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

Percentage Accurate: 88.8% → 99.5%

Time: 7.7s

Alternatives: 13

Speedup: 0.6×

• 21.6% 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: 88.8% 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: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+15}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.3e+86)
   (* x (+ -1.0 (/ y z)))
   (if (<= z 6.2e+15) (* (+ (- y z) 1.0) (/ x z)) (- (/ x (/ z y)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.3e+86) {
		tmp = x * (-1.0 + (y / z));
	} else if (z <= 6.2e+15) {
		tmp = ((y - z) + 1.0) * (x / z);
	} else {
		tmp = (x / (z / y)) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-3.3d+86)) then
        tmp = x * ((-1.0d0) + (y / z))
    else if (z <= 6.2d+15) then
        tmp = ((y - z) + 1.0d0) * (x / z)
    else
        tmp = (x / (z / y)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.3e+86) {
		tmp = x * (-1.0 + (y / z));
	} else if (z <= 6.2e+15) {
		tmp = ((y - z) + 1.0) * (x / z);
	} else {
		tmp = (x / (z / y)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.3e+86:
		tmp = x * (-1.0 + (y / z))
	elif z <= 6.2e+15:
		tmp = ((y - z) + 1.0) * (x / z)
	else:
		tmp = (x / (z / y)) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.3e+86)
		tmp = Float64(x * Float64(-1.0 + Float64(y / z)));
	elseif (z <= 6.2e+15)
		tmp = Float64(Float64(Float64(y - z) + 1.0) * Float64(x / z));
	else
		tmp = Float64(Float64(x / Float64(z / y)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.3e+86)
		tmp = x * (-1.0 + (y / z));
	elseif (z <= 6.2e+15)
		tmp = ((y - z) + 1.0) * (x / z);
	else
		tmp = (x / (z / y)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.3e+86], N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+15], N[(N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2999999999999999e86

   1. Initial program 67.4%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   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 100.0%

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

      5. *-inverses 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

      8. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   if -3.2999999999999999e86 < z < 6.2e15

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

      2. associate-/l* 99.9%

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

      3. +-commutative 99.9%

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

   4. Applied egg-rr 99.9%

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

   if 6.2e15 < z

   1. Initial program 67.4%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   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. metadata-eval 99.9%

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

      8. +-commutative 99.9%

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

   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 99.9%

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

      1. distribute-rgt-in 99.9%

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

      2. neg-mul-1 99.9%

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

      3. unsub-neg 99.9%

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

      4. clear-num 99.9%

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

      5. associate-*l/ 100.0%

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

      6. *-un-lft-identity 100.0%

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

   7. Applied egg-rr 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+15}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 9.6 \cdot 10^{-75}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y - z, x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + 1}} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 9.6e-75) (/ (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 <= 9.6e-75) {
		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 <= 9.6e-75)
		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, 9.6e-75], 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 < 9.60000000000000077e-75

   1. Initial program 89.6%

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

      1. distribute-lft-in 89.6%

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

      2. fma-define 89.6%

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

      3. *-rgt-identity 89.6%

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

   3. Simplified 89.6%

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

   if 9.60000000000000077e-75 < x

   1. Initial program 76.2%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   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. metadata-eval 99.9%

