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

Percentage Accurate: 88.0% → 99.8%

Time: 7.5s

Alternatives: 13

Speedup: 0.6×

• 20.8% 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: 88.0% 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, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-17} \lor \neg \left(z \leq 7 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(\frac{y + 1}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5e-17) (not (<= z 7e-23)))
   (* x (+ (/ (+ y 1.0) z) -1.0))
   (/ (+ x (* x y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5e-17) || !(z <= 7e-23)) {
		tmp = x * (((y + 1.0) / z) + -1.0);
	} else {
		tmp = (x + (x * y)) / 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 <= (-5d-17)) .or. (.not. (z <= 7d-23))) then
        tmp = x * (((y + 1.0d0) / z) + (-1.0d0))
    else
        tmp = (x + (x * y)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5e-17) || !(z <= 7e-23)) {
		tmp = x * (((y + 1.0) / z) + -1.0);
	} else {
		tmp = (x + (x * y)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5e-17) or not (z <= 7e-23):
		tmp = x * (((y + 1.0) / z) + -1.0)
	else:
		tmp = (x + (x * y)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5e-17) || !(z <= 7e-23))
		tmp = Float64(x * Float64(Float64(Float64(y + 1.0) / z) + -1.0));
	else
		tmp = Float64(Float64(x + Float64(x * y)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5e-17) || ~((z <= 7e-23)))
		tmp = x * (((y + 1.0) / z) + -1.0);
	else
		tmp = (x + (x * y)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5e-17], N[Not[LessEqual[z, 7e-23]], $MachinePrecision]], N[(x * N[(N[(N[(y + 1.0), $MachinePrecision] / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9999999999999999e-17 or 6.99999999999999987e-23 < z

   1. Initial program 70.8%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   if -4.9999999999999999e-17 < z < 6.99999999999999987e-23

   1. Initial program 99.9%

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

      1. distribute-lft-in 99.9%

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

      2. fma-define 99.9%

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

      3. *-rgt-identity 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-17} \lor \neg \left(z \leq 7 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(\frac{y + 1}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.1:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y - z, x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + 1}} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 0.1) (/ (fma x (- y z) x) z) (- (/ x (/ z (+ y 1.0))) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.1) {
		tmp = fma(x, (y - z), x) / z;
	} else {
		tmp = (x / (z / (y + 1.0))) - x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 0.1)
		tmp = Float64(fma(x, Float64(y - z), x) / z);
	else
		tmp = Float64(Float64(x / Float64(z / Float64(y + 1.0))) - x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 0.1], N[(N[(x * N[(y - z), $MachinePrecision] + x), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / N[(z / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.10000000000000001

   1. Initial program 88.3%

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

      1. distribute-lft-in 88.4%

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

      2. fma-define 88.4%

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

      3. *-rgt-identity 88.4%

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

   3. Simplified 88.4%

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

   if 0.10000000000000001 < x

   1. Initial program 73.5%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. distribute-lft-in 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 100.0%

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

      4. *-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

   6. Applied egg-rr 100.0%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.1:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y - z, x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + 1}} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0)
   (- x)
   (if (<= z 1.5e-23) (/ x z) (if (<= z 4.8e+31) (* x (/ y z)) (- x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= 1.5e-23) {
		tmp = x / z;
	} else if (z <= 4.8e+31) {
		tmp = x * (y / 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 <= 1.5d-23) then
        tmp = x / z
    else if (z <= 4.8d+31) then
        tmp = x * (y / 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 <= 1.5e-23) {
		tmp = x / z;
	} else if (z <= 4.8e+31) {
		tmp = x * (y / z);
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = -x
	elif z <= 1.5e-23:
		tmp = x / z
	elif z <= 4.8e+31:
		tmp = x * (y / z)
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(-x);
	elseif (z <= 1.5e-23)
		tmp = Float64(x / z);
	elseif (z <= 4.8e+31)
		tmp = Float64(x * Float64(y / 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 <= 1.5e-23)
		tmp = x / z;
	elseif (z <= 4.8e+31)
		tmp = x * (y / z);
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.0], (-x), If[LessEqual[z, 1.5e-23], N[(x / z), $MachinePrecision], If[LessEqual[z, 4.8e+31], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], (-x)]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 4.79999999999999965e31 < z

