 96.1%

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

   2. Taylor expanded in y around inf 97.9%

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

      1. neg-mul-1 97.9%

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

      2. +-commutative 97.9%

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

      3. sub-neg 97.9%

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

   4. Simplified 97.9%

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

   5. Taylor expanded in x around 0 70.0%

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

      1. associate-*r* 70.0%

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

      2. mul-1-neg 70.0%

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

   7. Simplified 70.0%

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

   if -9.9999999999999998e146 < y < -3.19999999999999989e91 or 9.4999999999999995e-19 < y < 6.4000000000000002e109 or 6.19999999999999971e199 < y < 2.00000000000000001e277

   1. Initial program 96.3%

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

   2. Taylor expanded in x around inf 77.9%

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

   if -1 < y < 9.4999999999999995e-19

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.5%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+147}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+91}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-19}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+109} \lor \neg \left(y \leq 6.2 \cdot 10^{+199}\right) \land y \leq 2 \cdot 10^{+277}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 83.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-29} \lor \neg \left(y \leq 3 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.1e-29) (not (<= y 3e-16))) (* y (- x z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1e-29) || !(y <= 3e-16)) {
		tmp = y * (x - z);
	} else {
		tmp = 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 ((y <= (-3.1d-29)) .or. (.not. (y <= 3d-16))) then
        tmp = y * (x - z)
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1e-29) || !(y <= 3e-16)) {
		tmp = y * (x - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.1e-29) or not (y <= 3e-16):
		tmp = y * (x - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.1e-29) || !(y <= 3e-16))
		tmp = Float64(y * Float64(x - z));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.1e-29) || ~((y <= 3e-16)))
		tmp = y * (x - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.1e-29], N[Not[LessEqual[y, 3e-16]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000026e-29 or 2.99999999999999994e-16 < y

   1. Initial program 96.4%

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

   2. Taylor expanded in y around inf 96.3%

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

      1. neg-mul-1 96.3%

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

      2. +-commutative 96.3%

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

      3. sub-neg 96.3%

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

   4. Simplified 96.3%

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

   if -3.10000000000000026e-29 < y < 2.99999999999999994e-16

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 84.4%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-29} \lor \neg \left(y \leq 3 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 4: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 7.8 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 7.8e-16))) (* y (- x z)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 7.8e-16)) {
		tmp = y * (x - z);
	} else {
		tmp = z + (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 <= (-1.0d0)) .or. (.not. (y <= 7.8d-16))) then
        tmp = y * (x - z)
    else
        tmp = z + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 7.8e-16)) {
		tmp = y * (x - z);
	} else {
		tmp = z + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 7.8e-16):
		tmp = y * (x - z)
	else:
		tmp = z + (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 7.8e-16))
		tmp = Float64(y * Float64(x - z));
	else
		tmp = Float64(z + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 7.8e-16)))
		tmp = y * (x - z);
	else
		tmp = z + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 7.8e-16]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 7.79999999999999954e-16 < y

   1. Initial program 96.2%

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

   2. Taylor expanded in y around inf 98.8%

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

      1. neg-mul-1 98.8%

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

      2. +-commutative 98.8%

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

      3. sub-neg 98.8%

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

   4. Simplified 98.8%

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

   if -1 < y < 7.79999999999999954e-16

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. *-lft-identity 100.0%

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

      5. associate-+l+ 100.0%

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

      6. +-commutative 100.0%

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

      7. *-commutative 100.0%

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

      8. neg-mul-1 100.0%

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

      9. associate-*r* 100.0%

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

      10. distribute-rgt-out 100.0%

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

      11. fma-def 100.0%

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

      12. +-commutative 100.0%

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

      13. *-commutative 100.0%

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

      14. neg-mul-1 100.0%

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

      15. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around inf 98.5%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 7.8 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]

Alternative 5: 61.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-33}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-19}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.95e-33) (* y x) (if (<= y 2.4e-19) z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.95e-33) {
		tmp = y * x;
	} else if (y <= 2.4e-19) {
		tmp = 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 <= (-2.95d-33)) then
        tmp = y * x
    else if (y <= 2.4d-19) then
        tmp = 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 <= -2.95e-33) {
		tmp = y * x;
	} else if (y <= 2.4e-19) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.95e-33:
		tmp = y * x
	elif y <= 2.4e-19:
		tmp = z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.95e-33)
		tmp = Float64(y * x);
	elseif (y <= 2.4e-19)
		tmp = z;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.95e-33)
		tmp = y * x;
	elseif (y <= 2.4e-19)
		tmp = z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.95e-33], N[(y * x), $MachinePrecision], If[LessEqual[y, 2.4e-19], z, N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.94999999999999993e-33 or 2.40000000000000023e-19 < y

   1. Initial program 96.4%

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

   2. Taylor expanded in x around inf 50.9%

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

   if -2.94999999999999993e-33 < y < 2.40000000000000023e-19

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 84.4%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-33}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-19}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 6: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

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 + (y * (x - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. +-commutative 98.0%

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

   2. sub-neg 98.0%

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

   3. distribute-rgt-in 98.0%

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

   4. *-lft-identity 98.0%

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

   5. associate-+l+ 98.0%

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

   6. +-commutative 98.0%

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

   7. *-commutative 98.0%

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

   8. neg-mul-1 98.0%

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

   9. associate-*r* 98.0%

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

   10. distribute-rgt-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. *-commutative 100.0%

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

   14. neg-mul-1 100.0%

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

   15. unsub-neg 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in y around 0 100.0%

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

5. Final simplification 100.0%

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

Alternative 7: 36.4% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 98.0%

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

2. Taylor expanded in y around 0 41.2%

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

3. Final simplification 41.2%

   \[\leadsto z \]

Developer target: 100.0% accurate, 1.3× 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 2023196 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (- z (* (- z x) y))

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