tan-example (used to crash)

Percentage Accurate: 79.6% → 99.7%

Time: 36.8s

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: 79.6% 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

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

FPCore

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

C

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

Python

def code(x, y, z, a):
	return x + (((math.tan(y) + math.tan(z)) / (1.0 - ((math.sin(y) * math.sin(z)) / (math.cos(y) * math.cos(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(Float64(sin(y) * sin(z)) / Float64(cos(y) * cos(z))))) - tan(a)))
end

MATLAB

function tmp = code(x, y, z, a)
	tmp = x + (((tan(y) + tan(z)) / (1.0 - ((sin(y) * sin(z)) / (cos(y) * cos(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[(N[Sin[y], $MachinePrecision] * N[Sin[z], $MachinePrecision]), $MachinePrecision] / N[(N[Cos[y], $MachinePrecision] * N[Cos[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.8%

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

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

3. Applied egg-rr 99.7%

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

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

5. Simplified 99.7%

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

6. Taylor expanded in y around inf 99.7%

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

7. Final simplification 99.7%

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

Alternative 2: 89.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -0.001 \lor \neg \left(\tan a \leq 2 \cdot 10^{-15}\right):\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 + \left(1 + \left(-1 - \tan y \cdot \tan z\right)\right)} - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= (tan a) -0.001) (not (<= (tan a) 2e-15)))
   (+ x (- (tan (+ y z)) (tan a)))
   (+
    x
    (-
     (/ (+ (tan y) (tan z)) (+ 1.0 (+ 1.0 (- -1.0 (* (tan y) (tan z))))))
     a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((tan(a) <= -0.001) || !(tan(a) <= 2e-15)) {
		tmp = x + (tan((y + z)) - tan(a));
	} else {
		tmp = x + (((tan(y) + tan(z)) / (1.0 + (1.0 + (-1.0 - (tan(y) * tan(z)))))) - 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 ((tan(a) <= (-0.001d0)) .or. (.not. (tan(a) <= 2d-15))) then
        tmp = x + (tan((y + z)) - tan(a))
    else
        tmp = x + (((tan(y) + tan(z)) / (1.0d0 + (1.0d0 + ((-1.0d0) - (tan(y) * tan(z)))))) - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((Math.tan(a) <= -0.001) || !(Math.tan(a) <= 2e-15)) {
		tmp = x + (Math.tan((y + z)) - Math.tan(a));
	} else {
		tmp = x + (((Math.tan(y) + Math.tan(z)) / (1.0 + (1.0 + (-1.0 - (Math.tan(y) * Math.tan(z)))))) - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (math.tan(a) <= -0.001) or not (math.tan(a) <= 2e-15):
		tmp = x + (math.tan((y + z)) - math.tan(a))
	else:
		tmp = x + (((math.tan(y) + math.tan(z)) / (1.0 + (1.0 + (-1.0 - (math.tan(y) * math.tan(z)))))) - a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((tan(a) <= -0.001) || !(tan(a) <= 2e-15))
		tmp = Float64(x + Float64(tan(Float64(y + z)) - tan(a)));
	else
		tmp = Float64(x + Float64(Float64(Float64(tan(y) + tan(z)) / Float64(1.0 + Float64(1.0 + Float64(-1.0 - Float64(tan(y) * tan(z)))))) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((tan(a) <= -0.001) || ~((tan(a) <= 2e-15)))
		tmp = x + (tan((y + z)) - tan(a));
	else
		tmp = x + (((tan(y) + tan(z)) / (1.0 + (1.0 + (-1.0 - (tan(y) * tan(z)))))) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[N[Tan[a], $MachinePrecision], -0.001], N[Not[LessEqual[N[Tan[a], $MachinePrecision], 2e-15]], $MachinePrecision]], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(1.0 + N[(-1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (tan.f64 a) < -1e-3 or 2.0000000000000002e-15 < (tan.f64 a)

   1. Initial program 82.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]

   if -1e-3 < (tan.f64 a) < 2.0000000000000002e-15

   1. Initial program 74.3%

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

      1. tan-sum 99.6%

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

      2. div-inv 99.6%

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

   3. Applied egg-rr 99.6%

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

      1. associate-*r/ 99.6%

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

      2. *-rgt-identity 99.6%

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

   5. Simplified 99.6%

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

      1. expm1-log1p-u 92.1%

         \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\tan y \cdot \tan z\right)\right)}} - \tan a\right) \]

      2. expm1-udef 92.2%

         \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \color{blue}{\left(e^{\mathsf{log1p}\left(\tan y \cdot \tan z\right)} - 1\right)}} - \tan a\right) \]