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

      8. +-commutative 99.9%

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

   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 99.8%

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

      3. un-div-inv 99.9%

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

      4. *-commutative 99.9%

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

      5. mul-1-neg 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 9.6 \cdot 10^{-75}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y - z, x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + 1}} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+104}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+43}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-243}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+15}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ y z))))
   (if (<= z -2.2e+104)
     (- x)
     (if (<= z -4.6e+43)
       t_0
       (if (<= z -1.0)
         (- x)
         (if (<= z -3.7e-196)
           (/ x z)
           (if (<= z -1.5e-243)
             t_0
             (if (<= z 1.4e-14) (/ x z) (if (<= z 8.5e+15) t_0 (- x))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (z <= -2.2e+104) {
		tmp = -x;
	} else if (z <= -4.6e+43) {
		tmp = t_0;
	} else if (z <= -1.0) {
		tmp = -x;
	} else if (z <= -3.7e-196) {
		tmp = x / z;
	} else if (z <= -1.5e-243) {
		tmp = t_0;
	} else if (z <= 1.4e-14) {
		tmp = x / z;
	} else if (z <= 8.5e+15) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x * (y / z)
    if (z <= (-2.2d+104)) then
        tmp = -x
    else if (z <= (-4.6d+43)) then
        tmp = t_0
    else if (z <= (-1.0d0)) then
        tmp = -x
    else if (z <= (-3.7d-196)) then
        tmp = x / z
    else if (z <= (-1.5d-243)) then
        tmp = t_0
    else if (z <= 1.4d-14) then
        tmp = x / z
    else if (z <= 8.5d+15) then
        tmp = t_0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (z <= -2.2e+104) {
		tmp = -x;
	} else if (z <= -4.6e+43) {
		tmp = t_0;
	} else if (z <= -1.0) {
		tmp = -x;
	} else if (z <= -3.7e-196) {
		tmp = x / z;
	} else if (z <= -1.5e-243) {
		tmp = t_0;
	} else if (z <= 1.4e-14) {
		tmp = x / z;
	} else if (z <= 8.5e+15) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y / z)
	tmp = 0
	if z <= -2.2e+104:
		tmp = -x
	elif z <= -4.6e+43:
		tmp = t_0
	elif z <= -1.0:
		tmp = -x
	elif z <= -3.7e-196:
		tmp = x / z
	elif z <= -1.5e-243:
		tmp = t_0
	elif z <= 1.4e-14:
		tmp = x / z
	elif z <= 8.5e+15:
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (z <= -2.2e+104)
		tmp = Float64(-x);
	elseif (z <= -4.6e+43)
		tmp = t_0;
	elseif (z <= -1.0)
		tmp = Float64(-x);
	elseif (z <= -3.7e-196)
		tmp = Float64(x / z);
	elseif (z <= -1.5e-243)
		tmp = t_0;
	elseif (z <= 1.4e-14)
		tmp = Float64(x / z);
	elseif (z <= 8.5e+15)
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y / z);
	tmp = 0.0;
	if (z <= -2.2e+104)
		tmp = -x;
	elseif (z <= -4.6e+43)
		tmp = t_0;
	elseif (z <= -1.0)
		tmp = -x;
	elseif (z <= -3.7e-196)
		tmp = x / z;
	elseif (z <= -1.5e-243)
		tmp = t_0;
	elseif (z <= 1.4e-14)
		tmp = x / z;
	elseif (z <= 8.5e+15)
		tmp = t_0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+104], (-x), If[LessEqual[z, -4.6e+43], t$95$0, If[LessEqual[z, -1.0], (-x), If[LessEqual[z, -3.7e-196], N[(x / z), $MachinePrecision], If[LessEqual[z, -1.5e-243], t$95$0, If[LessEqual[z, 1.4e-14], N[(x / z), $MachinePrecision], If[LessEqual[z, 8.5e+15], t$95$0, (-x)]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2e104 or -4.6000000000000005e43 < z < -1 or 8.5e15 < z

   1. Initial program 69.7%

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

      1. associate-/l* 99.9%

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

      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. metadata-eval 99.9%

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

      8. +-commutative 99.9%

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

   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 76.7%

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

      1. neg-mul-1 76.7%

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

   7. Simplified 76.7%

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

   if -2.2e104 < z < -4.6000000000000005e43 or -3.7000000000000001e-196 < z < -1.5000000000000001e-243 or 1.4e-14 < z < 8.5e15

