tan-example (used to crash)

Percentage Accurate: 78.9% → 99.7%

Time: 25.6s

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: 78.9% 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

\[\begin{array}{l} \\ x + \left(\frac{\tan y + \tan z}{1 - \sqrt[3]{{\left(\tan y \cdot \tan z\right)}^{3}}} - \tan a\right) \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (+
  x
  (-
   (/ (+ (tan y) (tan z)) (- 1.0 (cbrt (pow (* (tan y) (tan z)) 3.0))))
   (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + (((tan(y) + tan(z)) / (1.0 - cbrt(pow((tan(y) * tan(z)), 3.0)))) - tan(a));
}

Java

public static double code(double x, double y, double z, double a) {
	return x + (((Math.tan(y) + Math.tan(z)) / (1.0 - Math.cbrt(Math.pow((Math.tan(y) * Math.tan(z)), 3.0)))) - Math.tan(a));
}

Julia

function code(x, y, z, a)
	return Float64(x + Float64(Float64(Float64(tan(y) + tan(z)) / Float64(1.0 - cbrt((Float64(tan(y) * tan(z)) ^ 3.0)))) - 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[Power[N[Power[N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.6%

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

   1. tan-sum 99.8%

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

   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/ 99.8%

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

   2. *-rgt-identity 99.8%

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

5. Simplified 99.8%

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

   1. add-cbrt-cube 99.8%

      \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \color{blue}{\sqrt[3]{\left(\left(\tan y \cdot \tan z\right) \cdot \left(\tan y \cdot \tan z\right)\right) \cdot \left(\tan y \cdot \tan z\right)}}} - \tan a\right) \]

7. Applied egg-rr 99.8%

   \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \color{blue}{\sqrt[3]{\left(\left(\tan y \cdot \tan z\right) \cdot \left(\tan y \cdot \tan z\right)\right) \cdot \left(\tan y \cdot \tan z\right)}}} - \tan a\right) \]
8. Step-by-step derivation

   1. associate-*l* 99.8%

      \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \sqrt[3]{\color{blue}{\left(\tan y \cdot \tan z\right) \cdot \left(\left(\tan y \cdot \tan z\right) \cdot \left(\tan y \cdot \tan z\right)\right)}}} - \tan a\right) \]

   2. cube-unmult 99.8%

      \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \sqrt[3]{\color{blue}{{\left(\tan y \cdot \tan z\right)}^{3}}}} - \tan a\right) \]

9. Simplified 99.8%

   \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \color{blue}{\sqrt[3]{{\left(\tan y \cdot \tan z\right)}^{3}}}} - \tan a\right) \]

10. Final simplification 99.8%

    \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \sqrt[3]{{\left(\tan y \cdot \tan z\right)}^{3}}} - \tan a\right) \]

Alternative 2: 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 80.6%

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

   1. tan-sum 99.8%

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

   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/ 99.8%

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

   2. *-rgt-identity 99.8%

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

5. Simplified 99.8%

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

6. Final simplification 99.8%

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

Alternative 3: 89.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{-12} \lor \neg \left(a \leq 4.5 \cdot 10^{-13}\right):\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -1.22e-12) (not (<= a 4.5e-13)))
   (+ x (- (tan (+ y z)) (tan a)))
   (+ x (- (/ (+ (tan y) (tan z)) (- 1.0 (* (tan y) (tan z)))) a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -1.22e-12) || !(a <= 4.5e-13)) {
		tmp = x + (tan((y + z)) - tan(a));
	} else {
		tmp = x + (((tan(y) + tan(z)) / (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 ((a <= (-1.22d-12)) .or. (.not. (a <= 4.5d-13))) then
        tmp = x + (tan((y + z)) - tan(a))
    else
        tmp = x + (((tan(y) + tan(z)) / (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 ((a <= -1.22e-12) || !(a <= 4.5e-13)) {
		tmp = x + (Math.tan((y + z)) - Math.tan(a));
	} else {
		tmp = x + (((Math.tan(y) + Math.tan(z)) / (1.0 - (Math.tan(y) * Math.tan(z)))) - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (a <= -1.22e-12) or not (a <= 4.5e-13):
		tmp = x + (math.tan((y + z)) - math.tan(a))
	else:
		tmp = x + (((math.tan(y) + math.tan(z)) / (1.0 - (math.tan(y) * math.tan(z)))) - a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -1.22e-12) || !(a <= 4.5e-13))
		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(tan(y) * tan(z)))) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -1.22e-12) || ~((a <= 4.5e-13)))
		tmp = x + (tan((y + z)) - tan(a));
	else
		tmp = x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[a, -1.22e-12], N[Not[LessEqual[a, 4.5e-13]], $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[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.2200000000000001e-12 or 4.5e-13 < a