      3. log1p-udef 92.2%

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

      4. add-exp-log 99.6%

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

   7. Applied egg-rr 99.6%

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

   8. Taylor expanded in a around 0 99.6%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.001 \lor \neg \left(\tan a \leq 2 \cdot 10^{-15}\right):\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 + \left(1 + \left(-1 - \tan y \cdot \tan z\right)\right)} - a\right)\\ \end{array} \]

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 78.8%

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

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

3. Applied egg-rr 99.7%

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

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

5. Simplified 99.7%

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

6. Final simplification 99.7%

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

Alternative 4: 89.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.00048 \lor \neg \left(a \leq 2.8 \cdot 10^{-14}\right):\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} + \left(x - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -0.00048) (not (<= a 2.8e-14)))
   (+ x (- (tan (+ y z)) (tan a)))
   (+ (/ (+ (tan y) (tan z)) (- 1.0 (* (tan y) (tan z)))) (- x a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -0.00048) || !(a <= 2.8e-14)) {
		tmp = x + (tan((y + z)) - tan(a));
	} else {
		tmp = ((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) + (x - 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 <= (-0.00048d0)) .or. (.not. (a <= 2.8d-14))) then
        tmp = x + (tan((y + z)) - tan(a))
    else
        tmp = ((tan(y) + tan(z)) / (1.0d0 - (tan(y) * tan(z)))) + (x - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -0.00048) || !(a <= 2.8e-14)) {
		tmp = x + (Math.tan((y + z)) - Math.tan(a));
	} else {
		tmp = ((Math.tan(y) + Math.tan(z)) / (1.0 - (Math.tan(y) * Math.tan(z)))) + (x - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (a <= -0.00048) or not (a <= 2.8e-14):
		tmp = x + (math.tan((y + z)) - math.tan(a))
	else:
		tmp = ((math.tan(y) + math.tan(z)) / (1.0 - (math.tan(y) * math.tan(z)))) + (x - a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -0.00048) || !(a <= 2.8e-14))
		tmp = Float64(x + Float64(tan(Float64(y + z)) - tan(a)));
	else
		tmp = Float64(Float64(Float64(tan(y) + tan(z)) / Float64(1.0 - Float64(tan(y) * tan(z)))) + Float64(x - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -0.00048) || ~((a <= 2.8e-14)))
		tmp = x + (tan((y + z)) - tan(a));
	else
		tmp = ((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) + (x - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[a, -0.00048], N[Not[LessEqual[a, 2.8e-14]], $MachinePrecision]], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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[(x - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.80000000000000012e-4 or 2.8000000000000001e-14 < a

   1. Initial program 82.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]

   if -4.80000000000000012e-4 < a < 2.8000000000000001e-14

   1. Initial program 74.3%

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

      1. associate-+r- 74.3%

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

      2. +-commutative 74.3%

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

      3. associate--l+ 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in a around 0 74.3%

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

      1. tan-sum 99.5%

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

      2. div-inv 99.5%

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

      3. fma-def 99.6%

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

   6. Applied egg-rr 99.6%

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

      1. fma-udef 99.5%

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

      2. associate-*r/ 99.5%

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

      3. *-rgt-identity 99.5%

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

   8. Simplified 99.5%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00048 \lor \neg \left(a \leq 2.8 \cdot 10^{-14}\right):\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} + \left(x - a\right)\\ \end{array} \]

Alternative 5: 60.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + z \leq 5 \cdot 10^{-8}:\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\tan \left(y + z\right) + \frac{1}{\frac{1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= (+ y z) 5e-8)
   (+ x (- (tan y) (tan a)))
   (+ (tan (+ y z)) (/ 1.0 (/ 1.0 x)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= 5e-8) {
		tmp = x + (tan(y) - tan(a));
	} else {
		tmp = tan((y + z)) + (1.0 / (1.0 / 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 ((y + z) <= 5d-8) then
        tmp = x + (tan(y) - tan(a))
    else
        tmp = tan((y + z)) + (1.0d0 / (1.0d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= 5e-8) {
		tmp = x + (Math.tan(y) - Math.tan(a));
	} else {
		tmp = Math.tan((y + z)) + (1.0 / (1.0 / x));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (y + z) <= 5e-8:
		tmp = x + (math.tan(y) - math.tan(a))
	else:
		tmp = math.tan((y + z)) + (1.0 / (1.0 / x))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (Float64(y + z) <= 5e-8)
		tmp = Float64(x + Float64(tan(y) - tan(a)));
	else
		tmp = Float64(tan(Float64(y + z)) + Float64(1.0 / Float64(1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((y + z) <= 5e-8)
		tmp = x + (tan(y) - tan(a));
	else
		tmp = tan((y + z)) + (1.0 / (1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[N[(y + z), $MachinePrecision], 5e-8], N[(x + N[(N[Tan[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] + N[(1.0 / N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 y z) < 4.9999999999999998e-8

