tan-example (used to crash)

Percentage Accurate: 79.7% → 99.7%

Time: 39.9s

Alternatives: 13

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 78.4%

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

   1. +-commutative 78.4%

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

   2. sub-neg 78.4%

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

   3. associate-+l+ 78.3%

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

   4. tan-sum 99.7%

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

   5. div-inv 99.7%

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

   6. fma-define 99.7%

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

   7. neg-mul-1 99.7%

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

   8. fma-define 99.7%

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

4. Applied egg-rr 99.7%

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

   1. fma-undefine 99.7%

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

   2. fma-undefine 99.7%

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

   3. neg-mul-1 99.7%

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

   4. associate-+r+ 99.7%

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

   5. unsub-neg 99.7%

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

   6. associate-*r/ 99.7%

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

   7. *-rgt-identity 99.7%

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

6. Simplified 99.7%

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

   1. expm1-log1p-u 94.3%

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

   2. expm1-undefine 94.3%

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

   3. log1p-undefine 94.3%

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

   4. add-exp-log 99.7%

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

8. Applied egg-rr 99.7%

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

   1. associate--l+ 99.7%

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

   2. fma-neg 99.7%

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

   3. metadata-eval 99.7%

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

10. Simplified 99.7%

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

    1. sub-neg 99.7%

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

    2. associate--r+ 99.7%

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

    3. metadata-eval 99.7%

       \[\leadsto \left(\frac{\tan y + \tan z}{\color{blue}{0} - \mathsf{fma}\left(\tan y, \tan z, -1\right)} + \left(-\tan a\right)\right) + x \]

12. Applied egg-rr 99.7%

    \[\leadsto \color{blue}{\left(\frac{\tan y + \tan z}{0 - \mathsf{fma}\left(\tan y, \tan z, -1\right)} + \left(-\tan a\right)\right)} + x \]
13. Step-by-step derivation

    1. sub-neg 99.7%

       \[\leadsto \color{blue}{\left(\frac{\tan y + \tan z}{0 - \mathsf{fma}\left(\tan y, \tan z, -1\right)} - \tan a\right)} + x \]

    2. sub0-neg 99.7%

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

14. Simplified 99.7%

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

15. Final simplification 99.7%

    \[\leadsto x - \left(\tan a + \frac{\tan y + \tan z}{\mathsf{fma}\left(\tan y, \tan z, -1\right)}\right) \]
16. Add Preprocessing

Alternative 2: 89.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan y + \tan z\\ \mathbf{if}\;\tan a \leq -0.02 \lor \neg \left(\tan a \leq 10^{-6}\right):\\ \;\;\;\;x + \left(t\_0 - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{t\_0}{1 - \tan y \cdot \tan z} - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (+ (tan y) (tan z))))
   (if (or (<= (tan a) -0.02) (not (<= (tan a) 1e-6)))
     (+ x (- t_0 (tan a)))
     (+ x (- (/ t_0 (- 1.0 (* (tan y) (tan z)))) a)))))

C

double code(double x, double y, double z, double a) {
	double t_0 = tan(y) + tan(z);
	double tmp;
	if ((tan(a) <= -0.02) || !(tan(a) <= 1e-6)) {
		tmp = x + (t_0 - tan(a));
	} else {
		tmp = x + ((t_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) :: t_0
    real(8) :: tmp
    t_0 = tan(y) + tan(z)
    if ((tan(a) <= (-0.02d0)) .or. (.not. (tan(a) <= 1d-6))) then
        tmp = x + (t_0 - tan(a))
    else
        tmp = x + ((t_0 / (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 t_0 = Math.tan(y) + Math.tan(z);
	double tmp;
	if ((Math.tan(a) <= -0.02) || !(Math.tan(a) <= 1e-6)) {
		tmp = x + (t_0 - Math.tan(a));
	} else {
		tmp = x + ((t_0 / (1.0 - (Math.tan(y) * Math.tan(z)))) - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	t_0 = math.tan(y) + math.tan(z)
	tmp = 0
	if (math.tan(a) <= -0.02) or not (math.tan(a) <= 1e-6):
		tmp = x + (t_0 - math.tan(a))
	else:
		tmp = x + ((t_0 / (1.0 - (math.tan(y) * math.tan(z)))) - a)
	return tmp

