tan-example (used to crash)

Percentage Accurate: 79.7% → 99.7%

Time: 34.1s

Alternatives: 10

Speedup: 1.0×

Specification

\[\left(\left(\left(x = 0 \lor 0.5884142 \leq x \land x \leq 505.5909\right) \land \left(-1.796658 \cdot 10^{+308} \leq y \land y \leq -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \leq y \land y \leq 1.751224 \cdot 10^{+308}\right)\right) \land \left(-1.776707 \cdot 10^{+308} \leq z \land z \leq -8.599796 \cdot 10^{-310} \lor 3.293145 \cdot 10^{-311} \leq z \land z \leq 1.725154 \cdot 10^{+308}\right)\right) \land \left(-1.796658 \cdot 10^{+308} \leq a \land a \leq -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \leq a \land a \leq 1.751224 \cdot 10^{+308}\right)\]

Math

\[\begin{array}{l} \\ x + \left(\tan \left(y + z\right) - \tan a\right) \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + (tan((y + z)) - tan(a));
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (tan((y + z)) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	return x + (Math.tan((y + z)) - Math.tan(a));
}

Python

def code(x, y, z, a):
	return x + (math.tan((y + z)) - math.tan(a))

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 79.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\tan \left(y + z\right) - \tan a\right) \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + (tan((y + z)) - tan(a));
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (tan((y + z)) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	return x + (Math.tan((y + z)) - Math.tan(a));
}

Python

def code(x, y, z, a):
	return x + (math.tan((y + z)) - math.tan(a))

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z a)
 :precision binary64
 (+
  x
  (-
   (/
    1.0
    (/
     (- 1.0 (/ (* (sin z) (sin y)) (* (cos z) (cos y))))
     (+ (tan y) (tan z))))
   (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + ((1.0 / ((1.0 - ((sin(z) * sin(y)) / (cos(z) * cos(y)))) / (tan(y) + tan(z)))) - tan(a));
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + ((1.0d0 / ((1.0d0 - ((sin(z) * sin(y)) / (cos(z) * cos(y)))) / (tan(y) + tan(z)))) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	return x + ((1.0 / ((1.0 - ((Math.sin(z) * Math.sin(y)) / (Math.cos(z) * Math.cos(y)))) / (Math.tan(y) + Math.tan(z)))) - Math.tan(a));
}

Python

def code(x, y, z, a):
	return x + ((1.0 / ((1.0 - ((math.sin(z) * math.sin(y)) / (math.cos(z) * math.cos(y)))) / (math.tan(y) + math.tan(z)))) - math.tan(a))

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.3%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. tan-sum 99.7%

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

   2. clear-num 99.7%

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

4. Applied egg-rr 99.7%

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

   1. *-commutative 99.7%

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

   2. tan-quot 99.7%

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

   3. tan-quot 99.7%

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

   4. frac-times 99.7%

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

6. Applied egg-rr 99.7%

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

7. Final simplification 99.7%

   \[\leadsto x + \left(\frac{1}{\frac{1 - \frac{\sin z \cdot \sin y}{\cos z \cdot \cos y}}{\tan y + \tan z}} - \tan a\right) \]
8. Add Preprocessing

Alternative 2: 99.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + ((1.0d0 / ((1.0d0 - (tan(y) * tan(z))) / (tan(y) + tan(z)))) - tan(a))
end function

Java

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

Python

def code(x, y, z, a):
	return x + ((1.0 / ((1.0 - (math.tan(y) * math.tan(z))) / (math.tan(y) + math.tan(z)))) - math.tan(a))

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.3%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. tan-sum 99.7%

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

   2. clear-num 99.7%

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

4. Applied egg-rr 99.7%

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

5. Final simplification 99.7%

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

Alternative 3: 99.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (((tan(y) + tan(z)) / (1.0d0 - (tan(y) * tan(z)))) - tan(a))
end function

Java

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

Python

def code(x, y, z, a):
	return x + (((math.tan(y) + math.tan(z)) / (1.0 - (math.tan(y) * math.tan(z)))) - math.tan(a))

