tan-example (used to crash)

Percentage Accurate: 79.0% → 99.7%

Time: 31.5s

Alternatives: 9

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: 79.0% 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 80.9%

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

   1. tan-sum 99.7%

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

   2. div-inv 99.7%

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

3. Applied egg-rr 99.7%

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

   1. associate-*r/ 99.7%

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

   2. *-rgt-identity 99.7%

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

5. Simplified 99.7%

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

   1. add-cbrt-cube 99.7%

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

   2. pow3 99.7%

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

7. Applied egg-rr 99.7%

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

8. Final simplification 99.7%

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

Alternative 2: 87.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(y + z\right)\\ t_1 := \sin \left(y + z\right)\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{-11}:\\ \;\;\;\;x + \left(t_1 \cdot \frac{1}{t_0} - \tan a\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-91}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{1 - \tan y \cdot \tan z}, \tan y + \tan z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\frac{t_0}{t_1}} - \tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (cos (+ y z))) (t_1 (sin (+ y z))))
   (if (<= a -2.5e-11)
     (+ x (- (* t_1 (/ 1.0 t_0)) (tan a)))
     (if (<= a 4.8e-91)
       (fma (/ 1.0 (- 1.0 (* (tan y) (tan z)))) (+ (tan y) (tan z)) x)
       (+ x (- (/ 1.0 (/ t_0 t_1)) (tan a)))))))

C

double code(double x, double y, double z, double a) {
	double t_0 = cos((y + z));
	double t_1 = sin((y + z));
	double tmp;
	if (a <= -2.5e-11) {
		tmp = x + ((t_1 * (1.0 / t_0)) - tan(a));
	} else if (a <= 4.8e-91) {
		tmp = fma((1.0 / (1.0 - (tan(y) * tan(z)))), (tan(y) + tan(z)), x);
	} else {
		tmp = x + ((1.0 / (t_0 / t_1)) - tan(a));
	}
	return tmp;
}

Julia

function code(x, y, z, a)
	t_0 = cos(Float64(y + z))
	t_1 = sin(Float64(y + z))
	tmp = 0.0
	if (a <= -2.5e-11)
		tmp = Float64(x + Float64(Float64(t_1 * Float64(1.0 / t_0)) - tan(a)));
	elseif (a <= 4.8e-91)
		tmp = fma(Float64(1.0 / Float64(1.0 - Float64(tan(y) * tan(z)))), Float64(tan(y) + tan(z)), x);
	else
		tmp = Float64(x + Float64(Float64(1.0 / Float64(t_0 / t_1)) - tan(a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, a_] := Block[{t$95$0 = N[Cos[N[(y + z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Sin[N[(y + z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[a, -2.5e-11], N[(x + N[(N[(t$95$1 * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e-91], N[(N[(1.0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(1.0 / N[(t$95$0 / t$95$1), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.50000000000000009e-11

   1. Initial program 85.1%

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

      1. tan-quot 85.1%

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

      2. div-inv 85.1%

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

   3. Applied egg-rr 85.1%

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

   if -2.50000000000000009e-11 < a < 4.80000000000000022e-91

   1. Initial program 75.2%

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

      1. +-commutative 75.2%

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

      2. associate-+l- 75.2%

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

   3. Applied egg-rr 75.2%

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

   4. Taylor expanded in a around 0 75.2%

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

      1. neg-mul-1 75.2%

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

   6. Simplified 75.2%

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

      1. tan-sum 99.6%

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

      2. rem-cbrt-cube 99.6%

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

      3. clear-num 99.6%

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

      4. rem-cbrt-cube 99.6%

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

      5. associate-/r/ 99.6%

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

      6. fma-neg 99.6%

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

      7. add-sqr-sqrt 0.0%

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

      8. sqrt-unprod 4.0%

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

      9. sqr-neg 4.0%

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

      10. sqrt-unprod 4.0%

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

      11. add-sqr-sqrt 4.0%

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

   8. Applied egg-rr 99.6%

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

   if 4.80000000000000022e-91 < a

   1. Initial program 84.4%

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

      1. tan-quot 84.4%

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

      2. clear-num 84.4%

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

   3. Applied egg-rr 84.4%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-11}:\\ \;\;\;\;x + \left(\sin \left(y + z\right) \cdot \frac{1}{\cos \left(y + z\right)} - \tan a\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-91}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{1 - \tan y \cdot \tan z}, \tan y + \tan z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\frac{\cos \left(y + z\right)}{\sin \left(y + z\right)}} - \tan a\right)\\ \end{array} \]

