Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3

Percentage Accurate: 88.5% → 99.8%

Time: 5.7s

Alternatives: 12

Speedup: 0.8×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+36} \lor \neg \left(z \leq 3800000000\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(y + 1\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2e+36) (not (<= z 3800000000.0)))
   (- (* x (/ y z)) x)
   (* (/ x z) (- (+ y 1.0) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2e+36) || !(z <= 3800000000.0)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x / z) * ((y + 1.0) - 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 ((z <= (-2d+36)) .or. (.not. (z <= 3800000000.0d0))) then
        tmp = (x * (y / z)) - x
    else
        tmp = (x / z) * ((y + 1.0d0) - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2e+36) || !(z <= 3800000000.0)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x / z) * ((y + 1.0) - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2e+36) or not (z <= 3800000000.0):
		tmp = (x * (y / z)) - x
	else:
		tmp = (x / z) * ((y + 1.0) - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2e+36) || !(z <= 3800000000.0))
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	else
		tmp = Float64(Float64(x / z) * Float64(Float64(y + 1.0) - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2e+36) || ~((z <= 3800000000.0)))
		tmp = (x * (y / z)) - x;
	else
		tmp = (x / z) * ((y + 1.0) - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2e+36], N[Not[LessEqual[z, 3800000000.0]], $MachinePrecision]], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(N[(y + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000008e36 or 3.8e9 < z

   1. Initial program 72.2%

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

      1. +-commutative 72.2%

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

      2. sub-neg 72.2%

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

      3. +-commutative 72.2%

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

      4. associate-+r+ 72.2%

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

      5. unsub-neg 72.2%

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

      6. associate-+l- 72.2%

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

      7. distribute-lft-out-- 72.2%

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

      8. *-rgt-identity 72.2%

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

      9. distribute-rgt-out-- 70.2%

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

      10. sub-neg 70.2%

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

      11. +-commutative 70.2%

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

      12. associate--r+ 70.2%

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

      13. div-sub 70.2%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in y around inf 93.1%

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

      1. associate-/l* 95.4%

         \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}} - x \]

      2. associate-/r/ 100.0%

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

   6. Simplified 100.0%

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

   if -2.00000000000000008e36 < z < 3.8e9

   1. Initial program 99.9%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in x around 0 99.9%

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

      1. associate-*l/ 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+36} \lor \neg \left(z \leq 3800000000\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(y + 1\right) - z\right)\\ \end{array} \]

Alternative 2: 97.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - z\right) + 1\\ \mathbf{if}\;\frac{x \cdot t_0}{z} \leq 2 \cdot 10^{+191}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, x\right)}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t_0}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- y z) 1.0)))
   (if (<= (/ (* x t_0) z) 2e+191) (- (/ (fma x y x) z) x) (/ x (/ z t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if (((x * t_0) / z) <= 2e+191) {
		tmp = (fma(x, y, x) / z) - x;
	} else {
		tmp = x / (z / t_0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - z) + 1.0)
	tmp = 0.0
	if (Float64(Float64(x * t_0) / z) <= 2e+191)
		tmp = Float64(Float64(fma(x, y, x) / z) - x);
	else
		tmp = Float64(x / Float64(z / t_0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[N[(N[(x * t$95$0), $MachinePrecision] / z), $MachinePrecision], 2e+191], N[(N[(N[(x * y + x), $MachinePrecision] / z), $MachinePrecision] - x), $MachinePrecision], N[(x / N[(z / t$95$0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z) < 2.00000000000000015e191

   1. Initial program 93.3%

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

      1. +-commutative 93.3%

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

      2. sub-neg 93.3%

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

      3. +-commutative 93.3%

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

      4. associate-+r+ 93.3%

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

      5. unsub-neg 93.3%

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

      6. associate-+l- 93.3%

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

      7. distribute-lft-out-- 93.2%

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

      8. *-rgt-identity 93.2%

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

      9. distribute-rgt-out-- 92.2%

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

      10. sub-neg 92.2%

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

      11. +-commutative 92.2%

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

      12. associate--r+ 92.2%

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

      13. div-sub 92.2%

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

   3. Simplified 99.0%

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

   if 2.00000000000000015e191 < (/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