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.3%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. tan-sum 99.7%

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

   2. div-inv 99.7%

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

4. Applied egg-rr 99.7%

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

   1. associate-*r/ 99.7%

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

   2. *-rgt-identity 99.7%

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

6. Simplified 99.7%

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

7. Final simplification 99.7%

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

Alternative 4: 89.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.00034:\\ \;\;\;\;x + \left(\tan \left(z + y\right) - \tan a\right)\\ \mathbf{elif}\;a \leq 0.175:\\ \;\;\;\;x + \left(\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\frac{\cos \left(z + y\right)}{\sin \left(z + y\right)}} - \tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= a -0.00034)
   (+ x (- (tan (+ z y)) (tan a)))
   (if (<= a 0.175)
     (+ x (- (/ 1.0 (/ (- 1.0 (* (tan y) (tan z))) (+ (tan y) (tan z)))) a))
     (+ x (- (/ 1.0 (/ (cos (+ z y)) (sin (+ z y)))) (tan a))))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -0.00034) {
		tmp = x + (tan((z + y)) - tan(a));
	} else if (a <= 0.175) {
		tmp = x + ((1.0 / ((1.0 - (tan(y) * tan(z))) / (tan(y) + tan(z)))) - a);
	} else {
		tmp = x + ((1.0 / (cos((z + y)) / sin((z + y)))) - tan(a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-0.00034d0)) then
        tmp = x + (tan((z + y)) - tan(a))
    else if (a <= 0.175d0) then
        tmp = x + ((1.0d0 / ((1.0d0 - (tan(y) * tan(z))) / (tan(y) + tan(z)))) - a)
    else
        tmp = x + ((1.0d0 / (cos((z + y)) / sin((z + y)))) - tan(a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -0.00034) {
		tmp = x + (Math.tan((z + y)) - Math.tan(a));
	} else if (a <= 0.175) {
		tmp = x + ((1.0 / ((1.0 - (Math.tan(y) * Math.tan(z))) / (Math.tan(y) + Math.tan(z)))) - a);
	} else {
		tmp = x + ((1.0 / (Math.cos((z + y)) / Math.sin((z + y)))) - Math.tan(a));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if a <= -0.00034:
		tmp = x + (math.tan((z + y)) - math.tan(a))
	elif a <= 0.175:
		tmp = x + ((1.0 / ((1.0 - (math.tan(y) * math.tan(z))) / (math.tan(y) + math.tan(z)))) - a)
	else:
		tmp = x + ((1.0 / (math.cos((z + y)) / math.sin((z + y)))) - math.tan(a))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (a <= -0.00034)
		tmp = Float64(x + Float64(tan(Float64(z + y)) - tan(a)));
	elseif (a <= 0.175)
		tmp = Float64(x + Float64(Float64(1.0 / Float64(Float64(1.0 - Float64(tan(y) * tan(z))) / Float64(tan(y) + tan(z)))) - a));
	else
		tmp = Float64(x + Float64(Float64(1.0 / Float64(cos(Float64(z + y)) / sin(Float64(z + y)))) - tan(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -0.00034)
		tmp = x + (tan((z + y)) - tan(a));
	elseif (a <= 0.175)
		tmp = x + ((1.0 / ((1.0 - (tan(y) * tan(z))) / (tan(y) + tan(z)))) - a);
	else
		tmp = x + ((1.0 / (cos((z + y)) / sin((z + y)))) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[a, -0.00034], N[(x + N[(N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.175], N[(x + N[(N[(1.0 / N[(N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 / N[(N[Cos[N[(z + y), $MachinePrecision]], $MachinePrecision] / N[Sin[N[(z + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.4e-4

   1. Initial program 77.9%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   if -3.4e-4 < a < 0.17499999999999999

   1. Initial program 80.9%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. tan-sum 99.7%

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

      2. clear-num 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in a around 0 99.1%

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

   if 0.17499999999999999 < a

   1. Initial program 76.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. tan-quot 76.8%

         \[\leadsto x + \left(\color{blue}{\frac{\sin \left(y + z\right)}{\cos \left(y + z\right)}} - \tan a\right) \]

