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

Percentage Accurate: 98.0% → 100.0%

Time: 2.6s

Alternatives: 6

Speedup: 0.5×

• 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: 98.0% 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 96.9%

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

   1. distribute-lft-out-- 96.9%

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

   2. *-rgt-identity 96.9%

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

   3. cancel-sign-sub-inv 96.9%

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

   4. +-commutative 96.9%

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

   5. associate-+r+ 96.9%

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

   6. +-commutative 96.9%

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

   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. Final simplification 100.0%

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

Alternative 2: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+243}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+187}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-73}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-48}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+80} \lor \neg \left(y \leq 3.4 \cdot 10^{+163}\right) \land \left(y \leq 2.9 \cdot 10^{+199} \lor \neg \left(y \leq 1.4 \cdot 10^{+258}\right)\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z))))
   (if (<= y -6.2e+243)
     t_0
     (if (<= y -7e+187)
       (* y x)
       (if (<= y -2e+36)
         t_0
         (if (<= y -6e-73)
           (* y x)
           (if (<= y 1.15e-48)
             z
             (if (or (<= y 5.2e+80)
                     (and (not (<= y 3.4e+163))
                          (or (<= y 2.9e+199) (not (<= y 1.4e+258)))))
               (* y x)
               t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -z;
	double tmp;
	if (y <= -6.2e+243) {
		tmp = t_0;
	} else if (y <= -7e+187) {
		tmp = y * x;
	} else if (y <= -2e+36) {
		tmp = t_0;
	} else if (y <= -6e-73) {
		tmp = y * x;
	} else if (y <= 1.15e-48) {
		tmp = z;
	} else if ((y <= 5.2e+80) || (!(y <= 3.4e+163) && ((y <= 2.9e+199) || !(y <= 1.4e+258)))) {
		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 = y * -z
    if (y <= (-6.2d+243)) then
        tmp = t_0
    else if (y <= (-7d+187)) then
        tmp = y * x
    else if (y <= (-2d+36)) then
        tmp = t_0
    else if (y <= (-6d-73)) then
        tmp = y * x
    else if (y <= 1.15d-48) then
        tmp = z
    else if ((y <= 5.2d+80) .or. (.not. (y <= 3.4d+163)) .and. (y <= 2.9d+199) .or. (.not. (y <= 1.4d+258))) 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 = y * -z;
	double tmp;
	if (y <= -6.2e+243) {
		tmp = t_0;
	} else if (y <= -7e+187) {
		tmp = y * x;
	} else if (y <= -2e+36) {
		tmp = t_0;
	} else if (y <= -6e-73) {
		tmp = y * x;
	} else if (y <= 1.15e-48) {
		tmp = z;
	} else if ((y <= 5.2e+80) || (!(y <= 3.4e+163) && ((y <= 2.9e+199) || !(y <= 1.4e+258)))) {
		tmp = y * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -z
	tmp = 0
	if y <= -6.2e+243:
		tmp = t_0
	elif y <= -7e+187:
		tmp = y * x
	elif y <= -2e+36:
		tmp = t_0
	elif y <= -6e-73:
		tmp = y * x
	elif y <= 1.15e-48:
		tmp = z
	elif (y <= 5.2e+80) or (not (y <= 3.4e+163) and ((y <= 2.9e+199) or not (y <= 1.4e+258))):
		tmp = y * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -6.2e+243)
		tmp = t_0;
	elseif (y <= -7e+187)
		tmp = Float64(y * x);
	elseif (y <= -2e+36)
		tmp = t_0;
	elseif (y <= -6e-73)
		tmp = Float64(y * x);
	elseif (y <= 1.15e-48)
		tmp = z;
	elseif ((y <= 5.2e+80) || (!(y <= 3.4e+163) && ((y <= 2.9e+199) || !(y <= 1.4e+258))))
		tmp = Float64(y * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -z;
	tmp = 0.0;
	if (y <= -6.2e+243)
		tmp = t_0;
	elseif (y <= -7e+187)
		tmp = y * x;
	elseif (y <= -2e+36)
		tmp = t_0;
	elseif (y <= -6e-73)
		tmp = y * x;
	elseif (y <= 1.15e-48)
		tmp = z;
	elseif ((y <= 5.2e+80) || (~((y <= 3.4e+163)) && ((y <= 2.9e+199) || ~((y <= 1.4e+258)))))
		tmp = y * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -6.2e+243], t$95$0, If[LessEqual[y, -7e+187], N[(y * x), $MachinePrecision], If[LessEqual[y, -2e+36], t$95$0, If[LessEqual[y, -6e-73], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.15e-48], z, If[Or[LessEqual[y, 5.2e+80], And[N[Not[LessEqual[y, 3.4e+163]], $MachinePrecision], Or[LessEqual[y, 2.9e+199], N[Not[LessEqual[y, 1.4e+258]], $MachinePrecision]]]], N[(y * x), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.2e243 or -6.9999999999999995e187 < y < -2.00000000000000008e36 or 5.19999999999999963e80 < y < 3.4000000000000001e163 or 2.8999999999999999e199 < y < 1.39999999999999991e258

