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

Percentage Accurate: 97.9% → 100.0%

Time: 4.9s

Alternatives: 7

Speedup: 1.3×

• 20.1% 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, 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 97.2%

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

   1. distribute-lft-out-- 97.2%

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

   2. *-rgt-identity 97.2%

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

   3. cancel-sign-sub-inv 97.2%

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

   4. +-commutative 97.2%

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

   5. associate-+r+ 97.2%

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

   6. +-commutative 97.2%

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

   7. distribute-rgt-out 100.0%

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

   8. fma-def 100.0%

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

   9. +-commutative 100.0%

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

   10. 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. Step-by-step derivation

   1. fma-udef 100.0%

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

5. Applied egg-rr 100.0%

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

6. Final simplification 100.0%

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

Alternative 2: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+242}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -6.3 \cdot 10^{+215}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+150}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{+42}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-13} \lor \neg \left(y \leq -1.8 \cdot 10^{-100}\right) \land \left(y \leq -1.7 \cdot 10^{-116} \lor \neg \left(y \leq 6 \cdot 10^{-34}\right)\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z))))
   (if (<= y -9.5e+242)
     t_0
     (if (<= y -6.3e+215)
       (* y x)
       (if (<= y -1.9e+150)
         t_0
         (if (<= y -9.8e+42)
           (* y x)
           (if (<= y -5.2e+14)
             t_0
             (if (or (<= y -1.45e-13)
                     (and (not (<= y -1.8e-100))
                          (or (<= y -1.7e-116) (not (<= y 6e-34)))))
               (* y x)
               z))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -z;
	double tmp;
	if (y <= -9.5e+242) {
		tmp = t_0;
	} else if (y <= -6.3e+215) {
		tmp = y * x;
	} else if (y <= -1.9e+150) {
		tmp = t_0;
	} else if (y <= -9.8e+42) {
		tmp = y * x;
	} else if (y <= -5.2e+14) {
		tmp = t_0;
	} else if ((y <= -1.45e-13) || (!(y <= -1.8e-100) && ((y <= -1.7e-116) || !(y <= 6e-34)))) {
		tmp = y * x;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = y * -z
    if (y <= (-9.5d+242)) then
        tmp = t_0
    else if (y <= (-6.3d+215)) then
        tmp = y * x
    else if (y <= (-1.9d+150)) then
        tmp = t_0
    else if (y <= (-9.8d+42)) then
        tmp = y * x
    else if (y <= (-5.2d+14)) then
        tmp = t_0
    else if ((y <= (-1.45d-13)) .or. (.not. (y <= (-1.8d-100))) .and. (y <= (-1.7d-116)) .or. (.not. (y <= 6d-34))) then
        tmp = y * x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * -z;
	double tmp;
	if (y <= -9.5e+242) {
		tmp = t_0;
	} else if (y <= -6.3e+215) {
		tmp = y * x;
	} else if (y <= -1.9e+150) {
		tmp = t_0;
	} else if (y <= -9.8e+42) {
		tmp = y * x;
	} else if (y <= -5.2e+14) {
		tmp = t_0;
	} else if ((y <= -1.45e-13) || (!(y <= -1.8e-100) && ((y <= -1.7e-116) || !(y <= 6e-34)))) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -z
	tmp = 0
	if y <= -9.5e+242:
		tmp = t_0
	elif y <= -6.3e+215:
		tmp = y * x
	elif y <= -1.9e+150:
		tmp = t_0
	elif y <= -9.8e+42:
		tmp = y * x
	elif y <= -5.2e+14:
		tmp = t_0
	elif (y <= -1.45e-13) or (not (y <= -1.8e-100) and ((y <= -1.7e-116) or not (y <= 6e-34))):
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -9.5e+242)
		tmp = t_0;
	elseif (y <= -6.3e+215)
		tmp = Float64(y * x);
	elseif (y <= -1.9e+150)
		tmp = t_0;
	elseif (y <= -9.8e+42)
		tmp = Float64(y * x);
	elseif (y <= -5.2e+14)
		tmp = t_0;
	elseif ((y <= -1.45e-13) || (!(y <= -1.8e-100) && ((y <= -1.7e-116) || !(y <= 6e-34))))
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -z;
	tmp = 0.0;
	if (y <= -9.5e+242)
		tmp = t_0;
	elseif (y <= -6.3e+215)
		tmp = y * x;
	elseif (y <= -1.9e+150)
		tmp = t_0;
	elseif (y <= -9.8e+42)
		tmp = y * x;
	elseif (y <= -5.2e+14)
		tmp = t_0;
	elseif ((y <= -1.45e-13) || (~((y <= -1.8e-100)) && ((y <= -1.7e-116) || ~((y <= 6e-34)))))
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -9.5e+242], t$95$0, If[LessEqual[y, -6.3e+215], N[(y * x), $MachinePrecision], If[LessEqual[y, -1.9e+150], t$95$0, If[LessEqual[y, -9.8e+42], N[(y * x), $MachinePrecision], If[LessEqual[y, -5.2e+14], t$95$0, If[Or[LessEqual[y, -1.45e-13], And[N[Not[LessEqual[y, -1.8e-100]], $MachinePrecision], Or[LessEqual[y, -1.7e-116], N[Not[LessEqual[y, 6e-34]], $MachinePrecision]]]], N[(y * x), $MachinePrecision], z]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.49999999999999995e242 or -6.2999999999999997e215 < y < -1.89999999999999995e150 or -9.8000000000000004e42 < y < -5.2e14