      2. clear-num 76.8%

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

   4. Applied egg-rr 76.8%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00034:\\ \;\;\;\;x + \left(\tan \left(z + y\right) - \tan a\right)\\ \mathbf{elif}\;a \leq 0.175:\\ \;\;\;\;x + \left(\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\frac{\cos \left(z + y\right)}{\sin \left(z + y\right)}} - \tan a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.000165:\\ \;\;\;\;x + \left(\tan \left(z + y\right) - \tan a\right)\\ \mathbf{elif}\;a \leq 0.175:\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\frac{\cos \left(z + y\right)}{\sin \left(z + y\right)}} - \tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= a -0.000165)
   (+ x (- (tan (+ z y)) (tan a)))
   (if (<= a 0.175)
     (+ x (- (/ (+ (tan y) (tan z)) (- 1.0 (* (tan y) (tan z)))) a))
     (+ x (- (/ 1.0 (/ (cos (+ z y)) (sin (+ z y)))) (tan a))))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -0.000165) {
		tmp = x + (tan((z + y)) - tan(a));
	} else if (a <= 0.175) {
		tmp = x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) - a);
	} else {
		tmp = x + ((1.0 / (cos((z + y)) / sin((z + y)))) - tan(a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-0.000165d0)) then
        tmp = x + (tan((z + y)) - tan(a))
    else if (a <= 0.175d0) then
        tmp = x + (((tan(y) + tan(z)) / (1.0d0 - (tan(y) * tan(z)))) - a)
    else
        tmp = x + ((1.0d0 / (cos((z + y)) / sin((z + y)))) - tan(a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -0.000165) {
		tmp = x + (Math.tan((z + y)) - Math.tan(a));
	} else if (a <= 0.175) {
		tmp = x + (((Math.tan(y) + Math.tan(z)) / (1.0 - (Math.tan(y) * Math.tan(z)))) - a);
	} else {
		tmp = x + ((1.0 / (Math.cos((z + y)) / Math.sin((z + y)))) - Math.tan(a));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if a <= -0.000165:
		tmp = x + (math.tan((z + y)) - math.tan(a))
	elif a <= 0.175:
		tmp = x + (((math.tan(y) + math.tan(z)) / (1.0 - (math.tan(y) * math.tan(z)))) - a)
	else:
		tmp = x + ((1.0 / (math.cos((z + y)) / math.sin((z + y)))) - math.tan(a))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (a <= -0.000165)
		tmp = Float64(x + Float64(tan(Float64(z + y)) - tan(a)));
	elseif (a <= 0.175)
		tmp = Float64(x + Float64(Float64(Float64(tan(y) + tan(z)) / Float64(1.0 - Float64(tan(y) * tan(z)))) - a));
	else
		tmp = Float64(x + Float64(Float64(1.0 / Float64(cos(Float64(z + y)) / sin(Float64(z + y)))) - tan(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -0.000165)
		tmp = x + (tan((z + y)) - tan(a));
	elseif (a <= 0.175)
		tmp = x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) - a);
	else
		tmp = x + ((1.0 / (cos((z + y)) / sin((z + y)))) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[a, -0.000165], N[(x + N[(N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.175], N[(x + N[(N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 / N[(N[Cos[N[(z + y), $MachinePrecision]], $MachinePrecision] / N[Sin[N[(z + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.65e-4

   1. Initial program 77.9%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   if -1.65e-4 < a < 0.17499999999999999

   1. Initial program 80.9%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 80.7%

      \[\leadsto x + \left(\tan \left(y + z\right) - \color{blue}{a}\right) \]
   4. Step-by-step derivation

      1. tan-sum 99.1%

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

      2. *-un-lft-identity 99.1%

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

      3. associate-*l/ 99.1%

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

      4. *-commutative 99.1%

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

      5. fma-neg 99.1%

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

   5. Applied egg-rr 99.1%

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

      1. fma-undefine 99.1%

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

      2. *-commutative 99.1%

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

      3. unsub-neg 99.1%

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

      4. associate-*l/ 99.1%

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

      5. *-lft-identity 99.1%

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

   7. Simplified 99.1%

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

   if 0.17499999999999999 < a

   1. Initial program 76.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. tan-quot 76.8%

         \[\leadsto x + \left(\color{blue}{\frac{\sin \left(y + z\right)}{\cos \left(y + z\right)}} - \tan a\right) \]