   1. Initial program 67.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(y - z\right) + 1}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \leq 2 \cdot 10^{+191}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, x\right)}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array} \]

Alternative 3: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - z\right) + 1\\ \mathbf{if}\;\frac{x \cdot t_0}{z} \leq 5 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{\frac{z}{t_0}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(y + 1\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- y z) 1.0)))
   (if (<= (/ (* x t_0) z) 5e-74)
     (/ x (/ z t_0))
     (* (/ x z) (- (+ y 1.0) z)))))

C

double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if (((x * t_0) / z) <= 5e-74) {
		tmp = x / (z / t_0);
	} else {
		tmp = (x / z) * ((y + 1.0) - 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) + 1.0d0
    if (((x * t_0) / z) <= 5d-74) then
        tmp = x / (z / t_0)
    else
        tmp = (x / z) * ((y + 1.0d0) - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if (((x * t_0) / z) <= 5e-74) {
		tmp = x / (z / t_0);
	} else {
		tmp = (x / z) * ((y + 1.0) - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - z) + 1.0
	tmp = 0
	if ((x * t_0) / z) <= 5e-74:
		tmp = x / (z / t_0)
	else:
		tmp = (x / z) * ((y + 1.0) - z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - z) + 1.0)
	tmp = 0.0
	if (Float64(Float64(x * t_0) / z) <= 5e-74)
		tmp = Float64(x / Float64(z / t_0));
	else
		tmp = Float64(Float64(x / z) * Float64(Float64(y + 1.0) - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - z) + 1.0;
	tmp = 0.0;
	if (((x * t_0) / z) <= 5e-74)
		tmp = x / (z / t_0);
	else
		tmp = (x / z) * ((y + 1.0) - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[N[(N[(x * t$95$0), $MachinePrecision] / z), $MachinePrecision], 5e-74], N[(x / N[(z / t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(N[(y + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z) < 4.99999999999999998e-74

   1. Initial program 91.4%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   if 4.99999999999999998e-74 < (/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

   1. Initial program 82.0%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in x around 0 82.0%

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

      1. associate-*l/ 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \leq 5 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(y + 1\right) - z\right)\\ \end{array} \]

Alternative 4: 64.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+50} \lor \neg \left(z \leq 2.9 \cdot 10^{+72}\right) \land z \leq 3.3 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0)
   (- x)
   (if (<= z 3.45e-65)
     (/ x z)
     (if (or (<= z 1.5e+50) (and (not (<= z 2.9e+72)) (<= z 3.3e+102)))
       (* y (/ x z))
       (- x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= 3.45e-65) {
		tmp = x / z;
	} else if ((z <= 1.5e+50) || (!(z <= 2.9e+72) && (z <= 3.3e+102))) {
		tmp = y * (x / z);
	} else {
		tmp = -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 (z <= (-1.0d0)) then
        tmp = -x
    else if (z <= 3.45d-65) then
        tmp = x / z
    else if ((z <= 1.5d+50) .or. (.not. (z <= 2.9d+72)) .and. (z <= 3.3d+102)) then
        tmp = y * (x / z)
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= 3.45e-65) {
		tmp = x / z;
	} else if ((z <= 1.5e+50) || (!(z <= 2.9e+72) && (z <= 3.3e+102))) {
		tmp = y * (x / z);
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = -x
	elif z <= 3.45e-65:
		tmp = x / z
	elif (z <= 1.5e+50) or (not (z <= 2.9e+72) and (z <= 3.3e+102)):
		tmp = y * (x / z)
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(-x);
	elseif (z <= 3.45e-65)
		tmp = Float64(x / z);
	elseif ((z <= 1.5e+50) || (!(z <= 2.9e+72) && (z <= 3.3e+102)))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = -x;
	elseif (z <= 3.45e-65)
		tmp = x / z;
	elseif ((z <= 1.5e+50) || (~((z <= 2.9e+72)) && (z <= 3.3e+102)))
		tmp = y * (x / z);
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.0], (-x), If[LessEqual[z, 3.45e-65], N[(x / z), $MachinePrecision], If[Or[LessEqual[z, 1.5e+50], And[N[Not[LessEqual[z, 2.9e+72]], $MachinePrecision], LessEqual[z, 3.3e+102]]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], (-x)]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 1.4999999999999999e50 < z < 2.90000000000000017e72 or 3.29999999999999999e102 < z