Julia

function code(x, y, z, a)
	t_0 = Float64(tan(y) + tan(z))
	tmp = 0.0
	if ((tan(a) <= -0.02) || !(tan(a) <= 1e-6))
		tmp = Float64(x + Float64(t_0 - tan(a)));
	else
		tmp = Float64(x + Float64(Float64(t_0 / Float64(1.0 - Float64(tan(y) * tan(z)))) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	t_0 = tan(y) + tan(z);
	tmp = 0.0;
	if ((tan(a) <= -0.02) || ~((tan(a) <= 1e-6)))
		tmp = x + (t_0 - tan(a));
	else
		tmp = x + ((t_0 / (1.0 - (tan(y) * tan(z)))) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := Block[{t$95$0 = N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[Tan[a], $MachinePrecision], -0.02], N[Not[LessEqual[N[Tan[a], $MachinePrecision], 1e-6]], $MachinePrecision]], N[(x + N[(t$95$0 - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t$95$0 / 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 (tan.f64 a) < -0.0200000000000000004 or 9.99999999999999955e-7 < (tan.f64 a)

   1. Initial program 75.9%

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

      1. +-commutative 75.9%

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

      2. sub-neg 75.9%

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

      3. associate-+l+ 75.8%

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

      4. tan-sum 99.5%

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

      5. div-inv 99.5%

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

      6. fma-define 99.5%

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

      7. neg-mul-1 99.5%

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

      8. fma-define 99.5%

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

   4. Applied egg-rr 99.5%

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

      1. fma-undefine 99.5%

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

      2. fma-undefine 99.5%

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

      3. neg-mul-1 99.5%

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

      4. associate-+r+ 99.6%

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

      5. unsub-neg 99.6%

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

      6. associate-*r/ 99.7%

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

      7. *-rgt-identity 99.7%

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

   6. Simplified 99.7%

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

      1. expm1-log1p-u 93.3%

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

      2. expm1-undefine 93.3%

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

      3. log1p-undefine 93.3%

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

      4. add-exp-log 99.7%

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

   8. Applied egg-rr 99.7%

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

      1. associate--l+ 99.7%

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

      2. fma-neg 99.7%

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

      3. metadata-eval 99.7%

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

   10. Simplified 99.7%

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

   11. Taylor expanded in y around 0 76.7%

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

   if -0.0200000000000000004 < (tan.f64 a) < 9.99999999999999955e-7

   1. Initial program 80.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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 99.8%

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

      2. div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. associate-*r/ 99.8%

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

      2. *-rgt-identity 99.8%

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

   7. 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 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.02 \lor \neg \left(\tan a \leq 10^{-6}\right):\\ \;\;\;\;x + \left(\left(\tan y + \tan z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - a\right)\\ \end{array} \]
5. 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 78.4%

