tan-example (used to crash)

Percentage Accurate: 80.1% → 99.7%

Time: 35.5s

Alternatives: 15

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: 80.1% 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

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

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (+
  x
  (fma
   (+ (tan y) (tan z))
   (/ 1.0 (- 1.0 (/ (tan z) (/ (cos y) (sin y)))))
   (- (tan a)))))

C

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

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + fma(Float64(tan(y) + tan(z)), Float64(1.0 / Float64(1.0 - Float64(tan(z) / Float64(cos(y) / sin(y))))), Float64(-tan(a))))
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(1.0 - N[(N[Tan[z], $MachinePrecision] / N[(N[Cos[y], $MachinePrecision] / N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + (-N[Tan[a], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.8%

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

   1. tan-sum 99.7%

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

   2. div-inv 99.7%

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

   3. fma-neg 99.7%

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

3. Applied egg-rr 99.7%

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

   1. *-commutative 99.7%

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

   2. tan-quot 99.7%

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

   3. associate-*r/ 99.7%

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

5. Applied egg-rr 99.7%

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

   1. associate-/l* 99.7%

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

7. Simplified 99.7%

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

8. Final simplification 99.7%

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

Alternative 2: 89.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} t_0 := \tan \left(y + z\right)\\ \mathbf{if}\;\tan a \leq -1 \cdot 10^{-5}:\\ \;\;\;\;x + \left(\log \left(e^{t_0}\right) - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 5 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{1 - \tan y \cdot \tan z}, \tan y + \tan z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t_0 - \tan a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (tan (+ y z))))
   (if (<= (tan a) -1e-5)
     (+ x (- (log (exp t_0)) (tan a)))
     (if (<= (tan a) 5e-11)
       (fma (/ 1.0 (- 1.0 (* (tan y) (tan z)))) (+ (tan y) (tan z)) x)
       (+ x (- t_0 (tan a)))))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double t_0 = tan((y + z));
	double tmp;
	if (tan(a) <= -1e-5) {
		tmp = x + (log(exp(t_0)) - tan(a));
	} else if (tan(a) <= 5e-11) {
		tmp = fma((1.0 / (1.0 - (tan(y) * tan(z)))), (tan(y) + tan(z)), x);
	} else {
		tmp = x + (t_0 - tan(a));
	}
	return tmp;
}

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	t_0 = tan(Float64(y + z))
	tmp = 0.0
	if (tan(a) <= -1e-5)
		tmp = Float64(x + Float64(log(exp(t_0)) - tan(a)));
	elseif (tan(a) <= 5e-11)
		tmp = fma(Float64(1.0 / Float64(1.0 - Float64(tan(y) * tan(z)))), Float64(tan(y) + tan(z)), x);
	else
		tmp = Float64(x + Float64(t_0 - tan(a)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := Block[{t$95$0 = N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[Tan[a], $MachinePrecision], -1e-5], N[(x + N[(N[Log[N[Exp[t$95$0], $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Tan[a], $MachinePrecision], 5e-11], 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[(t$95$0 - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (tan.f64 a) < -1.00000000000000008e-5

   1. Initial program 80.5%

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

      1. add-log-exp 80.6%

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

   3. Applied egg-rr 80.6%

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

   if -1.00000000000000008e-5 < (tan.f64 a) < 5.00000000000000018e-11

   1. Initial program 76.5%

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

      1. +-commutative 76.5%

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

      2. associate-+l- 76.5%

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

   3. Applied egg-rr 76.5%

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

   4. Taylor expanded in a around 0 76.5%

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

      1. neg-mul-1 76.5%

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

   6. Simplified 76.5%

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

      1. sub-neg 76.5%

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

      2. +-commutative 76.5%

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

   8. Applied egg-rr 76.5%

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

      1. remove-double-neg 76.5%

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

      2. +-commutative 76.5%

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

   10. Simplified 76.5%

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

       1. +-commutative 76.5%

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

       2. +-commutative 76.5%

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

       3. tan-sum 99.2%

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

       4. un-div-inv 99.2%

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

       5. *-commutative 99.2%

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

       6. fma-def 99.2%

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

       7. *-commutative 99.2%

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

       8. +-commutative 99.2%

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

   12. Applied egg-rr 99.2%

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

   if 5.00000000000000018e-11 < (tan.f64 a)

   1. Initial program 86.0%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -1 \cdot 10^{-5}:\\ \;\;\;\;x + \left(\log \left(e^{\tan \left(y + z\right)}\right) - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 5 \cdot 10^{-11}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{1 - \tan y \cdot \tan z}, \tan y + \tan z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \end{array} \]