   1. Initial program 96.2%

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

      1. associate-/l* 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+r- 99.7%

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

      4. div-sub 99.7%

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

      5. *-inverses 99.7%

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

      6. sub-neg 99.7%

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

      7. metadata-eval 99.7%

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

      8. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 75.8%

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

      1. associate-/l* 75.8%

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

   7. Simplified 75.8%

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

   if -1 < z < -3.7000000000000001e-196 or -1.5000000000000001e-243 < z < 1.4e-14

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 62.1%

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

   4. Taylor expanded in z around 0 61.2%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+104}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-243}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+78}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+40}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-178}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= z -1.2e+78)
     (- x)
     (if (<= z -3.8e+40)
       t_0
       (if (<= z -1.0)
         (- x)
         (if (<= z -3.4e-53)
           (/ x z)
           (if (<= z 7.2e-178)
             t_0
             (if (<= z 1.2e-14)
               (/ x z)
               (if (<= z 6.5e+18) (* x (/ y z)) (- x))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (z <= -1.2e+78) {
		tmp = -x;
	} else if (z <= -3.8e+40) {
		tmp = t_0;
	} else if (z <= -1.0) {
		tmp = -x;
	} else if (z <= -3.4e-53) {
		tmp = x / z;
	} else if (z <= 7.2e-178) {
		tmp = t_0;
	} else if (z <= 1.2e-14) {
		tmp = x / z;
	} else if (z <= 6.5e+18) {
		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) :: t_0
    real(8) :: tmp
    t_0 = y * (x / z)
    if (z <= (-1.2d+78)) then
        tmp = -x
    else if (z <= (-3.8d+40)) then
        tmp = t_0
    else if (z <= (-1.0d0)) then
        tmp = -x
    else if (z <= (-3.4d-53)) then
        tmp = x / z
    else if (z <= 7.2d-178) then
        tmp = t_0
    else if (z <= 1.2d-14) then
        tmp = x / z
    else if (z <= 6.5d+18) 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 t_0 = y * (x / z);
	double tmp;
	if (z <= -1.2e+78) {
		tmp = -x;
	} else if (z <= -3.8e+40) {
		tmp = t_0;
	} else if (z <= -1.0) {
		tmp = -x;
	} else if (z <= -3.4e-53) {
		tmp = x / z;
	} else if (z <= 7.2e-178) {
		tmp = t_0;
	} else if (z <= 1.2e-14) {
		tmp = x / z;
	} else if (z <= 6.5e+18) {
		tmp = x * (y / z);
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if z <= -1.2e+78:
		tmp = -x
	elif z <= -3.8e+40:
		tmp = t_0
	elif z <= -1.0:
		tmp = -x
	elif z <= -3.4e-53:
		tmp = x / z
	elif z <= 7.2e-178:
		tmp = t_0
	elif z <= 1.2e-14:
		tmp = x / z
	elif z <= 6.5e+18:
		tmp = x * (y / z)
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (z <= -1.2e+78)
		tmp = Float64(-x);
	elseif (z <= -3.8e+40)
		tmp = t_0;
	elseif (z <= -1.0)
		tmp = Float64(-x);
	elseif (z <= -3.4e-53)
		tmp = Float64(x / z);
	elseif (z <= 7.2e-178)
		tmp = t_0;
	elseif (z <= 1.2e-14)
		tmp = Float64(x / z);
	elseif (z <= 6.5e+18)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (z <= -1.2e+78)
		tmp = -x;
	elseif (z <= -3.8e+40)
		tmp = t_0;
	elseif (z <= -1.0)
		tmp = -x;
	elseif (z <= -3.4e-53)
		tmp = x / z;
	elseif (z <= 7.2e-178)
		tmp = t_0;
	elseif (z <= 1.2e-14)
		tmp = x / z;
	elseif (z <= 6.5e+18)
		tmp = x * (y / z);
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+78], (-x), If[LessEqual[z, -3.8e+40], t$95$0, If[LessEqual[z, -1.0], (-x), If[LessEqual[z, -3.4e-53], N[(x / z), $MachinePrecision], If[LessEqual[z, 7.2e-178], t$95$0, If[LessEqual[z, 1.2e-14], N[(x / z), $MachinePrecision], If[LessEqual[z, 6.5e+18], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], (-x)]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1999999999999999e78 or -3.80000000000000004e40 < z < -1 or 6.5e18 < 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. metadata-eval 99.9%