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

   1. +-commutative 78.4%

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

   2. sub-neg 78.4%

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

   3. associate-+l+ 78.3%

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

   4. tan-sum 99.7%

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

   5. div-inv 99.7%

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

   6. fma-define 99.7%

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

   7. neg-mul-1 99.7%

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

   8. fma-define 99.7%

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

4. Applied egg-rr 99.7%

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

   1. fma-undefine 99.7%

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

   2. fma-undefine 99.7%

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

   3. neg-mul-1 99.7%

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

   4. associate-+r+ 99.7%

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

   5. unsub-neg 99.7%

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

   6. associate-*r/ 99.7%

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

   7. *-rgt-identity 99.7%

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

6. Simplified 99.7%

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

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: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -0.02 \lor \neg \left(\tan a \leq 10^{-6}\right):\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= (tan a) -0.02) (not (<= (tan a) 1e-6)))
   (+ x (- (tan y) (tan a)))
   (+ x (- (tan (+ y z)) a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((tan(a) <= -0.02) || !(tan(a) <= 1e-6)) {
		tmp = x + (tan(y) - 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 ((tan(a) <= (-0.02d0)) .or. (.not. (tan(a) <= 1d-6))) then
        tmp = x + (tan(y) - 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 ((Math.tan(a) <= -0.02) || !(Math.tan(a) <= 1e-6)) {
		tmp = x + (Math.tan(y) - Math.tan(a));
	} else {
		tmp = x + (Math.tan((y + z)) - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (math.tan(a) <= -0.02) or not (math.tan(a) <= 1e-6):
		tmp = x + (math.tan(y) - math.tan(a))
	else:
		tmp = x + (math.tan((y + z)) - a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((tan(a) <= -0.02) || !(tan(a) <= 1e-6))
		tmp = Float64(x + Float64(tan(y) - 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 ((tan(a) <= -0.02) || ~((tan(a) <= 1e-6)))
		tmp = x + (tan(y) - tan(a));
	else
		tmp = x + (tan((y + z)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[N[Tan[a], $MachinePrecision], -0.02], N[Not[LessEqual[N[Tan[a], $MachinePrecision], 1e-6]], $MachinePrecision]], N[(x + N[(N[Tan[y], $MachinePrecision] - 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 (tan.f64 a) < -0.0200000000000000004 or 9.99999999999999955e-7 < (tan.f64 a)

   1. Initial program 75.9%

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

   3. Taylor expanded in y around inf 57.8%

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

   if -0.0200000000000000004 < (tan.f64 a) < 9.99999999999999955e-7

   1. Initial program 80.7%

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

   3. Taylor expanded in a around 0 80.7%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.02 \lor \neg \left(\tan a \leq 10^{-6}\right):\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.1% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.4%

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

   1. +-commutative 78.4%

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

   2. sub-neg 78.4%

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

   3. associate-+l+ 78.3%

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

   4. tan-sum 99.7%

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

   5. div-inv 99.7%

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

   6. fma-define 99.7%

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

   7. neg-mul-1 99.7%

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

   8. fma-define 99.7%

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

4. Applied egg-rr 99.7%

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

   1. fma-undefine 99.7%

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

   2. fma-undefine 99.7%

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

   3. neg-mul-1 99.7%

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

   4. associate-+r+ 99.7%

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

   5. unsub-neg 99.7%

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

   6. associate-*r/ 99.7%

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

   7. *-rgt-identity 99.7%

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

6. Simplified 99.7%

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

   1. expm1-log1p-u 94.3%

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

   2. expm1-undefine 94.3%

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

   3. log1p-undefine 94.3%

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

   4. add-exp-log 99.7%

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

8. Applied egg-rr 99.7%

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

   1. associate--l+ 99.7%

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

   2. fma-neg 99.7%

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

   3. metadata-eval 99.7%

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

10. Simplified 99.7%

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

11. Taylor expanded in y around 0 78.6%

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

12. Final simplification 78.6%

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

Alternative 6: 60.3% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= (+ y z) -1e-13) (+ x (- (tan y) (tan a))) (+ x (- (tan z) (tan a)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -1e-13) {
		tmp = x + (tan(y) - tan(a));
	} else {
		tmp = x + (tan(z) - 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) <= (-1d-13)) then
        tmp = x + (tan(y) - tan(a))
    else
        tmp = x + (tan(z) - 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) <= -1e-13) {
		tmp = x + (Math.tan(y) - Math.tan(a));
	} else {
		tmp = x + (Math.tan(z) - Math.tan(a));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (y + z) <= -1e-13:
		tmp = x + (math.tan(y) - math.tan(a))
	else:
		tmp = x + (math.tan(z) - math.tan(a))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (Float64(y + z) <= -1e-13)
		tmp = Float64(x + Float64(tan(y) - tan(a)));
	else
		tmp = Float64(x + Float64(tan(z) - tan(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((y + z) <= -1e-13)
		tmp = x + (tan(y) - tan(a));
	else
		tmp = x + (tan(z) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[N[(y + z), $MachinePrecision], -1e-13], N[(x + N[(N[Tan[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[z], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 y z) < -1e-13

   1. Initial program 72.6%

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

   3. Taylor expanded in y around inf 49.5%

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

   if -1e-13 < (+.f64 y z)