   1. Initial program 71.9%

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

      1. +-commutative 71.9%

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

      2. sub-neg 71.9%

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

      3. +-commutative 71.9%

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

      4. associate-+r+ 71.9%

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

      5. unsub-neg 71.9%

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

      6. associate-+l- 71.9%

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

      7. distribute-lft-out-- 71.9%

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

      8. *-rgt-identity 71.9%

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

      9. distribute-rgt-out-- 69.7%

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

      10. sub-neg 69.7%

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

      11. +-commutative 69.7%

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

      12. associate--r+ 69.7%

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

      13. div-sub 69.7%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in z around inf 82.7%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   5. Step-by-step derivation

      1. neg-mul-1 82.7%

         \[\leadsto \color{blue}{-x} \]

   6. Simplified 82.7%

      \[\leadsto \color{blue}{-x} \]

   if -1 < z < 3.44999999999999996e-65

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 99.0%

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

   3. Taylor expanded in y around 0 63.2%

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

   if 3.44999999999999996e-65 < z < 1.4999999999999999e50 or 2.90000000000000017e72 < z < 3.29999999999999999e102

   1. Initial program 93.9%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in y around inf 68.4%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{y}}} \]
   5. Step-by-step derivation

      1. associate-/r/ 74.5%

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

   6. Applied egg-rr 74.5%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+50} \lor \neg \left(z \leq 2.9 \cdot 10^{+72}\right) \land z \leq 3.3 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 5: 94.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+27} \lor \neg \left(y \leq 3.8 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.7e+27) (not (<= y 3.8e-14)))
   (- (* x (/ y z)) x)
   (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.7e+27) || !(y <= 3.8e-14)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x / z) - 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 <= (-3.7d+27)) .or. (.not. (y <= 3.8d-14))) then
        tmp = (x * (y / z)) - x
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.7e+27) || !(y <= 3.8e-14)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.7e+27) or not (y <= 3.8e-14):
		tmp = (x * (y / z)) - x
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.7e+27) || !(y <= 3.8e-14))
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.7e+27) || ~((y <= 3.8e-14)))
		tmp = (x * (y / z)) - x;
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.7e+27], N[Not[LessEqual[y, 3.8e-14]], $MachinePrecision]], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.70000000000000002e27 or 3.8000000000000002e-14 < y

   1. Initial program 89.8%

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

      1. +-commutative 89.8%

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

      2. sub-neg 89.8%

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

      3. +-commutative 89.8%

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

      4. associate-+r+ 89.8%

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

      5. unsub-neg 89.8%

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

      6. associate-+l- 89.8%

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

      7. distribute-lft-out-- 89.8%

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

      8. *-rgt-identity 89.8%

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

      9. distribute-rgt-out-- 88.0%

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

      10. sub-neg 88.0%

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

      11. +-commutative 88.0%

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

      12. associate--r+ 88.0%

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

      13. div-sub 88.0%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around inf 92.8%

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

      1. associate-/l* 94.8%

         \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}} - x \]