   1. Initial program 67.9%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 75.1%

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

      1. neg-mul-1 75.1%

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

   7. Simplified 75.1%

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

   if -1 < z < 1.50000000000000001e-23

   1. Initial program 99.9%

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

      1. associate-/l* 92.8%

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

      2. +-commutative 92.8%

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

      3. associate-+r- 92.8%

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

      4. div-sub 92.8%

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

      5. *-inverses 92.8%

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

      6. sub-neg 92.8%

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

      7. +-commutative 92.8%

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

      8. metadata-eval 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in y around 0 64.5%

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

      1. sub-neg 64.5%

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

      2. metadata-eval 64.5%

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

      3. distribute-rgt-in 64.5%

         \[\leadsto \color{blue}{\frac{1}{z} \cdot x + -1 \cdot x} \]

      4. associate-*l/ 64.7%

         \[\leadsto \color{blue}{\frac{1 \cdot x}{z}} + -1 \cdot x \]

      5. *-lft-identity 64.7%

         \[\leadsto \frac{\color{blue}{x}}{z} + -1 \cdot x \]

      6. neg-mul-1 64.7%

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

      7. unsub-neg 64.7%

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

   7. Simplified 64.7%

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

   8. Taylor expanded in z around 0 64.3%

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

   if 1.50000000000000001e-23 < z < 4.79999999999999965e31

   1. Initial program 93.8%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 70.1%

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

      1. associate-/l* 70.2%

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

   7. Simplified 70.2%

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

Alternative 4: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 70.1%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 98.6%

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

   if -1 < z < 1

   1. Initial program 99.9%

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

      1. distribute-lft-in 99.9%

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

      2. fma-define 99.9%

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

      3. *-rgt-identity 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 99.5%

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

4. Final simplification 99.0%

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

Alternative 5: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + 1\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.05) (not (<= z 1.0)))
   (* x (+ -1.0 (/ y z)))
   (* (+ y 1.0) (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.05) || !(z <= 1.0)) {
		tmp = x * (-1.0 + (y / z));
	} else {
		tmp = (y + 1.0) * (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 ((z <= (-1.05d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * ((-1.0d0) + (y / z))
    else
        tmp = (y + 1.0d0) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.05) || !(z <= 1.0)) {
		tmp = x * (-1.0 + (y / z));
	} else {
		tmp = (y + 1.0) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.05) or not (z <= 1.0):
		tmp = x * (-1.0 + (y / z))
	else:
		tmp = (y + 1.0) * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.05) || !(z <= 1.0))
		tmp = Float64(x * Float64(-1.0 + Float64(y / z)));
	else
		tmp = Float64(Float64(y + 1.0) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.05) || ~((z <= 1.0)))
		tmp = x * (-1.0 + (y / z));
	else
		tmp = (y + 1.0) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.05], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + 1.0), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05000000000000004 or 1 < z

   1. Initial program 70.1%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 98.6%

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

   if -1.05000000000000004 < z < 1

   1. Initial program 99.9%

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

      1. distribute-lft-in 99.9%

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

      2. fma-define 99.9%

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

      3. *-rgt-identity 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 99.5%

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

      1. *-un-lft-identity 99.5%

         \[\leadsto \frac{\color{blue}{1 \cdot x} + x \cdot y}{z} \]

      2. *-commutative 99.5%

         \[\leadsto \frac{1 \cdot x + \color{blue}{y \cdot x}}{z} \]

      3. distribute-rgt-out 99.5%

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

      4. +-commutative 99.5%

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

      5. associate-*l/ 99.5%

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

   7. Applied egg-rr 99.5%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + 1\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+16} \lor \neg \left(y \leq 0.0034\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.2e+16) (not (<= y 0.0034)))
   (* x (+ -1.0 (/ y z)))
   (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e+16) || !(y <= 0.0034)) {
		tmp = x * (-1.0 + (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 <= (-5.2d+16)) .or. (.not. (y <= 0.0034d0))) then
        tmp = x * ((-1.0d0) + (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 <= -5.2e+16) || !(y <= 0.0034)) {
		tmp = x * (-1.0 + (y / z));
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.2e+16) or not (y <= 0.0034):
		tmp = x * (-1.0 + (y / z))
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.2e+16) || !(y <= 0.0034))
		tmp = Float64(x * Float64(-1.0 + Float64(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 <= -5.2e+16) || ~((y <= 0.0034)))
		tmp = x * (-1.0 + (y / z));
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.2e+16], N[Not[LessEqual[y, 0.0034]], $MachinePrecision]], N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2e16 or 0.00339999999999999981 < y