   1. Initial program 82.4%

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

   3. Taylor expanded in y around 0 66.4%

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

Alternative 7: 50.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.55:\\ \;\;\;\;\sqrt[3]{{x}^{3}}\\ \mathbf{elif}\;a \leq 0.9:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= a -1.55)
   (cbrt (pow x 3.0))
   (if (<= a 0.9) (+ x (- (tan (+ y z)) a)) (* a (/ x a)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.55) {
		tmp = cbrt(pow(x, 3.0));
	} else if (a <= 0.9) {
		tmp = x + (tan((y + z)) - a);
	} else {
		tmp = a * (x / a);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.55) {
		tmp = Math.cbrt(Math.pow(x, 3.0));
	} else if (a <= 0.9) {
		tmp = x + (Math.tan((y + z)) - a);
	} else {
		tmp = a * (x / a);
	}
	return tmp;
}

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (a <= -1.55)
		tmp = cbrt((x ^ 3.0));
	elseif (a <= 0.9)
		tmp = Float64(x + Float64(tan(Float64(y + z)) - a));
	else
		tmp = Float64(a * Float64(x / a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[a, -1.55], N[Power[N[Power[x, 3.0], $MachinePrecision], 1/3], $MachinePrecision], If[LessEqual[a, 0.9], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.55000000000000004

   1. Initial program 76.3%

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

      1. add-cbrt-cube 75.7%

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

      2. pow3 75.8%

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

      3. +-commutative 75.8%

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

      4. associate-+l- 75.7%

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

   4. Applied egg-rr 75.7%

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

   5. Taylor expanded in x around inf 24.3%

      \[\leadsto \sqrt[3]{\color{blue}{{x}^{3}}} \]

   if -1.55000000000000004 < a < 0.900000000000000022

   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 80.4%

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

   if 0.900000000000000022 < a

   1. Initial program 75.1%

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

   3. Taylor expanded in a around 0 1.4%

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

   4. Taylor expanded in a around inf 1.4%

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

   5. Taylor expanded in x around inf 21.5%

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

Alternative 8: 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]

Derivation

1. Initial program 78.4%

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

Alternative 9: 50.5% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= a -1.55)
   (exp (log x))
   (if (<= a 1.55) (+ x (- (tan (+ y z)) a)) (* a (/ x a)))))

C

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -1.55)
		tmp = exp(log(x));
	elseif (a <= 1.55)
		tmp = x + (tan((y + z)) - a);
	else
		tmp = a * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if a < -1.55000000000000004

   1. Initial program 76.3%

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

   3. Taylor expanded in a around inf 76.3%

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

      1. +-commutative 76.3%

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

      2. tan-quot 76.3%

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

      3. associate-+l- 76.1%

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

      4. rem-cbrt-cube 75.7%

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

      5. pow1/3 71.8%

         \[\leadsto \color{blue}{{\left({\left(\tan \left(y + z\right) - \left(\tan a - x\right)\right)}^{3}\right)}^{0.3333333333333333}} \]

      6. pow-to-exp 71.9%

         \[\leadsto \color{blue}{e^{\log \left({\left(\tan \left(y + z\right) - \left(\tan a - x\right)\right)}^{3}\right) \cdot 0.3333333333333333}} \]

   5. Applied egg-rr 71.9%

      \[\leadsto \color{blue}{e^{\log \left({\left(\tan \left(y + z\right) - \left(\tan a - x\right)\right)}^{3}\right) \cdot 0.3333333333333333}} \]

   6. Taylor expanded in x around inf 24.3%

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

      1. mul-1-neg 24.3%

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

      2. log-rec 24.3%

         \[\leadsto e^{-\color{blue}{\left(-\log x\right)}} \]

      3. remove-double-neg 24.3%

         \[\leadsto e^{\color{blue}{\log x}} \]