      2. clear-num 76.8%

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

   4. Applied egg-rr 76.8%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.000165:\\ \;\;\;\;x + \left(\tan \left(z + y\right) - \tan a\right)\\ \mathbf{elif}\;a \leq 0.175:\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\frac{\cos \left(z + y\right)}{\sin \left(z + y\right)}} - \tan a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \lor \neg \left(a \leq 4.7\right):\\ \;\;\;\;x + \frac{\sin y}{\cos y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(z + y\right) - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -1.6) (not (<= a 4.7)))
   (+ x (/ (sin y) (cos y)))
   (+ x (- (tan (+ z y)) a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -1.6) || !(a <= 4.7)) {
		tmp = x + (sin(y) / cos(y));
	} else {
		tmp = x + (tan((z + y)) - a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.6d0)) .or. (.not. (a <= 4.7d0))) then
        tmp = x + (sin(y) / cos(y))
    else
        tmp = x + (tan((z + y)) - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -1.6) || !(a <= 4.7)) {
		tmp = x + (Math.sin(y) / Math.cos(y));
	} else {
		tmp = x + (Math.tan((z + y)) - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (a <= -1.6) or not (a <= 4.7):
		tmp = x + (math.sin(y) / math.cos(y))
	else:
		tmp = x + (math.tan((z + y)) - a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -1.6) || !(a <= 4.7))
		tmp = Float64(x + Float64(sin(y) / cos(y)));
	else
		tmp = Float64(x + Float64(tan(Float64(z + y)) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -1.6) || ~((a <= 4.7)))
		tmp = x + (sin(y) / cos(y));
	else
		tmp = x + (tan((z + y)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[a, -1.6], N[Not[LessEqual[a, 4.7]], $MachinePrecision]], N[(x + N[(N[Sin[y], $MachinePrecision] / N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6000000000000001 or 4.70000000000000018 < a

   1. Initial program 77.2%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 77.2%

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

      2. sub-neg 77.2%

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

      3. associate-+l+ 77.0%

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

      4. tan-quot 77.0%

         \[\leadsto \color{blue}{\frac{\sin \left(y + z\right)}{\cos \left(y + z\right)}} + \left(\left(-\tan a\right) + x\right) \]

      5. div-inv 77.0%

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

      6. fma-define 77.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sin \left(y + z\right), \frac{1}{\cos \left(y + z\right)}, \left(-\tan a\right) + x\right)} \]

      7. neg-mul-1 77.0%

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

      8. fma-define 77.0%

         \[\leadsto \mathsf{fma}\left(\sin \left(y + z\right), \frac{1}{\cos \left(y + z\right)}, \color{blue}{\mathsf{fma}\left(-1, \tan a, x\right)}\right) \]

   4. Applied egg-rr 77.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sin \left(y + z\right), \frac{1}{\cos \left(y + z\right)}, \mathsf{fma}\left(-1, \tan a, x\right)\right)} \]
   5. Step-by-step derivation

      1. fma-undefine 77.0%

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

      2. associate-*r/ 77.0%

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

      3. *-rgt-identity 77.0%

         \[\leadsto \frac{\color{blue}{\sin \left(y + z\right)}}{\cos \left(y + z\right)} + \mathsf{fma}\left(-1, \tan a, x\right) \]

      4. +-commutative 77.0%

         \[\leadsto \frac{\sin \color{blue}{\left(z + y\right)}}{\cos \left(y + z\right)} + \mathsf{fma}\left(-1, \tan a, x\right) \]

      5. +-commutative 77.0%

         \[\leadsto \frac{\sin \left(z + y\right)}{\cos \color{blue}{\left(z + y\right)}} + \mathsf{fma}\left(-1, \tan a, x\right) \]