Alternative 3: 99.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.9%

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

   1. tan-sum 99.7%

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

   2. div-inv 99.7%

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

3. Applied egg-rr 99.7%

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

   1. associate-*r/ 99.7%

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

   2. *-rgt-identity 99.7%

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

5. Simplified 99.7%

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

6. Final simplification 99.7%

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

Alternative 4: 87.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos \left(y + z\right)\\ t_1 := \sin \left(y + z\right)\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{-9}:\\ \;\;\;\;x + \left(t_1 \cdot \frac{1}{t_0} - \tan a\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\frac{t_0}{t_1}} - \tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (cos (+ y z))) (t_1 (sin (+ y z))))
   (if (<= a -1.8e-9)
     (+ x (- (* t_1 (/ 1.0 t_0)) (tan a)))
     (if (<= a 4.8e-91)
       (+ x (/ (+ (tan y) (tan z)) (- 1.0 (* (tan y) (tan z)))))
       (+ x (- (/ 1.0 (/ t_0 t_1)) (tan a)))))))

C

double code(double x, double y, double z, double a) {
	double t_0 = cos((y + z));
	double t_1 = sin((y + z));
	double tmp;
	if (a <= -1.8e-9) {
		tmp = x + ((t_1 * (1.0 / t_0)) - tan(a));
	} else if (a <= 4.8e-91) {
		tmp = x + ((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z))));
	} else {
		tmp = x + ((1.0 / (t_0 / t_1)) - 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = cos((y + z))
    t_1 = sin((y + z))
    if (a <= (-1.8d-9)) then
        tmp = x + ((t_1 * (1.0d0 / t_0)) - tan(a))
    else if (a <= 4.8d-91) then
        tmp = x + ((tan(y) + tan(z)) / (1.0d0 - (tan(y) * tan(z))))
    else
        tmp = x + ((1.0d0 / (t_0 / t_1)) - tan(a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double t_0 = Math.cos((y + z));
	double t_1 = Math.sin((y + z));
	double tmp;
	if (a <= -1.8e-9) {
		tmp = x + ((t_1 * (1.0 / t_0)) - Math.tan(a));
	} else if (a <= 4.8e-91) {
		tmp = x + ((Math.tan(y) + Math.tan(z)) / (1.0 - (Math.tan(y) * Math.tan(z))));
	} else {
		tmp = x + ((1.0 / (t_0 / t_1)) - Math.tan(a));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	t_0 = math.cos((y + z))
	t_1 = math.sin((y + z))
	tmp = 0
	if a <= -1.8e-9:
		tmp = x + ((t_1 * (1.0 / t_0)) - math.tan(a))
	elif a <= 4.8e-91:
		tmp = x + ((math.tan(y) + math.tan(z)) / (1.0 - (math.tan(y) * math.tan(z))))
	else:
		tmp = x + ((1.0 / (t_0 / t_1)) - math.tan(a))
	return tmp

Julia

function code(x, y, z, a)
	t_0 = cos(Float64(y + z))
	t_1 = sin(Float64(y + z))
	tmp = 0.0
	if (a <= -1.8e-9)
		tmp = Float64(x + Float64(Float64(t_1 * Float64(1.0 / t_0)) - tan(a)));
	elseif (a <= 4.8e-91)
		tmp = Float64(x + Float64(Float64(tan(y) + tan(z)) / Float64(1.0 - Float64(tan(y) * tan(z)))));
	else
		tmp = Float64(x + Float64(Float64(1.0 / Float64(t_0 / t_1)) - tan(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	t_0 = cos((y + z));
	t_1 = sin((y + z));
	tmp = 0.0;
	if (a <= -1.8e-9)
		tmp = x + ((t_1 * (1.0 / t_0)) - tan(a));
	elseif (a <= 4.8e-91)
		tmp = x + ((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z))));
	else
		tmp = x + ((1.0 / (t_0 / t_1)) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := Block[{t$95$0 = N[Cos[N[(y + z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Sin[N[(y + z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[a, -1.8e-9], N[(x + N[(N[(t$95$1 * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e-91], N[(x + 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]), $MachinePrecision], N[(x + N[(N[(1.0 / N[(t$95$0 / t$95$1), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8e-9

   1. Initial program 85.1%

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

      1. tan-quot 85.1%

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

      2. div-inv 85.1%

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

   3. Applied egg-rr 85.1%

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

   if -1.8e-9 < a < 4.80000000000000022e-91

   1. Initial program 75.2%

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

      1. +-commutative 75.2%

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

      2. associate-+l- 75.2%

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

   3. Applied egg-rr 75.2%

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

   4. Taylor expanded in a around 0 75.2%

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

      1. neg-mul-1 75.2%

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

   6. Simplified 75.2%

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

      1. tan-sum 99.6%

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

      2. rem-cbrt-cube 99.6%

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

      3. div-inv 99.6%

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

      4. rem-cbrt-cube 99.6%

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

      5. fma-neg 99.6%

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

      6. add-sqr-sqrt 0.0%

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

      7. sqrt-unprod 4.0%

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

      8. sqr-neg 4.0%

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

      9. sqrt-unprod 4.0%

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

      10. add-sqr-sqrt 4.0%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 99.6%

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

      13. sqr-neg 99.6%

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

   8. Applied egg-rr 99.6%

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

      1. fma-udef 99.6%

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

      2. associate-*r/ 99.6%

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

      3. *-rgt-identity 99.6%

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

   10. Simplified 99.6%

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

   if 4.80000000000000022e-91 < a

   1. Initial program 84.4%

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

      1. tan-quot 84.4%

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

      2. clear-num 84.4%

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

   3. Applied egg-rr 84.4%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-9}:\\ \;\;\;\;x + \left(\sin \left(y + z\right) \cdot \frac{1}{\cos \left(y + z\right)} - \tan a\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\frac{\cos \left(y + z\right)}{\sin \left(y + z\right)}} - \tan a\right)\\ \end{array} \]