   1. Initial program 81.0%

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

      1. associate-/l* 92.5%

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

      2. +-commutative 92.5%

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

      3. associate-+r- 92.5%

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

      4. div-sub 92.6%

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

      5. *-inverses 92.6%

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

      6. sub-neg 92.6%

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

      7. +-commutative 92.6%

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

      8. metadata-eval 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in y around inf 91.4%

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

   if -5.2e16 < y < 0.00339999999999999981

   1. Initial program 87.2%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.8%

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

      5. *-inverses 99.8%

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

      6. sub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 99.3%

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

      1. sub-neg 99.3%

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

      2. metadata-eval 99.3%

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

      3. distribute-rgt-in 99.3%

         \[\leadsto \color{blue}{\frac{1}{z} \cdot x + -1 \cdot x} \]

      4. associate-*l/ 99.4%

         \[\leadsto \color{blue}{\frac{1 \cdot x}{z}} + -1 \cdot x \]

      5. *-lft-identity 99.4%

         \[\leadsto \frac{\color{blue}{x}}{z} + -1 \cdot x \]

      6. neg-mul-1 99.4%

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

      7. unsub-neg 99.4%

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

   7. Simplified 99.4%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+16} \lor \neg \left(y \leq 0.0034\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+17} \lor \neg \left(y \leq 1.55 \cdot 10^{+68}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9e+17) (not (<= y 1.55e+68))) (* y (/ x z)) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9e+17) || !(y <= 1.55e+68)) {
		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 <= (-9d+17)) .or. (.not. (y <= 1.55d+68))) 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 <= -9e+17) || !(y <= 1.55e+68)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9e+17) or not (y <= 1.55e+68):
		tmp = y * (x / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9e+17) || !(y <= 1.55e+68))
		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 <= -9e+17) || ~((y <= 1.55e+68)))
		tmp = y * (x / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9e+17], N[Not[LessEqual[y, 1.55e+68]], $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 < -9e17 or 1.5499999999999999e68 < y

   1. Initial program 83.1%

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

      1. distribute-lft-in 83.1%

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

      2. fma-define 83.1%

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

      3. *-rgt-identity 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in z around 0 79.9%

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

      1. *-un-lft-identity 79.9%

         \[\leadsto \frac{\color{blue}{1 \cdot x} + x \cdot y}{z} \]

      2. *-commutative 79.9%

         \[\leadsto \frac{1 \cdot x + \color{blue}{y \cdot x}}{z} \]

      3. distribute-rgt-out 79.9%

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

      4. +-commutative 79.9%

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

      5. associate-*l/ 80.0%

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

   7. Applied egg-rr 80.0%

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

   8. Taylor expanded in y around inf 80.0%

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

   if -9e17 < y < 1.5499999999999999e68

   1. Initial program 85.2%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.8%

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

      5. *-inverses 99.8%

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

      6. sub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 95.4%

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

      1. sub-neg 95.4%

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

      2. metadata-eval 95.4%

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

      3. distribute-rgt-in 95.4%

         \[\leadsto \color{blue}{\frac{1}{z} \cdot x + -1 \cdot x} \]

      4. associate-*l/ 95.5%

         \[\leadsto \color{blue}{\frac{1 \cdot x}{z}} + -1 \cdot x \]

      5. *-lft-identity 95.5%

         \[\leadsto \frac{\color{blue}{x}}{z} + -1 \cdot x \]

      6. neg-mul-1 95.5%

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

      7. unsub-neg 95.5%

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

   7. Simplified 95.5%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+17} \lor \neg \left(y \leq 1.55 \cdot 10^{+68}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.2e+16)
   (/ (* x y) z)
   (if (<= y 1.26e+65) (- (/ x z) x) (* y (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.2e+16) {
		tmp = (x * y) / z;
	} else if (y <= 1.26e+65) {
		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 <= (-5.2d+16)) then
        tmp = (x * y) / z
    else if (y <= 1.26d+65) 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 <= -5.2e+16) {
		tmp = (x * y) / z;
	} else if (y <= 1.26e+65) {
		tmp = (x / z) - x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.2e+16:
		tmp = (x * y) / z
	elif y <= 1.26e+65:
		tmp = (x / z) - x
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.2e+16)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= 1.26e+65)
		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 <= -5.2e+16)
		tmp = (x * y) / z;
	elseif (y <= 1.26e+65)
		tmp = (x / z) - x;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.2e+16], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.26e+65], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2e16