Alternative 3: 89.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} t_0 := \tan \left(y + z\right)\\ \mathbf{if}\;\tan a \leq -1 \cdot 10^{-5}:\\ \;\;\;\;x + \left(\log \left(e^{t_0}\right) - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 5 \cdot 10^{-11}:\\ \;\;\;\;x + \left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t_0 - \tan a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (tan (+ y z))))
   (if (<= (tan a) -1e-5)
     (+ x (- (log (exp t_0)) (tan a)))
     (if (<= (tan a) 5e-11)
       (+ x (* (+ (tan y) (tan z)) (/ 1.0 (- 1.0 (* (tan y) (tan z))))))
       (+ x (- t_0 (tan a)))))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double t_0 = tan((y + z));
	double tmp;
	if (tan(a) <= -1e-5) {
		tmp = x + (log(exp(t_0)) - tan(a));
	} else if (tan(a) <= 5e-11) {
		tmp = x + ((tan(y) + tan(z)) * (1.0 / (1.0 - (tan(y) * tan(z)))));
	} else {
		tmp = x + (t_0 - tan(a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
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 + z))
    if (tan(a) <= (-1d-5)) then
        tmp = x + (log(exp(t_0)) - tan(a))
    else if (tan(a) <= 5d-11) then
        tmp = x + ((tan(y) + tan(z)) * (1.0d0 / (1.0d0 - (tan(y) * tan(z)))))
    else
        tmp = x + (t_0 - tan(a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double t_0 = Math.tan((y + z));
	double tmp;
	if (Math.tan(a) <= -1e-5) {
		tmp = x + (Math.log(Math.exp(t_0)) - Math.tan(a));
	} else if (Math.tan(a) <= 5e-11) {
		tmp = x + ((Math.tan(y) + Math.tan(z)) * (1.0 / (1.0 - (Math.tan(y) * Math.tan(z)))));
	} else {
		tmp = x + (t_0 - Math.tan(a));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	t_0 = math.tan((y + z))
	tmp = 0
	if math.tan(a) <= -1e-5:
		tmp = x + (math.log(math.exp(t_0)) - math.tan(a))
	elif math.tan(a) <= 5e-11:
		tmp = x + ((math.tan(y) + math.tan(z)) * (1.0 / (1.0 - (math.tan(y) * math.tan(z)))))
	else:
		tmp = x + (t_0 - math.tan(a))
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	t_0 = tan(Float64(y + z))
	tmp = 0.0
	if (tan(a) <= -1e-5)
		tmp = Float64(x + Float64(log(exp(t_0)) - tan(a)));
	elseif (tan(a) <= 5e-11)
		tmp = Float64(x + Float64(Float64(tan(y) + tan(z)) * Float64(1.0 / Float64(1.0 - Float64(tan(y) * tan(z))))));
	else
		tmp = Float64(x + Float64(t_0 - tan(a)));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	t_0 = tan((y + z));
	tmp = 0.0;
	if (tan(a) <= -1e-5)
		tmp = x + (log(exp(t_0)) - tan(a));
	elseif (tan(a) <= 5e-11)
		tmp = x + ((tan(y) + tan(z)) * (1.0 / (1.0 - (tan(y) * tan(z)))));
	else
		tmp = x + (t_0 - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := Block[{t$95$0 = N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[Tan[a], $MachinePrecision], -1e-5], N[(x + N[(N[Log[N[Exp[t$95$0], $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Tan[a], $MachinePrecision], 5e-11], N[(x + N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$0 - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (tan.f64 a) < -1.00000000000000008e-5

   1. Initial program 80.5%

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

      1. add-log-exp 80.6%

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

   3. Applied egg-rr 80.6%

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

   if -1.00000000000000008e-5 < (tan.f64 a) < 5.00000000000000018e-11

   1. Initial program 76.5%

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

      1. +-commutative 76.5%

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

      2. associate-+l- 76.5%

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

   3. Applied egg-rr 76.5%

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

   4. Taylor expanded in a around 0 76.5%

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

      1. neg-mul-1 76.5%

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

   6. Simplified 76.5%

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

      1. sub-neg 76.5%

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

      2. +-commutative 76.5%

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

   8. Applied egg-rr 76.5%

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

      1. remove-double-neg 76.5%

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

      2. +-commutative 76.5%

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

   10. Simplified 76.5%

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

       1. +-commutative 76.5%

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

       2. tan-sum 99.2%

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

       3. un-div-inv 99.2%

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

       4. *-commutative 99.2%

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

       5. *-commutative 99.2%

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

       6. +-commutative 99.2%

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

   12. Applied egg-rr 99.2%

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

   if 5.00000000000000018e-11 < (tan.f64 a)

   1. Initial program 86.0%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -1 \cdot 10^{-5}:\\ \;\;\;\;x + \left(\log \left(e^{\tan \left(y + z\right)}\right) - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 5 \cdot 10^{-11}:\\ \;\;\;\;x + \left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \end{array} \]