      2. associate-/r/ 93.6%

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

   6. Simplified 93.6%

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

   if -3.70000000000000002e27 < y < 3.8000000000000002e-14

   1. Initial program 85.9%

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

      1. +-commutative 85.9%

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

      2. sub-neg 85.9%

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

      3. +-commutative 85.9%

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

      4. associate-+r+ 85.9%

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

      5. unsub-neg 85.9%

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

      6. associate-+l- 85.9%

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

      7. distribute-lft-out-- 85.8%

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

      8. *-rgt-identity 85.8%

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

      9. distribute-rgt-out-- 85.8%

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

      10. sub-neg 85.8%

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

      11. +-commutative 85.8%

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

      12. associate--r+ 85.8%

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

      13. div-sub 85.9%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 99.6%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+27} \lor \neg \left(y \leq 3.8 \cdot 10^{-14}\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 6: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.06) (not (<= z 1.0)))
   (- (* x (/ y z)) x)
   (/ (* x (+ y 1.0)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.06) || !(z <= 1.0)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x * (y + 1.0)) / 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 ((z <= (-1.06d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (x * (y / z)) - x
    else
        tmp = (x * (y + 1.0d0)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.06) || !(z <= 1.0)) {
		tmp = (x * (y / z)) - x;
	} else {
		tmp = (x * (y + 1.0)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.06) or not (z <= 1.0):
		tmp = (x * (y / z)) - x
	else:
		tmp = (x * (y + 1.0)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.06) || !(z <= 1.0))
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	else
		tmp = Float64(Float64(x * Float64(y + 1.0)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.06) || ~((z <= 1.0)))
		tmp = (x * (y / z)) - x;
	else
		tmp = (x * (y + 1.0)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.06], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0600000000000001 or 1 < z

   1. Initial program 73.8%

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

      1. +-commutative 73.8%

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

      2. sub-neg 73.8%

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

      3. +-commutative 73.8%

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

      4. associate-+r+ 73.8%

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

      5. unsub-neg 73.8%

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

      6. associate-+l- 73.8%

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

      7. distribute-lft-out-- 73.8%

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

      8. *-rgt-identity 73.8%

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

      9. distribute-rgt-out-- 72.0%

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

      10. sub-neg 72.0%

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

      11. +-commutative 72.0%

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

      12. associate--r+ 72.0%

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

      13. div-sub 72.0%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in y around inf 92.4%

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

      1. associate-/l* 94.5%

         \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}} - x \]

      2. associate-/r/ 98.8%

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

   6. Simplified 98.8%

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

   if -1.0600000000000001 < z < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 98.5%

      \[\leadsto \frac{\color{blue}{\left(1 + y\right) \cdot x}}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \end{array} \]

Alternative 7: 95.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.7e+27)
   (- (* x (/ y z)) x)
   (if (<= y 3.8e-14) (- (/ x z) x) (- (/ y (/ z x)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.7e+27) {
		tmp = (x * (y / z)) - x;
	} else if (y <= 3.8e-14) {
		tmp = (x / z) - x;
	} else {
		tmp = (y / (z / x)) - 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 <= (-3.7d+27)) then
        tmp = (x * (y / z)) - x
    else if (y <= 3.8d-14) then
        tmp = (x / z) - x
    else
        tmp = (y / (z / x)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.7e+27) {
		tmp = (x * (y / z)) - x;
	} else if (y <= 3.8e-14) {
		tmp = (x / z) - x;
	} else {
		tmp = (y / (z / x)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.7e+27:
		tmp = (x * (y / z)) - x
	elif y <= 3.8e-14:
		tmp = (x / z) - x
	else:
		tmp = (y / (z / x)) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.7e+27)
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	elseif (y <= 3.8e-14)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(Float64(y / Float64(z / x)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.7e+27)
		tmp = (x * (y / z)) - x;
	elseif (y <= 3.8e-14)
		tmp = (x / z) - x;
	else
		tmp = (y / (z / x)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.7e+27], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[y, 3.8e-14], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.70000000000000002e27

   1. Initial program 86.9%

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

      1. +-commutative 86.9%

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

      2. sub-neg 86.9%

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

      3. +-commutative 86.9%

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

      4. associate-+r+ 86.9%

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

      5. unsub-neg 86.9%

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

      6. associate-+l- 86.9%

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

      7. distribute-lft-out-- 86.9%

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

      8. *-rgt-identity 86.9%

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

      9. distribute-rgt-out-- 86.5%

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

      10. sub-neg 86.5%

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

      11. +-commutative 86.5%

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

      12. associate--r+ 86.5%

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

      13. div-sub 86.6%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in y around inf 91.7%