   1. Initial program 86.1%

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

   2. Taylor expanded in x around 0 82.1%

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

   3. Taylor expanded in y around inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. distribute-lft-neg-out 82.1%

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

      3. *-commutative 82.1%

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

   5. Simplified 82.1%

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

   if -9.49999999999999995e242 < y < -6.2999999999999997e215 or -1.89999999999999995e150 < y < -9.8000000000000004e42 or -5.2e14 < y < -1.4499999999999999e-13 or -1.7999999999999999e-100 < y < -1.69999999999999996e-116 or 6e-34 < y

   1. Initial program 97.2%

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

   2. Taylor expanded in x around inf 68.1%

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

      1. *-commutative 68.1%

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

   4. Simplified 68.1%

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

   if -1.4499999999999999e-13 < y < -1.7999999999999999e-100 or -1.69999999999999996e-116 < y < 6e-34

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 78.7%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+242}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -6.3 \cdot 10^{+215}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+150}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{+42}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+14}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-13} \lor \neg \left(y \leq -1.8 \cdot 10^{-100}\right) \land \left(y \leq -1.7 \cdot 10^{-116} \lor \neg \left(y \leq 6 \cdot 10^{-34}\right)\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 3: 84.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x - z\right)\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{-18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-100}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-116}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-23}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x z))))
   (if (<= y -6.4e-18)
     t_0
     (if (<= y -1.6e-100)
       z
       (if (<= y -2.8e-116) (* y x) (if (<= y 1.18e-23) z t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double tmp;
	if (y <= -6.4e-18) {
		tmp = t_0;
	} else if (y <= -1.6e-100) {
		tmp = z;
	} else if (y <= -2.8e-116) {
		tmp = y * x;
	} else if (y <= 1.18e-23) {
		tmp = 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 = y * (x - z)
    if (y <= (-6.4d-18)) then
        tmp = t_0
    else if (y <= (-1.6d-100)) then
        tmp = z
    else if (y <= (-2.8d-116)) then
        tmp = y * x
    else if (y <= 1.18d-23) then
        tmp = 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 = y * (x - z);
	double tmp;
	if (y <= -6.4e-18) {
		tmp = t_0;
	} else if (y <= -1.6e-100) {
		tmp = z;
	} else if (y <= -2.8e-116) {
		tmp = y * x;
	} else if (y <= 1.18e-23) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x - z)
	tmp = 0
	if y <= -6.4e-18:
		tmp = t_0
	elif y <= -1.6e-100:
		tmp = z
	elif y <= -2.8e-116:
		tmp = y * x
	elif y <= 1.18e-23:
		tmp = 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 <= -6.4e-18)
		tmp = t_0;
	elseif (y <= -1.6e-100)
		tmp = z;
	elseif (y <= -2.8e-116)
		tmp = Float64(y * x);
	elseif (y <= 1.18e-23)
		tmp = z;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x - z);
	tmp = 0.0;
	if (y <= -6.4e-18)
		tmp = t_0;
	elseif (y <= -1.6e-100)
		tmp = z;
	elseif (y <= -2.8e-116)
		tmp = y * x;
	elseif (y <= 1.18e-23)
		tmp = z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.4e-18], t$95$0, If[LessEqual[y, -1.6e-100], z, If[LessEqual[y, -2.8e-116], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.18e-23], z, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.3999999999999998e-18 or 1.18e-23 < y