   1. Initial program 83.0%

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

   if -1.2200000000000001e-12 < a < 4.5e-13

   1. Initial program 77.8%

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

   2. Taylor expanded in a around 0 77.8%

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

      1. tan-sum 99.8%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

      1. associate-*r/ 99.8%

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

      2. *-rgt-identity 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{-12} \lor \neg \left(a \leq 4.5 \cdot 10^{-13}\right):\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - a\right)\\ \end{array} \]

Alternative 4: 69.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -1 \cdot 10^{-31}:\\ \;\;\;\;\left(x + \tan z\right) - \tan a\\ \mathbf{elif}\;\tan a \leq 0.01:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;\tan z + \left(x - \tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= (tan a) -1e-31)
   (- (+ x (tan z)) (tan a))
   (if (<= (tan a) 0.01) (+ x (- (tan (+ y z)) a)) (+ (tan z) (- x (tan a))))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (tan(a) <= -1e-31) {
		tmp = (x + tan(z)) - tan(a);
	} else if (tan(a) <= 0.01) {
		tmp = x + (tan((y + z)) - a);
	} else {
		tmp = tan(z) + (x - 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 (tan(a) <= (-1d-31)) then
        tmp = (x + tan(z)) - tan(a)
    else if (tan(a) <= 0.01d0) then
        tmp = x + (tan((y + z)) - a)
    else
        tmp = tan(z) + (x - tan(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) <= -1e-31) {
		tmp = (x + Math.tan(z)) - Math.tan(a);
	} else if (Math.tan(a) <= 0.01) {
		tmp = x + (Math.tan((y + z)) - a);
	} else {
		tmp = Math.tan(z) + (x - Math.tan(a));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if math.tan(a) <= -1e-31:
		tmp = (x + math.tan(z)) - math.tan(a)
	elif math.tan(a) <= 0.01:
		tmp = x + (math.tan((y + z)) - a)
	else:
		tmp = math.tan(z) + (x - math.tan(a))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (tan(a) <= -1e-31)
		tmp = Float64(Float64(x + tan(z)) - tan(a));
	elseif (tan(a) <= 0.01)
		tmp = Float64(x + Float64(tan(Float64(y + z)) - a));
	else
		tmp = Float64(tan(z) + Float64(x - tan(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (tan(a) <= -1e-31)
		tmp = (x + tan(z)) - tan(a);
	elseif (tan(a) <= 0.01)
		tmp = x + (tan((y + z)) - a);
	else
		tmp = tan(z) + (x - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[N[Tan[a], $MachinePrecision], -1e-31], N[(N[(x + N[Tan[z], $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Tan[a], $MachinePrecision], 0.01], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(N[Tan[z], $MachinePrecision] + N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (tan.f64 a) < -1e-31

   1. Initial program 80.9%

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

   2. Taylor expanded in y around 0 62.5%

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

      1. tan-quot 62.6%

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

      2. sub-neg 62.6%

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

      3. tan-quot 62.6%

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

   4. Applied egg-rr 62.6%

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

   if -1e-31 < (tan.f64 a) < 0.0100000000000000002

   1. Initial program 78.3%

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

   2. Taylor expanded in a around 0 78.0%

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

   if 0.0100000000000000002 < (tan.f64 a)

   1. Initial program 83.8%

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

   2. Taylor expanded in y around 0 63.5%

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

      1. tan-quot 63.5%

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

      2. tan-quot 63.6%

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

      3. associate--l+ 63.6%

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

   4. Applied egg-rr 63.6%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -1 \cdot 10^{-31}:\\ \;\;\;\;\left(x + \tan z\right) - \tan a\\ \mathbf{elif}\;\tan a \leq 0.01:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;\tan z + \left(x - \tan a\right)\\ \end{array} \]