   1. Initial program 92.3%

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

   2. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 68.9%

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

      1. mul-1-neg 68.9%

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

      2. distribute-rgt-neg-out 68.9%

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

   7. Simplified 68.9%

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

   if -6.2e243 < y < -6.9999999999999995e187 or -2.00000000000000008e36 < y < -6e-73 or 1.15e-48 < y < 5.19999999999999963e80 or 3.4000000000000001e163 < y < 2.8999999999999999e199 or 1.39999999999999991e258 < y

   1. Initial program 97.6%

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

   2. Taylor expanded in x around inf 67.6%

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

   if -6e-73 < y < 1.15e-48

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.9%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+243}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+187}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-73}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-48}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+80} \lor \neg \left(y \leq 3.4 \cdot 10^{+163}\right) \land \left(y \leq 2.9 \cdot 10^{+199} \lor \neg \left(y \leq 1.4 \cdot 10^{+258}\right)\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 3: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right) + y \cdot x\\ \mathbf{if}\;t_0 \leq 8 \cdot 10^{+298}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* z (- 1.0 y)) (* y x))))
   (if (<= t_0 8e+298) t_0 (* y (- x z)))))

C

double code(double x, double y, double z) {
	double t_0 = (z * (1.0 - y)) + (y * x);
	double tmp;
	if (t_0 <= 8e+298) {
		tmp = t_0;
	} else {
		tmp = y * (x - 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 = (z * (1.0d0 - y)) + (y * x)
    if (t_0 <= 8d+298) then
        tmp = t_0
    else
        tmp = y * (x - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * (1.0 - y)) + (y * x);
	double tmp;
	if (t_0 <= 8e+298) {
		tmp = t_0;
	} else {
		tmp = y * (x - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * (1.0 - y)) + (y * x)
	tmp = 0
	if t_0 <= 8e+298:
		tmp = t_0
	else:
		tmp = y * (x - z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * Float64(1.0 - y)) + Float64(y * x))
	tmp = 0.0
	if (t_0 <= 8e+298)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(x - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * (1.0 - y)) + (y * x);
	tmp = 0.0;
	if (t_0 <= 8e+298)
		tmp = t_0;
	else
		tmp = y * (x - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 8e+298], t$95$0, N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x y) (*.f64 z (-.f64 1 y))) < 7.9999999999999997e298

   1. Initial program 100.0%

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

   if 7.9999999999999997e298 < (+.f64 (*.f64 x y) (*.f64 z (-.f64 1 y)))

   1. Initial program 80.5%

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

   2. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) + y \cdot x \leq 8 \cdot 10^{+298}:\\ \;\;\;\;z \cdot \left(1 - y\right) + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x - z\right)\\ \end{array} \]

Alternative 4: 84.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-70} \lor \neg \left(y \leq 4.5 \cdot 10^{-49}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.35e-70) (not (<= y 4.5e-49))) (* y (- x z)) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.35e-70) || !(y <= 4.5e-49)) {
		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 <= (-1.35d-70)) .or. (.not. (y <= 4.5d-49))) 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 <= -1.35e-70) || !(y <= 4.5e-49)) {
		tmp = y * (x - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.35e-70) or not (y <= 4.5e-49):
		tmp = y * (x - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.35e-70) || !(y <= 4.5e-49))
		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 <= -1.35e-70) || ~((y <= 4.5e-49)))
		tmp = y * (x - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.35e-70], N[Not[LessEqual[y, 4.5e-49]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -1.3500000000000001e-70 or 4.5000000000000002e-49 < y

   1. Initial program 95.1%

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

   2. Taylor expanded in y around inf 93.8%

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

      1. +-commutative 93.8%

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

      2. mul-1-neg 93.8%

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

      3. unsub-neg 93.8%

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

   4. Simplified 93.8%

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

   if -1.3500000000000001e-70 < y < 4.5000000000000002e-49

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.9%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-70} \lor \neg \left(y \leq 4.5 \cdot 10^{-49}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 5: 61.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-73}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-49}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6e-73) (* y x) (if (<= y 1.26e-49) z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e-73) {
		tmp = y * x;
	} else if (y <= 1.26e-49) {
		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 <= (-6d-73)) then
        tmp = y * x
    else if (y <= 1.26d-49) 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 <= -6e-73) {
		tmp = y * x;
	} else if (y <= 1.26e-49) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6e-73:
		tmp = y * x
	elif y <= 1.26e-49:
		tmp = z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6e-73)
		tmp = Float64(y * x);
	elseif (y <= 1.26e-49)
		tmp = z;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6e-73)
		tmp = y * x;
	elseif (y <= 1.26e-49)
		tmp = z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6e-73], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.26e-49], z, N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6e-73 or 1.26000000000000005e-49 < y

   1. Initial program 95.1%

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

   2. Taylor expanded in x around inf 53.2%

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

   if -6e-73 < y < 1.26000000000000005e-49

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.9%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-73}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-49}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 6: 36.7% 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 96.9%

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

2. Taylor expanded in y around 0 34.1%

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

3. Final simplification 34.1%

   \[\leadsto z \]

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 2023266 
(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))))