   1. Initial program 84.5%

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

      1. associate-/l* 88.6%

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

      2. +-commutative 88.6%

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

      3. associate-+r- 88.6%

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

      4. div-sub 88.6%

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

      5. *-inverses 88.6%

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

      6. sub-neg 88.6%

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

      7. +-commutative 88.6%

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

      8. metadata-eval 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in y around inf 84.2%

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

   if -5.2e16 < y < 1.2599999999999999e65

   1. Initial program 85.2%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.8%

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

      5. *-inverses 99.8%

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

      6. sub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 95.4%

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

      1. sub-neg 95.4%

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

      2. metadata-eval 95.4%

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

      3. distribute-rgt-in 95.4%

         \[\leadsto \color{blue}{\frac{1}{z} \cdot x + -1 \cdot x} \]

      4. associate-*l/ 95.5%

         \[\leadsto \color{blue}{\frac{1 \cdot x}{z}} + -1 \cdot x \]

      5. *-lft-identity 95.5%

         \[\leadsto \frac{\color{blue}{x}}{z} + -1 \cdot x \]

      6. neg-mul-1 95.5%

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

      7. unsub-neg 95.5%

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

   7. Simplified 95.5%

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

   if 1.2599999999999999e65 < y

   1. Initial program 81.7%

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

      1. distribute-lft-in 81.7%

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

      2. fma-define 81.7%

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

      3. *-rgt-identity 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in z around 0 75.3%

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

      1. *-un-lft-identity 75.3%

         \[\leadsto \frac{\color{blue}{1 \cdot x} + x \cdot y}{z} \]

      2. *-commutative 75.3%

         \[\leadsto \frac{1 \cdot x + \color{blue}{y \cdot x}}{z} \]

      3. distribute-rgt-out 75.3%

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

      4. +-commutative 75.3%

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

      5. associate-*l/ 78.8%

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

   7. Applied egg-rr 78.8%

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

   8. Taylor expanded in y around inf 78.8%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+65}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 94.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.1:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + 1}} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 0.1) (/ (* x (+ (- y z) 1.0)) z) (- (/ x (/ z (+ y 1.0))) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.1) {
		tmp = (x * ((y - z) + 1.0)) / z;
	} else {
		tmp = (x / (z / (y + 1.0))) - 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 (x <= 0.1d0) then
        tmp = (x * ((y - z) + 1.0d0)) / z
    else
        tmp = (x / (z / (y + 1.0d0))) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 0.1) {
		tmp = (x * ((y - z) + 1.0)) / z;
	} else {
		tmp = (x / (z / (y + 1.0))) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 0.1:
		tmp = (x * ((y - z) + 1.0)) / z
	else:
		tmp = (x / (z / (y + 1.0))) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 0.1)
		tmp = Float64(Float64(x * Float64(Float64(y - z) + 1.0)) / z);
	else
		tmp = Float64(Float64(x / Float64(z / Float64(y + 1.0))) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 0.1)
		tmp = (x * ((y - z) + 1.0)) / z;
	else
		tmp = (x / (z / (y + 1.0))) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 0.1], N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / N[(z / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.10000000000000001

   1. Initial program 88.3%

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

   if 0.10000000000000001 < x

   1. Initial program 73.5%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. distribute-lft-in 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 100.0%

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

      4. *-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

   6. Applied egg-rr 100.0%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.1:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + 1}} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 94.4% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1e-5) (/ (* x (+ (- y z) 1.0)) z) (* x (+ (/ (+ y 1.0) z) -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1e-5) {
		tmp = (x * ((y - z) + 1.0)) / z;
	} else {
		tmp = x * (((y + 1.0) / z) + -1.0);
	}
	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) :: tmp
    if (x <= 1d-5) then
        tmp = (x * ((y - z) + 1.0d0)) / z
    else
        tmp = x * (((y + 1.0d0) / z) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1e-5) {
		tmp = (x * ((y - z) + 1.0)) / z;
	} else {
		tmp = x * (((y + 1.0) / z) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1e-5:
		tmp = (x * ((y - z) + 1.0)) / z
	else:
		tmp = x * (((y + 1.0) / z) + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1e-5)
		tmp = Float64(Float64(x * Float64(Float64(y - z) + 1.0)) / z);
	else
		tmp = Float64(x * Float64(Float64(Float64(y + 1.0) / z) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1e-5)
		tmp = (x * ((y - z) + 1.0)) / z;
	else
		tmp = x * (((y + 1.0) / z) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1e-5], N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(N[(N[(y + 1.0), $MachinePrecision] / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.00000000000000008e-5