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

      8. +-commutative 99.9%

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

   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 75.8%

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

      1. neg-mul-1 75.8%

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

   7. Simplified 75.8%

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

   if -1.1999999999999999e78 < z < -3.80000000000000004e40 or -3.4e-53 < z < 7.19999999999999987e-178

   1. Initial program 99.9%

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

      1. associate-/l* 91.3%

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

      2. +-commutative 91.3%

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

      3. associate-+r- 91.3%

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

      4. div-sub 91.3%

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

      5. *-inverses 91.3%

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

      6. sub-neg 91.3%

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

      7. metadata-eval 91.3%

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

      8. +-commutative 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in y around inf 61.9%

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

      1. *-commutative 61.9%

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

      2. associate-/l* 67.3%

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

   7. Applied egg-rr 67.3%

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

   if -1 < z < -3.4e-53 or 7.19999999999999987e-178 < z < 1.2e-14

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 68.2%

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

   4. Taylor expanded in z around 0 65.7%

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

   if 1.2e-14 < z < 6.5e18

   1. Initial program 99.4%

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

      1. associate-/l* 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-+r- 99.6%

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

      4. div-sub 99.4%

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

      5. *-inverses 99.4%

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

      6. sub-neg 99.4%

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

      7. metadata-eval 99.4%

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

      8. +-commutative 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around inf 75.8%

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

      1. associate-/l* 76.0%

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

   7. Simplified 76.0%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+78}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+40}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-178}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-16} \lor \neg \left(z \leq 4 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(\frac{y + 1}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1e-16) (not (<= z 4e-17)))
   (* x (+ (/ (+ y 1.0) z) -1.0))
   (/ (+ x (* x y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e-16) || !(z <= 4e-17)) {
		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 <= (-1d-16)) .or. (.not. (z <= 4d-17))) 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 <= -1e-16) || !(z <= 4e-17)) {
		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 <= -1e-16) or not (z <= 4e-17):
		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 <= -1e-16) || !(z <= 4e-17))
		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 <= -1e-16) || ~((z <= 4e-17)))
		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, -1e-16], N[Not[LessEqual[z, 4e-17]], $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 < -9.9999999999999998e-17 or 4.00000000000000029e-17 < z

   1. Initial program 74.5%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   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. metadata-eval 99.9%

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

      8. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   if -9.9999999999999998e-17 < z < 4.00000000000000029e-17

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-16} \lor \neg \left(z \leq 4 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot \left(\frac{y + 1}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.0))
		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 <= -1.0) || ~((y <= 1.0)))
		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, -1.0], N[Not[LessEqual[y, 1.0]], $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 < -1 or 1 < y

   1. Initial program 86.9%

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

      1. associate-/l* 90.7%

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

      2. +-commutative 90.7%

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

      3. associate-+r- 90.7%

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

      4. div-sub 90.8%

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

      5. *-inverses 90.8%

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

      6. sub-neg 90.8%

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

      7. metadata-eval 90.8%

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

      8. +-commutative 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in y around inf 90.4%

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

   if -1 < y < 1

   1. Initial program 85.7%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   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. metadata-eval 99.8%

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

      8. +-commutative 99.8%

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

   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 98.1%

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

      1. sub-neg 98.1%

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

      2. metadata-eval 98.1%

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

      3. distribute-rgt-in 98.2%

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

      4. associate-*l/ 98.3%

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

      5. *-lft-identity 98.3%

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

      6. neg-mul-1 98.3%

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

      7. unsub-neg 98.3%

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

   7. Simplified 98.3%

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

4. Final simplification 94.5%

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

Alternative 7: 95.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.0d0)) then
        tmp = x * ((-1.0d0) + (y / z))
    else if (y <= 1.0d0) then
        tmp = (x / z) - x
    else
        tmp = (x / (z / y)) - x
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if y < -1

   1. Initial program 87.8%

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

      1. associate-/l* 86.4%

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

      2. +-commutative 86.4%

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

      3. associate-+r- 86.4%

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

      4. div-sub 86.4%

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

      5. *-inverses 86.4%

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

      6. sub-neg 86.4%

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

      7. metadata-eval 86.4%

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

      8. +-commutative 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in y around inf 86.4%