Alternative 5: 59.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + z \leq -5 \cdot 10^{-11}:\\ \;\;\;\;x + \left(\tan a + \tan \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\tan z + \left(x - \tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= (+ y z) -5e-11)
   (+ x (+ (tan a) (tan (+ y z))))
   (+ (tan z) (- x (tan a)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -5e-11) {
		tmp = x + (tan(a) + tan((y + z)));
	} else {
		tmp = tan(z) + (x - 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) <= (-5d-11)) then
        tmp = x + (tan(a) + tan((y + z)))
    else
        tmp = tan(z) + (x - 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) <= -5e-11) {
		tmp = x + (Math.tan(a) + Math.tan((y + z)));
	} else {
		tmp = Math.tan(z) + (x - Math.tan(a));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (y + z) <= -5e-11:
		tmp = x + (math.tan(a) + math.tan((y + z)))
	else:
		tmp = math.tan(z) + (x - math.tan(a))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (Float64(y + z) <= -5e-11)
		tmp = Float64(x + Float64(tan(a) + tan(Float64(y + z))));
	else
		tmp = Float64(tan(z) + Float64(x - tan(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((y + z) <= -5e-11)
		tmp = x + (tan(a) + tan((y + z)));
	else
		tmp = tan(z) + (x - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[N[(y + z), $MachinePrecision], -5e-11], N[(x + N[(N[Tan[a], $MachinePrecision] + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Tan[z], $MachinePrecision] + N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 y z) < -5.00000000000000018e-11

   1. Initial program 73.6%

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

      1. sub-neg 73.6%

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

   3. Applied egg-rr 73.6%

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

      1. +-commutative 73.6%

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

      2. rem-square-sqrt 29.4%

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

      3. fabs-sqr 29.4%

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

      4. rem-square-sqrt 54.0%

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

      5. fabs-neg 54.0%

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

      6. rem-square-sqrt 24.6%

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

      7. fabs-sqr 24.6%

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

      8. rem-square-sqrt 45.6%

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

   5. Simplified 45.6%

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

   if -5.00000000000000018e-11 < (+.f64 y z)

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0 71.0%

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

      1. tan-quot 71.0%

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

      2. tan-quot 71.0%

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

      3. associate--l+ 71.0%

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

   4. Applied egg-rr 71.0%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + z \leq -5 \cdot 10^{-11}:\\ \;\;\;\;x + \left(\tan a + \tan \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\tan z + \left(x - \tan a\right)\\ \end{array} \]

Alternative 6: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-31} \lor \neg \left(a \leq 0.0054\right):\\ \;\;\;\;\tan z + \left(x - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -1.1e-31) (not (<= a 0.0054)))
   (+ (tan z) (- x (tan a)))
   (+ x (- (tan (+ y z)) a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -1.1e-31) || !(a <= 0.0054)) {
		tmp = tan(z) + (x - tan(a));
	} else {
		tmp = x + (tan((y + 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 ((a <= (-1.1d-31)) .or. (.not. (a <= 0.0054d0))) then
        tmp = tan(z) + (x - tan(a))
    else
        tmp = x + (tan((y + z)) - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -1.1e-31) || !(a <= 0.0054)) {
		tmp = Math.tan(z) + (x - Math.tan(a));
	} else {
		tmp = x + (Math.tan((y + z)) - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (a <= -1.1e-31) or not (a <= 0.0054):
		tmp = math.tan(z) + (x - math.tan(a))
	else:
		tmp = x + (math.tan((y + z)) - a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -1.1e-31) || !(a <= 0.0054))
		tmp = Float64(tan(z) + Float64(x - tan(a)));
	else
		tmp = Float64(x + Float64(tan(Float64(y + z)) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -1.1e-31) || ~((a <= 0.0054)))
		tmp = tan(z) + (x - tan(a));
	else
		tmp = x + (tan((y + z)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[a, -1.1e-31], N[Not[LessEqual[a, 0.0054]], $MachinePrecision]], N[(N[Tan[z], $MachinePrecision] + N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.10000000000000005e-31 or 0.0054000000000000003 < a

   1. Initial program 82.5%

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

   2. Taylor expanded in y around 0 63.1%

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

      1. tan-quot 63.1%

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

      2. tan-quot 63.1%

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

      3. associate--l+ 63.1%

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

   4. Applied egg-rr 63.1%

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

   if -1.10000000000000005e-31 < a < 0.0054000000000000003

   1. Initial program 78.3%

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

   2. Taylor expanded in a around 0 78.0%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-31} \lor \neg \left(a \leq 0.0054\right):\\ \;\;\;\;\tan z + \left(x - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \]