   1. Initial program 94.6%

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

   2. Taylor expanded in y around inf 94.8%

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

      1. neg-mul-1 94.8%

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

      2. sub-neg 94.8%

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

   4. Simplified 94.8%

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

   if -6.3999999999999998e-18 < y < -1.60000000000000008e-100 or -2.7999999999999999e-116 < y < 1.18e-23

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 78.2%

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

   if -1.60000000000000008e-100 < y < -2.7999999999999999e-116

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-100}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-116}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-23}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]

Alternative 4: 84.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x - z\right)\\ t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;y \leq -0.000112:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -7.3 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-116}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- x z))) (t_1 (* z (- 1.0 y))))
   (if (<= y -0.000112)
     t_0
     (if (<= y -7.3e-100)
       t_1
       (if (<= y -2.8e-116) (* y x) (if (<= y 2.2e-11) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double t_1 = z * (1.0 - y);
	double tmp;
	if (y <= -0.000112) {
		tmp = t_0;
	} else if (y <= -7.3e-100) {
		tmp = t_1;
	} else if (y <= -2.8e-116) {
		tmp = y * x;
	} else if (y <= 2.2e-11) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y * (x - z)
    t_1 = z * (1.0d0 - y)
    if (y <= (-0.000112d0)) then
        tmp = t_0
    else if (y <= (-7.3d-100)) then
        tmp = t_1
    else if (y <= (-2.8d-116)) then
        tmp = y * x
    else if (y <= 2.2d-11) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x - z);
	double t_1 = z * (1.0 - y);
	double tmp;
	if (y <= -0.000112) {
		tmp = t_0;
	} else if (y <= -7.3e-100) {
		tmp = t_1;
	} else if (y <= -2.8e-116) {
		tmp = y * x;
	} else if (y <= 2.2e-11) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x - z)
	t_1 = z * (1.0 - y)
	tmp = 0
	if y <= -0.000112:
		tmp = t_0
	elif y <= -7.3e-100:
		tmp = t_1
	elif y <= -2.8e-116:
		tmp = y * x
	elif y <= 2.2e-11:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x - z))
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (y <= -0.000112)
		tmp = t_0;
	elseif (y <= -7.3e-100)
		tmp = t_1;
	elseif (y <= -2.8e-116)
		tmp = Float64(y * x);
	elseif (y <= 2.2e-11)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x - z);
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if (y <= -0.000112)
		tmp = t_0;
	elseif (y <= -7.3e-100)
		tmp = t_1;
	elseif (y <= -2.8e-116)
		tmp = y * x;
	elseif (y <= 2.2e-11)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.000112], t$95$0, If[LessEqual[y, -7.3e-100], t$95$1, If[LessEqual[y, -2.8e-116], N[(y * x), $MachinePrecision], If[LessEqual[y, 2.2e-11], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.11999999999999998e-4 or 2.2000000000000002e-11 < y