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

   if -1 < y < 1

   1. Initial program 85.7%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   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. metadata-eval 99.8%

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

      8. +-commutative 99.8%

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

   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 98.1%

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

      1. sub-neg 98.1%

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

      2. metadata-eval 98.1%

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

      3. distribute-rgt-in 98.2%

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

      4. associate-*l/ 98.3%

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

      5. *-lft-identity 98.3%

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

      6. neg-mul-1 98.3%

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

      7. unsub-neg 98.3%

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

   7. Simplified 98.3%

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

   if 1 < y

   1. Initial program 85.9%

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

      1. associate-/l* 95.2%

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

      2. +-commutative 95.2%

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

      3. associate-+r- 95.2%

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

      4. div-sub 95.2%

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

      5. *-inverses 95.2%

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

      6. sub-neg 95.2%

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

      7. metadata-eval 95.2%

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

      8. +-commutative 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in y around inf 94.6%

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

      1. distribute-rgt-in 94.6%

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

      2. neg-mul-1 94.6%

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

      3. unsub-neg 94.6%

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

      4. clear-num 94.4%

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

      5. associate-*l/ 95.3%

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

      6. *-un-lft-identity 95.3%

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

   7. Applied egg-rr 95.3%

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

4. Final simplification 94.7%

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

Alternative 8: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.95:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 0.0063:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.95)
   (* x (+ -1.0 (/ y z)))
   (if (<= z 0.0063) (/ (+ x (* x y)) z) (- (/ x (/ z y)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.95) {
		tmp = x * (-1.0 + (y / z));
	} else if (z <= 0.0063) {
		tmp = (x + (x * y)) / z;
	} else {
		tmp = (x / (z / y)) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.95d0)) then
        tmp = x * ((-1.0d0) + (y / z))
    else if (z <= 0.0063d0) then
        tmp = (x + (x * y)) / z
    else
        tmp = (x / (z / y)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.95) {
		tmp = x * (-1.0 + (y / z));
	} else if (z <= 0.0063) {
		tmp = (x + (x * y)) / z;
	} else {
		tmp = (x / (z / y)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.95:
		tmp = x * (-1.0 + (y / z))
	elif z <= 0.0063:
		tmp = (x + (x * y)) / z
	else:
		tmp = (x / (z / y)) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.95)
		tmp = Float64(x * Float64(-1.0 + Float64(y / z)));
	elseif (z <= 0.0063)
		tmp = Float64(Float64(x + Float64(x * y)) / z);
	else
		tmp = Float64(Float64(x / Float64(z / y)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.95)
		tmp = x * (-1.0 + (y / z));
	elseif (z <= 0.0063)
		tmp = (x + (x * y)) / z;
	else
		tmp = (x / (z / y)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.95], N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0063], N[(N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.94999999999999996

   1. Initial program 76.8%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   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. metadata-eval 99.8%

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

      8. +-commutative 99.8%

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

   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 inf 96.1%

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

   if -0.94999999999999996 < z < 0.0063

   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 98.6%

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

   if 0.0063 < z

   1. Initial program 69.4%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   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. metadata-eval 99.9%

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

      8. +-commutative 99.9%

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

   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 99.7%

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

      1. distribute-rgt-in 99.8%

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

      2. neg-mul-1 99.8%

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

      3. unsub-neg 99.8%

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

      4. clear-num 99.8%

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

      5. associate-*l/ 99.8%

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

      6. *-un-lft-identity 99.8%

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

   7. Applied egg-rr 99.8%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.95:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 0.0063:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+22} \lor \neg \left(y \leq 3.05 \cdot 10^{+33}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.3e+22) (not (<= y 3.05e+33))) (* y (/ x z)) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.3e+22) || !(y <= 3.05e+33)) {
		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 <= (-5.3d+22)) .or. (.not. (y <= 3.05d+33))) 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 <= -5.3e+22) || !(y <= 3.05e+33)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.3e+22) or not (y <= 3.05e+33):
		tmp = y * (x / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.3e+22) || !(y <= 3.05e+33))
		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 <= -5.3e+22) || ~((y <= 3.05e+33)))
		tmp = y * (x / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.3e+22], N[Not[LessEqual[y, 3.05e+33]], $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 < -5.2999999999999998e22 or 3.0500000000000002e33 < y