Alternative 7: 78.9% 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 80.6%

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

2. Final simplification 80.6%

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

Alternative 8: 49.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05:\\ \;\;\;\;x + -1\\ \mathbf{elif}\;a \leq 3.1:\\ \;\;\;\;x + \left(a + \tan \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= a -1.05) (+ x -1.0) (if (<= a 3.1) (+ x (+ a (tan (+ y z)))) x)))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.05) {
		tmp = x + -1.0;
	} else if (a <= 3.1) {
		tmp = x + (a + tan((y + z)));
	} 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 <= (-1.05d0)) then
        tmp = x + (-1.0d0)
    else if (a <= 3.1d0) then
        tmp = x + (a + tan((y + z)))
    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 <= -1.05) {
		tmp = x + -1.0;
	} else if (a <= 3.1) {
		tmp = x + (a + Math.tan((y + z)));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if a <= -1.05:
		tmp = x + -1.0
	elif a <= 3.1:
		tmp = x + (a + math.tan((y + z)))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (a <= -1.05)
		tmp = Float64(x + -1.0);
	elseif (a <= 3.1)
		tmp = Float64(x + Float64(a + tan(Float64(y + z))));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -1.05)
		tmp = x + -1.0;
	elseif (a <= 3.1)
		tmp = x + (a + tan((y + z)));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[a, -1.05], N[(x + -1.0), $MachinePrecision], If[LessEqual[a, 3.1], N[(x + N[(a + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if a < -1.05000000000000004

   1. Initial program 79.9%

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

   2. Taylor expanded in a around 0 4.9%

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

      1. expm1-log1p-u 4.9%

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

      2. expm1-udef 4.9%

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

   4. Applied egg-rr 4.9%

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

   5. Taylor expanded in x around inf 21.4%

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

      1. sub-neg 21.4%

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

      2. unpow-1 21.4%

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

      3. remove-double-div 21.4%

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

      4. metadata-eval 21.4%

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

   7. Simplified 21.4%

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

   if -1.05000000000000004 < a < 3.10000000000000009

   1. Initial program 78.7%

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

      1. sub-neg 78.7%

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

   3. Applied egg-rr 78.7%

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

      1. +-commutative 78.7%

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

      2. rem-square-sqrt 42.9%

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

      3. fabs-sqr 42.9%

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

      4. rem-square-sqrt 78.0%

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

      5. fabs-neg 78.0%

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

      6. rem-square-sqrt 35.1%

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

      7. fabs-sqr 35.1%

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

      8. rem-square-sqrt 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in a around 0 77.0%

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

   if 3.10000000000000009 < a

   1. Initial program 84.5%

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

   2. Taylor expanded in x around inf 21.1%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05:\\ \;\;\;\;x + -1\\ \mathbf{elif}\;a \leq 3.1:\\ \;\;\;\;x + \left(a + \tan \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 50.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55:\\ \;\;\;\;x + -1\\ \mathbf{elif}\;a \leq 4.7:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= a -1.55) (+ x -1.0) (if (<= a 4.7) (+ x (- (tan (+ y z)) a)) x)))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.55) {
		tmp = x + -1.0;
	} else if (a <= 4.7) {
		tmp = x + (tan((y + z)) - 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 <= (-1.55d0)) then
        tmp = x + (-1.0d0)
    else if (a <= 4.7d0) then
        tmp = x + (tan((y + z)) - 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 <= -1.55) {
		tmp = x + -1.0;
	} else if (a <= 4.7) {
		tmp = x + (Math.tan((y + z)) - a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if a <= -1.55:
		tmp = x + -1.0
	elif a <= 4.7:
		tmp = x + (math.tan((y + z)) - a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (a <= -1.55)
		tmp = Float64(x + -1.0);
	elseif (a <= 4.7)
		tmp = Float64(x + Float64(tan(Float64(y + z)) - a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -1.55)
		tmp = x + -1.0;
	elseif (a <= 4.7)
		tmp = x + (tan((y + z)) - a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[a, -1.55], N[(x + -1.0), $MachinePrecision], If[LessEqual[a, 4.7], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if a < -1.55000000000000004

   1. Initial program 79.9%

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

   2. Taylor expanded in a around 0 4.9%

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

      1. expm1-log1p-u 4.9%

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

      2. expm1-udef 4.9%

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

   4. Applied egg-rr 4.9%

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

   5. Taylor expanded in x around inf 21.4%

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

      1. sub-neg 21.4%

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

      2. unpow-1 21.4%

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

      3. remove-double-div 21.4%

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

      4. metadata-eval 21.4%

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

   7. Simplified 21.4%

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

   if -1.55000000000000004 < a < 4.70000000000000018

   1. Initial program 78.7%

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

   2. Taylor expanded in a around 0 77.7%

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

   if 4.70000000000000018 < a

   1. Initial program 84.5%

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

   2. Taylor expanded in x around inf 21.1%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55:\\ \;\;\;\;x + -1\\ \mathbf{elif}\;a \leq 4.7:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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 80.6%

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

2. Taylor expanded in x around inf 32.6%

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

3. Final simplification 32.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023199 
(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))))