      6. fma-undefine 77.0%

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

      7. neg-mul-1 77.0%

         \[\leadsto \frac{\sin \left(z + y\right)}{\cos \left(z + y\right)} + \left(\color{blue}{\left(-\tan a\right)} + x\right) \]

      8. rem-square-sqrt 44.7%

         \[\leadsto \frac{\sin \left(z + y\right)}{\cos \left(z + y\right)} + \left(\color{blue}{\sqrt{-\tan a} \cdot \sqrt{-\tan a}} + x\right) \]

      9. fabs-sqr 44.7%

         \[\leadsto \frac{\sin \left(z + y\right)}{\cos \left(z + y\right)} + \left(\color{blue}{\left|\sqrt{-\tan a} \cdot \sqrt{-\tan a}\right|} + x\right) \]

      10. rem-square-sqrt 54.5%

          \[\leadsto \frac{\sin \left(z + y\right)}{\cos \left(z + y\right)} + \left(\left|\color{blue}{-\tan a}\right| + x\right) \]

      11. fabs-neg 54.5%

          \[\leadsto \frac{\sin \left(z + y\right)}{\cos \left(z + y\right)} + \left(\color{blue}{\left|\tan a\right|} + x\right) \]

      12. rem-square-sqrt 9.7%

          \[\leadsto \frac{\sin \left(z + y\right)}{\cos \left(z + y\right)} + \left(\left|\color{blue}{\sqrt{\tan a} \cdot \sqrt{\tan a}}\right| + x\right) \]

      13. fabs-sqr 9.7%

          \[\leadsto \frac{\sin \left(z + y\right)}{\cos \left(z + y\right)} + \left(\color{blue}{\sqrt{\tan a} \cdot \sqrt{\tan a}} + x\right) \]

      14. rem-square-sqrt 21.7%

          \[\leadsto \frac{\sin \left(z + y\right)}{\cos \left(z + y\right)} + \left(\color{blue}{\tan a} + x\right) \]

      15. +-commutative 21.7%

          \[\leadsto \frac{\sin \left(z + y\right)}{\cos \left(z + y\right)} + \color{blue}{\left(x + \tan a\right)} \]

   6. Simplified 21.7%

      \[\leadsto \color{blue}{\frac{\sin \left(z + y\right)}{\cos \left(z + y\right)} + \left(x + \tan a\right)} \]

   7. Taylor expanded in z around 0 21.6%

      \[\leadsto \color{blue}{x + \left(\frac{\sin a}{\cos a} + \frac{\sin y}{\cos y}\right)} \]
   8. Step-by-step derivation

      1. associate-+r+ 21.6%

         \[\leadsto \color{blue}{\left(x + \frac{\sin a}{\cos a}\right) + \frac{\sin y}{\cos y}} \]

   9. Simplified 21.6%

      \[\leadsto \color{blue}{\left(x + \frac{\sin a}{\cos a}\right) + \frac{\sin y}{\cos y}} \]

   10. Taylor expanded in a around 0 23.2%

       \[\leadsto \color{blue}{x + \frac{\sin y}{\cos y}} \]
   11. Step-by-step derivation

       1. +-commutative 23.2%

          \[\leadsto \color{blue}{\frac{\sin y}{\cos y} + x} \]

   12. Simplified 23.2%

       \[\leadsto \color{blue}{\frac{\sin y}{\cos y} + x} \]

   if -1.6000000000000001 < a < 4.70000000000000018

   1. Initial program 81.0%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 80.5%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \lor \neg \left(a \leq 4.7\right):\\ \;\;\;\;x + \frac{\sin y}{\cos y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(z + y\right) - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\tan a + \tan \left(z + y\right)\right) \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 (+ x (+ (tan a) (tan (+ z y)))))

C

double code(double x, double y, double z, double a) {
	return x + (tan(a) + tan((z + y)));
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (tan(a) + tan((z + y)))
end function

Java

public static double code(double x, double y, double z, double a) {
	return x + (Math.tan(a) + Math.tan((z + y)));
}

Python

def code(x, y, z, a):
	return x + (math.tan(a) + math.tan((z + y)))