   1. Initial program 87.6%

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

      1. associate-/l* 90.1%

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

      2. +-commutative 90.1%

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

      3. associate-+r- 90.1%

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

      4. div-sub 90.1%

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

      5. *-inverses 90.1%

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

      6. sub-neg 90.1%

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

      7. metadata-eval 90.1%

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

      8. +-commutative 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in y around inf 73.4%

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

      1. *-commutative 73.4%

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

      2. associate-/l* 77.2%

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

   7. Applied egg-rr 77.2%

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

   if -5.2999999999999998e22 < y < 3.0500000000000002e33

   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. metadata-eval 99.8%

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

      8. +-commutative 99.8%

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

   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 96.5%

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

      1. sub-neg 96.5%

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

      2. metadata-eval 96.5%

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

      3. distribute-rgt-in 96.6%

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

      4. associate-*l/ 96.7%

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

      5. *-lft-identity 96.7%

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

      6. neg-mul-1 96.7%

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

      7. unsub-neg 96.7%

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

   7. Simplified 96.7%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+22} \lor \neg \left(y \leq 3.05 \cdot 10^{+33}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 94.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y + 1}{z} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 4e+28) (/ (* 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 <= 4e+28) {
		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 <= 4d+28) 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 <= 4e+28) {
		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 <= 4e+28:
		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 <= 4e+28)
		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 <= 4e+28)
		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, 4e+28], 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 < 3.99999999999999983e28

   1. Initial program 90.5%

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

   if 3.99999999999999983e28 < x

   1. Initial program 65.3%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   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 100.0%

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

      5. *-inverses 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

      8. +-commutative 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y + 1}{z} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 94.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 8.2 \cdot 10^{-75}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + 1}} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 8.2e-75) (/ (* 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 <= 8.2e-75) {
		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 <= 8.2d-75) 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 <= 8.2e-75) {
		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 <= 8.2e-75:
		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 <= 8.2e-75)
		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 <= 8.2e-75)
		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, 8.2e-75], 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 < 8.20000000000000005e-75

   1. Initial program 89.6%

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

   if 8.20000000000000005e-75 < x

   1. Initial program 76.2%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   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. metadata-eval 99.9%

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

      8. +-commutative 99.9%

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

   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 99.8%

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

      3. un-div-inv 99.9%

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

      4. *-commutative 99.9%

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

      5. mul-1-neg 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 8.2 \cdot 10^{-75}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + 1}} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 2400000000\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 2400000000.0))) (- x) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 2400000000.0)) {
		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 <= 2400000000.0d0))) 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 <= 2400000000.0)) {
		tmp = -x;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 2400000000.0):
		tmp = -x
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 2400000000.0))
		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 <= 2400000000.0)))
		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, 2400000000.0]], $MachinePrecision]], (-x), N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 2.4e9 < z

   1. Initial program 72.5%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   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. metadata-eval 99.9%

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

      8. +-commutative 99.9%

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

   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 71.7%

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

      1. neg-mul-1 71.7%

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

   7. Simplified 71.7%

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

   if -1 < z < 2.4e9

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 58.0%

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

   4. Taylor expanded in z around 0 56.7%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 2400000000\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.9% 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 86.3%

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

   1. associate-/l* 95.4%

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

   2. +-commutative 95.4%

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

   3. associate-+r- 95.4%

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

   4. div-sub 95.4%

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

   5. *-inverses 95.4%

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

   6. sub-neg 95.4%

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

   7. metadata-eval 95.4%

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

   8. +-commutative 95.4%

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

3. Simplified 95.4%

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

5. Taylor expanded in z around inf 37.3%

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

   1. neg-mul-1 37.3%

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

7. Simplified 37.3%

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

8. Final simplification 37.3%

   \[\leadsto -x \]
9. Add Preprocessing

Developer target: 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 2024039 
(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))