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

      1. associate-/l* 93.3%

         \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}} - x \]

      2. associate-/r/ 93.3%

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

   6. Simplified 93.3%

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

   if -3.70000000000000002e27 < y < 3.8000000000000002e-14

   1. Initial program 85.9%

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

      1. +-commutative 85.9%

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

      2. sub-neg 85.9%

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

      3. +-commutative 85.9%

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

      4. associate-+r+ 85.9%

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

      5. unsub-neg 85.9%

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

      6. associate-+l- 85.9%

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

      7. distribute-lft-out-- 85.8%

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

      8. *-rgt-identity 85.8%

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

      9. distribute-rgt-out-- 85.8%

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

      10. sub-neg 85.8%

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

      11. +-commutative 85.8%

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

      12. associate--r+ 85.8%

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

      13. div-sub 85.9%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 99.6%

      \[\leadsto \color{blue}{\frac{x}{z}} - x \]

   if 3.8000000000000002e-14 < y

   1. Initial program 92.5%

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

      1. +-commutative 92.5%

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

      2. sub-neg 92.5%

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

      3. +-commutative 92.5%

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

      4. associate-+r+ 92.5%

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

      5. unsub-neg 92.5%

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

      6. associate-+l- 92.5%

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

      7. distribute-lft-out-- 92.4%

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

      8. *-rgt-identity 92.4%

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

      9. distribute-rgt-out-- 89.3%

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

      10. sub-neg 89.3%

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

      11. +-commutative 89.3%

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

      12. associate--r+ 89.3%

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

      13. div-sub 89.3%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in y around inf 93.7%

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

      1. associate-/l* 96.2%

         \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}} - x \]

   6. Simplified 96.2%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}} - x\\ \end{array} \]

Alternative 8: 85.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+27} \lor \neg \left(y \leq 3.05 \cdot 10^{+32}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.6e+27) (not (<= y 3.05e+32))) (* y (/ x z)) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.6e+27) || !(y <= 3.05e+32)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - 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 <= (-6.6d+27)) .or. (.not. (y <= 3.05d+32))) then
        tmp = y * (x / z)
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.6e+27) || !(y <= 3.05e+32)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.6e+27) or not (y <= 3.05e+32):
		tmp = y * (x / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.6e+27) || !(y <= 3.05e+32))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.6e+27) || ~((y <= 3.05e+32)))
		tmp = y * (x / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.6e+27], N[Not[LessEqual[y, 3.05e+32]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5999999999999996e27 or 3.05000000000000014e32 < y

   1. Initial program 90.6%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in y around inf 74.2%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{y}}} \]
   5. Step-by-step derivation

      1. associate-/r/ 75.5%

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

   6. Applied egg-rr 75.5%

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

   if -6.5999999999999996e27 < y < 3.05000000000000014e32

   1. Initial program 85.5%

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

      1. +-commutative 85.5%

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

      2. sub-neg 85.5%

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

      3. +-commutative 85.5%

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

      4. associate-+r+ 85.5%

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

      5. unsub-neg 85.5%

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

      6. associate-+l- 85.5%

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

      7. distribute-lft-out-- 85.5%

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

      8. *-rgt-identity 85.5%

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

      9. distribute-rgt-out-- 85.5%

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

      10. sub-neg 85.5%

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

      11. +-commutative 85.5%

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

      12. associate--r+ 85.5%

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

      13. div-sub 85.5%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 97.8%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+27} \lor \neg \left(y \leq 3.05 \cdot 10^{+32}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 9: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+27} \lor \neg \left(y \leq 7 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9.5e+27) (not (<= y 7e+30))) (/ (* x y) z) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.5e+27) || !(y <= 7e+30)) {
		tmp = (x * y) / z;
	} else {
		tmp = (x / z) - 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 <= (-9.5d+27)) .or. (.not. (y <= 7d+30))) then
        tmp = (x * y) / z
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.5e+27) || !(y <= 7e+30)) {
		tmp = (x * y) / z;
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9.5e+27) or not (y <= 7e+30):
		tmp = (x * y) / z
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9.5e+27) || !(y <= 7e+30))
		tmp = Float64(Float64(x * y) / z);
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -9.5e+27) || ~((y <= 7e+30)))
		tmp = (x * y) / z;
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9.5e+27], N[Not[LessEqual[y, 7e+30]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.4999999999999997e27 or 7.00000000000000042e30 < y