   1. Initial program 88.3%

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

   if 1.00000000000000008e-5 < x

   1. Initial program 73.9%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

Alternative 11: 65.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 3.5\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 3.5))) (- x) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 3.5)) {
		tmp = -x;
	} else {
		tmp = 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 ((z <= (-1.0d0)) .or. (.not. (z <= 3.5d0))) then
        tmp = -x
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 3.5)) {
		tmp = -x;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 3.5):
		tmp = -x
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 3.5))
		tmp = Float64(-x);
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 3.5)))
		tmp = -x;
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 3.5]], $MachinePrecision]], (-x), N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 3.5 < z

   1. Initial program 69.9%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 70.9%

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

      1. neg-mul-1 70.9%

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

   7. Simplified 70.9%

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

   if -1 < z < 3.5

   1. Initial program 99.9%

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

      1. associate-/l* 93.0%

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

      2. +-commutative 93.0%

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

      3. associate-+r- 93.0%

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

      4. div-sub 93.0%

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

      5. *-inverses 93.0%

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

      6. sub-neg 93.0%

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

      7. +-commutative 93.0%

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

      8. metadata-eval 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in y around 0 63.3%

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

      1. sub-neg 63.3%

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

      2. metadata-eval 63.3%

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

      3. distribute-rgt-in 63.3%

         \[\leadsto \color{blue}{\frac{1}{z} \cdot x + -1 \cdot x} \]

      4. associate-*l/ 63.4%

         \[\leadsto \color{blue}{\frac{1 \cdot x}{z}} + -1 \cdot x \]

      5. *-lft-identity 63.4%

         \[\leadsto \frac{\color{blue}{x}}{z} + -1 \cdot x \]

      6. neg-mul-1 63.4%

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

      7. unsub-neg 63.4%

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

   7. Simplified 63.4%

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

   8. Taylor expanded in z around 0 63.1%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 3.5\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.1% 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 84.4%

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

   1. associate-/l* 96.6%

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

   2. +-commutative 96.6%

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

   3. associate-+r- 96.6%

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

   4. div-sub 96.6%

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

   5. *-inverses 96.6%

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

   6. sub-neg 96.6%

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

   7. +-commutative 96.6%

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

   8. metadata-eval 96.6%

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

3. Simplified 96.6%

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

5. Taylor expanded in z around inf 38.2%

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

   1. neg-mul-1 38.2%

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

7. Simplified 38.2%

   \[\leadsto \color{blue}{-x} \]
8. Add Preprocessing

Alternative 13: 3.0% accurate, 9.0× 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 x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 84.4%

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

   1. associate-/l* 96.6%

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

   2. +-commutative 96.6%

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

   3. associate-+r- 96.6%

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

   4. div-sub 96.6%

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

   5. *-inverses 96.6%

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

   6. sub-neg 96.6%

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

   7. +-commutative 96.6%

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

   8. metadata-eval 96.6%

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

3. Simplified 96.6%

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

5. Taylor expanded in z around inf 38.2%

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

   1. neg-mul-1 38.2%

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

7. Simplified 38.2%

   \[\leadsto \color{blue}{-x} \]
8. Step-by-step derivation

   1. neg-sub0 38.2%

      \[\leadsto \color{blue}{0 - x} \]

   2. sub-neg 38.2%

      \[\leadsto \color{blue}{0 + \left(-x\right)} \]

   3. add-sqr-sqrt 19.4%

      \[\leadsto 0 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}} \]

   4. sqrt-unprod 19.0%

      \[\leadsto 0 + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \]

   5. sqr-neg 19.0%

      \[\leadsto 0 + \sqrt{\color{blue}{x \cdot x}} \]

   6. sqrt-unprod 1.4%

      \[\leadsto 0 + \color{blue}{\sqrt{x} \cdot \sqrt{x}} \]

   7. add-sqr-sqrt 2.9%

      \[\leadsto 0 + \color{blue}{x} \]

9. Applied egg-rr 2.9%

   \[\leadsto \color{blue}{0 + x} \]

10. Taylor expanded in x around 0 2.9%

    \[\leadsto \color{blue}{x} \]
11. Add Preprocessing

Developer Target 1: 99.4% accurate, 0.4× 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 2024182 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -67870776678359/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (+ 1 y) (/ x z)) x) (if (< x 1937054408219773/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* (* x (+ (- y z) 1)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x))))

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