   8. Simplified 24.3%

      \[\leadsto e^{\color{blue}{\log x}} \]

   if -1.55000000000000004 < a < 1.55000000000000004

   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 80.4%

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

   if 1.55000000000000004 < a

   1. Initial program 75.1%

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

   3. Taylor expanded in a around 0 1.4%

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

   4. Taylor expanded in a around inf 1.4%

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

   5. Taylor expanded in x around inf 21.5%

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

Alternative 10: 50.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if a < -1.55000000000000004

   1. Initial program 76.3%

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

   3. Taylor expanded in x around inf 24.3%

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

   if -1.55000000000000004 < a < 1.55000000000000004

   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 80.4%

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

   if 1.55000000000000004 < a

   1. Initial program 75.1%

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

   3. Taylor expanded in a around 0 1.4%

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

   4. Taylor expanded in a around inf 1.4%

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

   5. Taylor expanded in x around inf 21.5%

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

Alternative 11: 41.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.55:\\ \;\;\;\;x + \left(\tan y - a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= a -1.65) x (if (<= a 1.55) (+ x (- (tan y) a)) (* a (/ x a)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.65) {
		tmp = x;
	} else if (a <= 1.55) {
		tmp = x + (tan(y) - a);
	} else {
		tmp = a * (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 <= (-1.65d0)) then
        tmp = x
    else if (a <= 1.55d0) then
        tmp = x + (tan(y) - a)
    else
        tmp = a * (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 <= -1.65) {
		tmp = x;
	} else if (a <= 1.55) {
		tmp = x + (Math.tan(y) - a);
	} else {
		tmp = a * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if a <= -1.65:
		tmp = x
	elif a <= 1.55:
		tmp = x + (math.tan(y) - a)
	else:
		tmp = a * (x / a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (a <= -1.65)
		tmp = x;
	elseif (a <= 1.55)
		tmp = Float64(x + Float64(tan(y) - a));
	else
		tmp = Float64(a * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -1.65)
		tmp = x;
	elseif (a <= 1.55)
		tmp = x + (tan(y) - a);
	else
		tmp = a * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[a, -1.65], x, If[LessEqual[a, 1.55], N[(x + N[(N[Tan[y], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6499999999999999

   1. Initial program 76.3%

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

   3. Taylor expanded in x around inf 24.3%

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

   if -1.6499999999999999 < a < 1.55000000000000004

   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 80.4%

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

   4. Taylor expanded in y around inf 61.2%

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

   if 1.55000000000000004 < a

   1. Initial program 75.1%

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

   3. Taylor expanded in a around 0 1.4%

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

   4. Taylor expanded in a around inf 1.4%

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

   5. Taylor expanded in x around inf 21.5%

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

Alternative 12: 36.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.8 \cdot 10^{-14}:\\ \;\;\;\;x + \left(\tan y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= z 1.8e-14) (+ x (- (tan y) a)) (+ x (- (tan z) a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= 1.8e-14) {
		tmp = x + (tan(y) - a);
	} else {
		tmp = x + (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 (z <= 1.8d-14) then
        tmp = x + (tan(y) - a)
    else
        tmp = x + (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 (z <= 1.8e-14) {
		tmp = x + (Math.tan(y) - a);
	} else {
		tmp = x + (Math.tan(z) - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if z <= 1.8e-14:
		tmp = x + (math.tan(y) - a)
	else:
		tmp = x + (math.tan(z) - a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (z <= 1.8e-14)
		tmp = Float64(x + Float64(tan(y) - a));
	else
		tmp = Float64(x + Float64(tan(z) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (z <= 1.8e-14)
		tmp = x + (tan(y) - a);
	else
		tmp = x + (tan(z) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[z, 1.8e-14], N[(x + N[(N[Tan[y], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[z], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.7999999999999999e-14

   1. Initial program 86.0%

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

   3. Taylor expanded in a around 0 48.0%

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

   4. Taylor expanded in y around inf 40.1%

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

   if 1.7999999999999999e-14 < z

   1. Initial program 59.3%

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

   3. Taylor expanded in a around 0 30.5%

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

   4. Taylor expanded in y around 0 30.2%

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

Alternative 13: 31.4% 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 78.4%

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

3. Taylor expanded in x around inf 31.7%

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

Reproduce

herbie shell --seed 2024121 
(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))))