   1. Initial program 90.6%

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

   2. Taylor expanded in y around inf 76.4%

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

   if -9.4999999999999997e27 < y < 7.00000000000000042e30

   1. Initial program 85.5%

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

      1. +-commutative 85.5%

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

      2. sub-neg 85.5%

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

      3. +-commutative 85.5%

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

      4. associate-+r+ 85.5%

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

      5. unsub-neg 85.5%

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

      6. associate-+l- 85.5%

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

      7. distribute-lft-out-- 85.5%

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

      8. *-rgt-identity 85.5%

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

      9. distribute-rgt-out-- 85.5%

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

      10. sub-neg 85.5%

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

      11. +-commutative 85.5%

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

      12. associate--r+ 85.5%

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

      13. div-sub 85.5%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 97.8%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+27} \lor \neg \left(y \leq 7 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 10: 84.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.6e+28)
   (/ x (/ z y))
   (if (<= y 1.2e+33) (- (/ x z) x) (* y (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.6e+28) {
		tmp = x / (z / y);
	} else if (y <= 1.2e+33) {
		tmp = (x / z) - x;
	} 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) :: tmp
    if (y <= (-2.6d+28)) then
        tmp = x / (z / y)
    else if (y <= 1.2d+33) then
        tmp = (x / z) - x
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.6e+28) {
		tmp = x / (z / y);
	} else if (y <= 1.2e+33) {
		tmp = (x / z) - x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.6e+28:
		tmp = x / (z / y)
	elif y <= 1.2e+33:
		tmp = (x / z) - x
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.6e+28)
		tmp = Float64(x / Float64(z / y));
	elseif (y <= 1.2e+33)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.6e+28)
		tmp = x / (z / y);
	elseif (y <= 1.2e+33)
		tmp = (x / z) - x;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.6e+28], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+33], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6000000000000002e28

   1. Initial program 86.9%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around inf 71.1%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{y}}} \]

   if -2.6000000000000002e28 < y < 1.2e33

   1. Initial program 85.5%

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

      1. +-commutative 85.5%

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

      2. sub-neg 85.5%

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

      3. +-commutative 85.5%

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

      4. associate-+r+ 85.5%

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

      5. unsub-neg 85.5%

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

      6. associate-+l- 85.5%

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

      7. distribute-lft-out-- 85.5%

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

      8. *-rgt-identity 85.5%

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

      9. distribute-rgt-out-- 85.5%

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

      10. sub-neg 85.5%

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

      11. +-commutative 85.5%

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

      12. associate--r+ 85.5%

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

      13. div-sub 85.5%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 97.8%

      \[\leadsto \color{blue}{\frac{x}{z}} - x \]

   if 1.2e33 < y

   1. Initial program 94.6%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in y around inf 77.4%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{y}}} \]
   5. Step-by-step derivation

      1. associate-/r/ 80.7%

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

   6. Applied egg-rr 80.7%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 11: 64.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 3900000000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0) (- x) (if (<= z 3900000000.0) (/ x z) (- x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= 3900000000.0) {
		tmp = x / z;
	} else {
		tmp = -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 (z <= (-1.0d0)) then
        tmp = -x
    else if (z <= 3900000000.0d0) then
        tmp = x / z
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= 3900000000.0) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = -x
	elif z <= 3900000000.0:
		tmp = x / z
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(-x);
	elseif (z <= 3900000000.0)
		tmp = Float64(x / z);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = -x;
	elseif (z <= 3900000000.0)
		tmp = x / z;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.0], (-x), If[LessEqual[z, 3900000000.0], N[(x / z), $MachinePrecision], (-x)]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 3.9e9 < z