Julia

function code(x, y, z, a)
	return Float64(x + Float64(tan(a) + tan(Float64(z + y))))
end

MATLAB

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

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[Tan[a], $MachinePrecision] + N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.3%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. sub-neg 79.3%

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

4. Applied egg-rr 79.3%

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

   1. +-commutative 79.3%

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

   2. rem-square-sqrt 41.8%

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

   3. fabs-sqr 41.8%

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

   4. rem-square-sqrt 68.6%

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

   5. fabs-neg 68.6%

      \[\leadsto x + \left(\tan \left(z + y\right) + \color{blue}{\left|\tan a\right|}\right) \]

   6. rem-square-sqrt 26.8%

      \[\leadsto x + \left(\tan \left(z + y\right) + \left|\color{blue}{\sqrt{\tan a} \cdot \sqrt{\tan a}}\right|\right) \]

   7. fabs-sqr 26.8%

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

   8. rem-square-sqrt 52.6%

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

6. Simplified 52.6%

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

7. Final simplification 52.6%

   \[\leadsto x + \left(\tan a + \tan \left(z + y\right)\right) \]
8. Add Preprocessing

Alternative 8: 79.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\tan \left(z + y\right) - \tan a\right) \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ z y)) (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + (tan((z + y)) - tan(a));
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (tan((z + y)) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	return x + (Math.tan((z + y)) - Math.tan(a));
}

Python

def code(x, y, z, a):
	return x + (math.tan((z + y)) - math.tan(a))

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.3%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing

3. Final simplification 79.3%

   \[\leadsto x + \left(\tan \left(z + y\right) - \tan a\right) \]
4. Add Preprocessing

Alternative 9: 50.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.17:\\ \;\;\;\;x + \left(\tan \left(z + y\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= a -7.8) x (if (<= a 0.17) (+ x (- (tan (+ z y)) a)) x)))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -7.8) {
		tmp = x;
	} else if (a <= 0.17) {
		tmp = x + (tan((z + y)) - a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7.8d0)) then
        tmp = x
    else if (a <= 0.17d0) then
        tmp = x + (tan((z + y)) - a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -7.8) {
		tmp = x;
	} else if (a <= 0.17) {
		tmp = x + (Math.tan((z + y)) - a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if a <= -7.8:
		tmp = x
	elif a <= 0.17:
		tmp = x + (math.tan((z + y)) - a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (a <= -7.8)
		tmp = x;
	elseif (a <= 0.17)
		tmp = Float64(x + Float64(tan(Float64(z + y)) - a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -7.8)
		tmp = x;
	elseif (a <= 0.17)
		tmp = x + (tan((z + y)) - a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[a, -7.8], x, If[LessEqual[a, 0.17], N[(x + N[(N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -7.79999999999999982 or 0.170000000000000012 < a

   1. Initial program 76.5%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 22.6%

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

   if -7.79999999999999982 < a < 0.170000000000000012

   1. Initial program 81.6%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 81.1%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.17:\\ \;\;\;\;x + \left(\tan \left(z + y\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 31.8% accurate, 207.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double a) {
	return x;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x
end function

Java

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

Python

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

Julia

function code(x, y, z, a)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, a_] := x

Derivation

1. Initial program 79.3%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf 33.6%

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

4. Final simplification 33.6%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024039 
(FPCore (x y z a)
  :name "tan-example (used to crash)"
  :precision binary64
  :pre (and (and (and (or (== x 0.0) (and (<= 0.5884142 x) (<= x 505.5909))) (or (and (<= -1.796658e+308 y) (<= y -9.425585e-310)) (and (<= 1.284938e-309 y) (<= y 1.751224e+308)))) (or (and (<= -1.776707e+308 z) (<= z -8.599796e-310)) (and (<= 3.293145e-311 z) (<= z 1.725154e+308)))) (or (and (<= -1.796658e+308 a) (<= a -9.425585e-310)) (and (<= 1.284938e-309 a) (<= a 1.751224e+308))))
  (+ x (- (tan (+ y z)) (tan a))))