Alternative 5: 78.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double a) {
	return x + ((sin((y + z)) * (1.0 / cos((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 + ((sin((y + z)) * (1.0d0 / cos((y + z)))) - tan(a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.9%

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

   1. tan-quot 80.9%

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

   2. div-inv 80.9%

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

3. Applied egg-rr 80.9%

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

4. Final simplification 80.9%

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

Alternative 6: 59.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.05 \lor \neg \left(a \leq 1.5 \cdot 10^{-6}\right):\\ \;\;\;\;x - \frac{\sin a}{\cos a}\\ \mathbf{else}:\\ \;\;\;\;\tan \left(y + z\right) + \left(x - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -0.05) (not (<= a 1.5e-6)))
   (- x (/ (sin a) (cos a)))
   (+ (tan (+ y z)) (- x a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -0.05) || !(a <= 1.5e-6)) {
		tmp = x - (sin(a) / cos(a));
	} else {
		tmp = tan((y + z)) + (x - a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-0.05d0)) .or. (.not. (a <= 1.5d-6))) then
        tmp = x - (sin(a) / cos(a))
    else
        tmp = tan((y + z)) + (x - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -0.05) || !(a <= 1.5e-6)) {
		tmp = x - (Math.sin(a) / Math.cos(a));
	} else {
		tmp = Math.tan((y + z)) + (x - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (a <= -0.05) or not (a <= 1.5e-6):
		tmp = x - (math.sin(a) / math.cos(a))
	else:
		tmp = math.tan((y + z)) + (x - a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -0.05) || !(a <= 1.5e-6))
		tmp = Float64(x - Float64(sin(a) / cos(a)));
	else
		tmp = Float64(tan(Float64(y + z)) + Float64(x - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -0.05) || ~((a <= 1.5e-6)))
		tmp = x - (sin(a) / cos(a));
	else
		tmp = tan((y + z)) + (x - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[a, -0.05], N[Not[LessEqual[a, 1.5e-6]], $MachinePrecision]], N[(x - N[(N[Sin[a], $MachinePrecision] / N[Cos[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] + N[(x - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.050000000000000003 or 1.5e-6 < a

   1. Initial program 82.5%

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

      1. tan-quot 82.5%

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

      2. div-inv 82.5%

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

   3. Applied egg-rr 82.5%

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

   4. Taylor expanded in z around 0 63.2%

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

   5. Taylor expanded in y around 0 44.1%

      \[\leadsto \color{blue}{x - \frac{\sin a}{\cos a}} \]

   if -0.050000000000000003 < a < 1.5e-6

   1. Initial program 79.0%

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

      1. +-commutative 79.0%

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

      2. associate-+l- 79.0%

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

   3. Applied egg-rr 79.0%

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

   4. Taylor expanded in a around 0 79.0%

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

      1. neg-mul-1 79.0%

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

      2. unsub-neg 79.0%

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

   6. Simplified 79.0%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.05 \lor \neg \left(a \leq 1.5 \cdot 10^{-6}\right):\\ \;\;\;\;x - \frac{\sin a}{\cos a}\\ \mathbf{else}:\\ \;\;\;\;\tan \left(y + z\right) + \left(x - a\right)\\ \end{array} \]

Alternative 7: 79.0% 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 80.9%

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

2. Final simplification 80.9%

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

Alternative 8: 50.0% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

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))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.9%

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

   1. +-commutative 80.9%

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

   2. associate-+l- 80.8%

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

3. Applied egg-rr 80.8%

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

4. Taylor expanded in a around 0 49.9%

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

   1. neg-mul-1 49.9%

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

6. Simplified 49.9%

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

   1. sub-neg 49.9%

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

   2. add-sqr-sqrt 0.0%

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

   3. sqrt-unprod 3.4%

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

   4. sqr-neg 3.4%

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

   5. sqrt-unprod 3.4%

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

   6. add-sqr-sqrt 3.4%

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

   7. add-sqr-sqrt 0.0%

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

   8. sqrt-unprod 49.9%

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

   9. sqr-neg 49.9%

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

   10. sqrt-unprod 49.7%

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

   11. add-sqr-sqrt 49.9%

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

8. Applied egg-rr 49.9%

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

9. Final simplification 49.9%

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

Alternative 9: 31.2% 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 80.9%

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

2. Taylor expanded in x around inf 31.1%

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

3. Final simplification 31.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023318 
(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))))