   1. Initial program 73.6%

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

      1. +-commutative 73.6%

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

      2. sub-neg 73.6%

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

      3. +-commutative 73.6%

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

      4. associate-+r+ 73.6%

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

      5. unsub-neg 73.6%

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

      6. associate-+l- 73.6%

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

      7. distribute-lft-out-- 73.6%

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

      8. *-rgt-identity 73.6%

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

      9. distribute-rgt-out-- 71.7%

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

      10. sub-neg 71.7%

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

      11. +-commutative 71.7%

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

      12. associate--r+ 71.7%

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

      13. div-sub 71.7%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in z around inf 76.6%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   5. Step-by-step derivation

      1. neg-mul-1 76.6%

         \[\leadsto \color{blue}{-x} \]

   6. Simplified 76.6%

      \[\leadsto \color{blue}{-x} \]

   if -1 < z < 3.9e9

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 98.5%

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

   3. Taylor expanded in y around 0 58.4%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 3900000000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 12: 38.7% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ -x \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := (-x)

Derivation

1. Initial program 87.8%

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

   1. +-commutative 87.8%

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

   2. sub-neg 87.8%

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

   3. +-commutative 87.8%

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

   4. associate-+r+ 87.8%

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

   5. unsub-neg 87.8%

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

   6. associate-+l- 87.8%

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

   7. distribute-lft-out-- 87.8%

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

   8. *-rgt-identity 87.8%

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

   9. distribute-rgt-out-- 86.9%

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

   10. sub-neg 86.9%

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

   11. +-commutative 86.9%

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

   12. associate--r+ 86.9%

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

   13. div-sub 86.9%

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

3. Simplified 96.9%

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

4. Taylor expanded in z around inf 37.0%

   \[\leadsto \color{blue}{-1 \cdot x} \]
5. Step-by-step derivation

   1. neg-mul-1 37.0%

      \[\leadsto \color{blue}{-x} \]

6. Simplified 37.0%

   \[\leadsto \color{blue}{-x} \]

7. Final simplification 37.0%

   \[\leadsto -x \]

Developer target: 99.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{if}\;x < -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x < 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (+ 1.0 y) (/ x z)) x)))
   (if (< x -2.71483106713436e-162)
     t_0
     (if (< x 3.874108816439546e-197)
       (* (* x (+ (- y z) 1.0)) (/ 1.0 z))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((1.0 + y) * (x / z)) - x;
	double tmp;
	if (x < -2.71483106713436e-162) {
		tmp = t_0;
	} else if (x < 3.874108816439546e-197) {
		tmp = (x * ((y - z) + 1.0)) * (1.0 / 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 = ((1.0d0 + y) * (x / z)) - x
    if (x < (-2.71483106713436d-162)) then
        tmp = t_0
    else if (x < 3.874108816439546d-197) then
        tmp = (x * ((y - z) + 1.0d0)) * (1.0d0 / 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 = ((1.0 + y) * (x / z)) - x;
	double tmp;
	if (x < -2.71483106713436e-162) {
		tmp = t_0;
	} else if (x < 3.874108816439546e-197) {
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((1.0 + y) * (x / z)) - x
	tmp = 0
	if x < -2.71483106713436e-162:
		tmp = t_0
	elif x < 3.874108816439546e-197:
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(1.0 + y) * Float64(x / z)) - x)
	tmp = 0.0
	if (x < -2.71483106713436e-162)
		tmp = t_0;
	elseif (x < 3.874108816439546e-197)
		tmp = Float64(Float64(x * Float64(Float64(y - z) + 1.0)) * Float64(1.0 / z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((1.0 + y) * (x / z)) - x;
	tmp = 0.0;
	if (x < -2.71483106713436e-162)
		tmp = t_0;
	elseif (x < 3.874108816439546e-197)
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(1.0 + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[Less[x, -2.71483106713436e-162], t$95$0, If[Less[x, 3.874108816439546e-197], N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2023178 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1.0 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1.0 z)) (- (* (+ 1.0 y) (/ x z)) x)))

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