   1. Initial program 94.2%

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

   2. Taylor expanded in y around inf 98.2%

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

      1. neg-mul-1 98.2%

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

      2. sub-neg 98.2%

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

   4. Simplified 98.2%

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

   if -1.11999999999999998e-4 < y < -7.2999999999999995e-100 or -2.7999999999999999e-116 < y < 2.2000000000000002e-11

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.7%

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

   if -7.2999999999999995e-100 < y < -2.7999999999999999e-116

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.000112:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{elif}\;y \leq -7.3 \cdot 10^{-100}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-116}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-11}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]

Alternative 5: 61.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-13} \lor \neg \left(y \leq -1.6 \cdot 10^{-100} \lor \neg \left(y \leq -2.35 \cdot 10^{-116}\right) \land y \leq 1.5 \cdot 10^{-33}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.65e-13)
         (not
          (or (<= y -1.6e-100) (and (not (<= y -2.35e-116)) (<= y 1.5e-33)))))
   (* y x)
   z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.65e-13) || !((y <= -1.6e-100) || (!(y <= -2.35e-116) && (y <= 1.5e-33)))) {
		tmp = y * x;
	} 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 <= (-1.65d-13)) .or. (.not. (y <= (-1.6d-100)) .or. (.not. (y <= (-2.35d-116))) .and. (y <= 1.5d-33))) then
        tmp = y * x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.65e-13) || !((y <= -1.6e-100) || (!(y <= -2.35e-116) && (y <= 1.5e-33)))) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.65e-13) or not ((y <= -1.6e-100) or (not (y <= -2.35e-116) and (y <= 1.5e-33))):
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.65e-13) || !((y <= -1.6e-100) || (!(y <= -2.35e-116) && (y <= 1.5e-33))))
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.65e-13) || ~(((y <= -1.6e-100) || (~((y <= -2.35e-116)) && (y <= 1.5e-33)))))
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.65e-13], N[Not[Or[LessEqual[y, -1.6e-100], And[N[Not[LessEqual[y, -2.35e-116]], $MachinePrecision], LessEqual[y, 1.5e-33]]]], $MachinePrecision]], N[(y * x), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e-13 or -1.60000000000000008e-100 < y < -2.34999999999999997e-116 or 1.5000000000000001e-33 < y

   1. Initial program 94.8%

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

   2. Taylor expanded in x around inf 58.9%

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

      1. *-commutative 58.9%

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

   4. Simplified 58.9%

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

   if -1.65e-13 < y < -1.60000000000000008e-100 or -2.34999999999999997e-116 < y < 1.5000000000000001e-33

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 78.7%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-13} \lor \neg \left(y \leq -1.6 \cdot 10^{-100} \lor \neg \left(y \leq -2.35 \cdot 10^{-116}\right) \land y \leq 1.5 \cdot 10^{-33}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 6: 98.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 5 \cdot 10^{-9}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 5e-9))) (* y (- x z)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 5e-9)) {
		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 <= 5d-9))) 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 <= 5e-9)) {
		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 <= 5e-9):
		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 <= 5e-9))
		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 <= 5e-9)))
		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, 5e-9]], $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 5.0000000000000001e-9 < y

   1. Initial program 94.1%

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

   2. Taylor expanded in y around inf 98.1%

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

      1. neg-mul-1 98.1%

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

      2. sub-neg 98.1%

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

   4. Simplified 98.1%

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

   if -1 < y < 5.0000000000000001e-9

   1. Initial program 100.0%

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

      1. distribute-lft-out-- 100.0%

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

      2. *-rgt-identity 100.0%

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

      3. cancel-sign-sub-inv 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+r+ 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-rgt-out 100.0%

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

      8. fma-def 100.0%

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

      9. +-commutative 100.0%

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

      10. 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. Step-by-step derivation

      1. fma-udef 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 98.9%

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

      1. *-commutative 98.9%

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

   8. Simplified 98.9%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 5 \cdot 10^{-9}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]

Alternative 7: 36.6% 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 97.2%

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

2. Taylor expanded in y around 0 39.9%

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

3. Final simplification 39.9%

   \[\leadsto z \]

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 2024024 
(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))))