   1. Initial program 81.3%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]

   2. Taylor expanded in z around 0 72.7%

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

      1. tan-quot 72.8%

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

      2. expm1-log1p-u 66.1%

         \[\leadsto x + \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\tan y\right)\right)} - \tan a\right) \]

      3. expm1-udef 66.1%

         \[\leadsto x + \left(\color{blue}{\left(e^{\mathsf{log1p}\left(\tan y\right)} - 1\right)} - \tan a\right) \]

   4. Applied egg-rr 66.1%

      \[\leadsto x + \left(\color{blue}{\left(e^{\mathsf{log1p}\left(\tan y\right)} - 1\right)} - \tan a\right) \]
   5. Step-by-step derivation

      1. expm1-def 66.1%

         \[\leadsto x + \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\tan y\right)\right)} - \tan a\right) \]

      2. expm1-log1p 72.8%

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

   6. Simplified 72.8%

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

   if 4.9999999999999998e-8 < (+.f64 y z)

   1. Initial program 75.1%

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

      1. associate-+r- 75.0%

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

      2. +-commutative 75.0%

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

      3. associate--l+ 75.0%

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

   3. Simplified 75.0%

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

      1. flip-- 74.8%

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

      2. clear-num 74.7%

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

      3. pow2 74.7%

         \[\leadsto \tan \left(y + z\right) + \frac{1}{\frac{x + \tan a}{x \cdot x - \color{blue}{{\tan a}^{2}}}} \]

   5. Applied egg-rr 74.7%

      \[\leadsto \tan \left(y + z\right) + \color{blue}{\frac{1}{\frac{x + \tan a}{x \cdot x - {\tan a}^{2}}}} \]

   6. Taylor expanded in x around inf 50.0%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + z \leq 5 \cdot 10^{-8}:\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\tan \left(y + z\right) + \frac{1}{\frac{1}{x}}\\ \end{array} \]

Alternative 6: 79.6% 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]

Derivation

1. Initial program 78.8%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]

2. Final simplification 78.8%

   \[\leadsto x + \left(\tan \left(y + z\right) - \tan a\right) \]

Alternative 7: 59.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + z \leq -10000000 \lor \neg \left(y + z \leq 5 \cdot 10^{-8}\right):\\ \;\;\;\;\tan \left(y + z\right) + \frac{1}{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= (+ y z) -10000000.0) (not (<= (+ y z) 5e-8)))
   (+ (tan (+ y z)) (/ 1.0 (/ 1.0 x)))
   (+ x (- y (tan a)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (((y + z) <= -10000000.0) || !((y + z) <= 5e-8)) {
		tmp = tan((y + z)) + (1.0 / (1.0 / x));
	} else {
		tmp = x + (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 (((y + z) <= (-10000000.0d0)) .or. (.not. ((y + z) <= 5d-8))) then
        tmp = tan((y + z)) + (1.0d0 / (1.0d0 / x))
    else
        tmp = x + (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 (((y + z) <= -10000000.0) || !((y + z) <= 5e-8)) {
		tmp = Math.tan((y + z)) + (1.0 / (1.0 / x));
	} else {
		tmp = x + (y - Math.tan(a));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if ((y + z) <= -10000000.0) or not ((y + z) <= 5e-8):
		tmp = math.tan((y + z)) + (1.0 / (1.0 / x))
	else:
		tmp = x + (y - math.tan(a))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((Float64(y + z) <= -10000000.0) || !(Float64(y + z) <= 5e-8))
		tmp = Float64(tan(Float64(y + z)) + Float64(1.0 / Float64(1.0 / x)));
	else
		tmp = Float64(x + Float64(y - tan(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (((y + z) <= -10000000.0) || ~(((y + z) <= 5e-8)))
		tmp = tan((y + z)) + (1.0 / (1.0 / x));
	else
		tmp = x + (y - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[N[(y + z), $MachinePrecision], -10000000.0], N[Not[LessEqual[N[(y + z), $MachinePrecision], 5e-8]], $MachinePrecision]], N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] + N[(1.0 / N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 y z) < -1e7 or 4.9999999999999998e-8 < (+.f64 y z)

   1. Initial program 71.4%

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

      1. associate-+r- 71.3%

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

      2. +-commutative 71.3%

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

      3. associate--l+ 71.3%

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

   3. Simplified 71.3%

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

      1. flip-- 71.2%

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

      2. clear-num 71.1%

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

      3. pow2 71.1%

         \[\leadsto \tan \left(y + z\right) + \frac{1}{\frac{x + \tan a}{x \cdot x - \color{blue}{{\tan a}^{2}}}} \]

   5. Applied egg-rr 71.1%

      \[\leadsto \tan \left(y + z\right) + \color{blue}{\frac{1}{\frac{x + \tan a}{x \cdot x - {\tan a}^{2}}}} \]

   6. Taylor expanded in x around inf 45.5%

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

   if -1e7 < (+.f64 y z) < 4.9999999999999998e-8

   1. Initial program 99.9%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]

   2. Taylor expanded in z around 0 99.0%

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

   3. Taylor expanded in y around 0 99.0%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + z \leq -10000000 \lor \neg \left(y + z \leq 5 \cdot 10^{-8}\right):\\ \;\;\;\;\tan \left(y + z\right) + \frac{1}{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \tan a\right)\\ \end{array} \]

Alternative 8: 55.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+24} \lor \neg \left(a \leq 0.24\right):\\ \;\;\;\;x + \left(y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\tan \left(y + z\right) + \left(x - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -8.8e+24) (not (<= a 0.24)))
   (+ x (- y (tan a)))
   (+ (tan (+ y z)) (- x a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -8.8e+24) || !(a <= 0.24)) {
		tmp = x + (y - tan(a));
	} else {
		tmp = tan((y + z)) + (x - 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 <= (-8.8d+24)) .or. (.not. (a <= 0.24d0))) then
        tmp = x + (y - tan(a))
    else
        tmp = tan((y + z)) + (x - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -8.8e+24) || !(a <= 0.24)) {
		tmp = x + (y - Math.tan(a));
	} else {
		tmp = Math.tan((y + z)) + (x - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (a <= -8.8e+24) or not (a <= 0.24):
		tmp = x + (y - math.tan(a))
	else:
		tmp = math.tan((y + z)) + (x - a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -8.8e+24) || !(a <= 0.24))
		tmp = Float64(x + Float64(y - tan(a)));
	else
		tmp = Float64(tan(Float64(y + z)) + Float64(x - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -8.8e+24) || ~((a <= 0.24)))
		tmp = x + (y - tan(a));
	else
		tmp = tan((y + z)) + (x - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[a, -8.8e+24], N[Not[LessEqual[a, 0.24]], $MachinePrecision]], N[(x + N[(y - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] + N[(x - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.80000000000000007e24 or 0.23999999999999999 < a

   1. Initial program 81.8%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]

   2. Taylor expanded in z around 0 69.8%

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

   3. Taylor expanded in y around 0 35.0%

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

   if -8.80000000000000007e24 < a < 0.23999999999999999

   1. Initial program 75.9%

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

      1. associate-+r- 75.8%

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

      2. +-commutative 75.8%

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

      3. associate--l+ 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in a around 0 72.5%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+24} \lor \neg \left(a \leq 0.24\right):\\ \;\;\;\;x + \left(y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\tan \left(y + z\right) + \left(x - a\right)\\ \end{array} \]

Alternative 9: 40.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -18000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-54}:\\ \;\;\;\;x + \left(y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= y -18000000.0) x (if (<= y 8.2e-54) (+ x (- y (tan a))) x)))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -18000000.0) {
		tmp = x;
	} else if (y <= 8.2e-54) {
		tmp = x + (y - tan(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 (y <= (-18000000.0d0)) then
        tmp = x
    else if (y <= 8.2d-54) then
        tmp = x + (y - tan(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 (y <= -18000000.0) {
		tmp = x;
	} else if (y <= 8.2e-54) {
		tmp = x + (y - Math.tan(a));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if y <= -18000000.0:
		tmp = x
	elif y <= 8.2e-54:
		tmp = x + (y - math.tan(a))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (y <= -18000000.0)
		tmp = x;
	elseif (y <= 8.2e-54)
		tmp = Float64(x + Float64(y - tan(a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (y <= -18000000.0)
		tmp = x;
	elseif (y <= 8.2e-54)
		tmp = x + (y - tan(a));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[y, -18000000.0], x, If[LessEqual[y, 8.2e-54], N[(x + N[(y - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e7 or 8.2000000000000001e-54 < y

   1. Initial program 63.6%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]

   2. Taylor expanded in x around inf 23.6%

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

   if -1.8e7 < y < 8.2000000000000001e-54

   1. Initial program 99.1%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]

   2. Taylor expanded in z around 0 67.2%

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

   3. Taylor expanded in y around 0 66.4%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -18000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-54}:\\ \;\;\;\;x + \left(y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 31.5% 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 78.8%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]

2. Taylor expanded in x around inf 31.6%

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

3. Final simplification 31.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023275 
(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))))