Alternative 4: 89.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} t_0 := \tan \left(y + z\right)\\ \mathbf{if}\;\tan a \leq -1 \cdot 10^{-5}:\\ \;\;\;\;x + \left(\log \left(e^{t_0}\right) - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 5 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t_0 - \tan a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (tan (+ y z))))
   (if (<= (tan a) -1e-5)
     (+ x (- (log (exp t_0)) (tan a)))
     (if (<= (tan a) 5e-11)
       (+ x (/ (+ (tan y) (tan z)) (- 1.0 (* (tan y) (tan z)))))
       (+ x (- t_0 (tan a)))))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double t_0 = tan((y + z));
	double tmp;
	if (tan(a) <= -1e-5) {
		tmp = x + (log(exp(t_0)) - tan(a));
	} else if (tan(a) <= 5e-11) {
		tmp = x + ((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z))));
	} else {
		tmp = x + (t_0 - tan(a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
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 + z))
    if (tan(a) <= (-1d-5)) then
        tmp = x + (log(exp(t_0)) - tan(a))
    else if (tan(a) <= 5d-11) then
        tmp = x + ((tan(y) + tan(z)) / (1.0d0 - (tan(y) * tan(z))))
    else
        tmp = x + (t_0 - tan(a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double t_0 = Math.tan((y + z));
	double tmp;
	if (Math.tan(a) <= -1e-5) {
		tmp = x + (Math.log(Math.exp(t_0)) - Math.tan(a));
	} else if (Math.tan(a) <= 5e-11) {
		tmp = x + ((Math.tan(y) + Math.tan(z)) / (1.0 - (Math.tan(y) * Math.tan(z))));
	} else {
		tmp = x + (t_0 - Math.tan(a));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	t_0 = math.tan((y + z))
	tmp = 0
	if math.tan(a) <= -1e-5:
		tmp = x + (math.log(math.exp(t_0)) - math.tan(a))
	elif math.tan(a) <= 5e-11:
		tmp = x + ((math.tan(y) + math.tan(z)) / (1.0 - (math.tan(y) * math.tan(z))))
	else:
		tmp = x + (t_0 - math.tan(a))
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	t_0 = tan(Float64(y + z))
	tmp = 0.0
	if (tan(a) <= -1e-5)
		tmp = Float64(x + Float64(log(exp(t_0)) - tan(a)));
	elseif (tan(a) <= 5e-11)
		tmp = Float64(x + Float64(Float64(tan(y) + tan(z)) / Float64(1.0 - Float64(tan(y) * tan(z)))));
	else
		tmp = Float64(x + Float64(t_0 - tan(a)));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	t_0 = tan((y + z));
	tmp = 0.0;
	if (tan(a) <= -1e-5)
		tmp = x + (log(exp(t_0)) - tan(a));
	elseif (tan(a) <= 5e-11)
		tmp = x + ((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z))));
	else
		tmp = x + (t_0 - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := Block[{t$95$0 = N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[Tan[a], $MachinePrecision], -1e-5], N[(x + N[(N[Log[N[Exp[t$95$0], $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Tan[a], $MachinePrecision], 5e-11], 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[(t$95$0 - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (tan.f64 a) < -1.00000000000000008e-5

   1. Initial program 80.5%

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

      1. add-log-exp 80.6%

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

   3. Applied egg-rr 80.6%

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

   if -1.00000000000000008e-5 < (tan.f64 a) < 5.00000000000000018e-11

   1. Initial program 76.5%

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

      1. +-commutative 76.5%

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

      2. associate-+l- 76.5%

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

   3. Applied egg-rr 76.5%

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

   4. Taylor expanded in a around 0 76.5%

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

      1. neg-mul-1 76.5%

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

   6. Simplified 76.5%

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

      1. sub-neg 76.5%

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

      2. +-commutative 76.5%

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

   8. Applied egg-rr 76.5%

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

      1. remove-double-neg 76.5%

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

      2. +-commutative 76.5%

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

   10. Simplified 76.5%

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

       1. +-commutative 76.5%

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

       2. +-commutative 76.5%

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

       3. tan-sum 99.2%

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

       4. un-div-inv 99.2%

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

       5. fma-def 99.2%

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

       6. +-commutative 99.2%

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

       7. *-commutative 99.2%

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

   12. Applied egg-rr 99.2%

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

       1. fma-udef 99.2%

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

       2. associate-*r/ 99.2%

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

       3. *-rgt-identity 99.2%

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

   14. Simplified 99.2%

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

   if 5.00000000000000018e-11 < (tan.f64 a)

   1. Initial program 86.0%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -1 \cdot 10^{-5}:\\ \;\;\;\;x + \left(\log \left(e^{\tan \left(y + z\right)}\right) - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 5 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \end{array} \]

Alternative 5: 99.7% accurate, 0.3× speedup

Math

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

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (+
  x
  (fma (+ (tan y) (tan z)) (/ 1.0 (- 1.0 (* (tan y) (tan z)))) (- (tan a)))))

C

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

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + fma(Float64(tan(y) + tan(z)), Float64(1.0 / Float64(1.0 - Float64(tan(y) * tan(z)))), Float64(-tan(a))))
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + (-N[Tan[a], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.8%

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

   1. tan-sum 99.7%

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

   2. div-inv 99.7%

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

   3. fma-neg 99.7%

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

3. Applied egg-rr 99.7%

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

4. Final simplification 99.7%

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

Alternative 6: 99.7% accurate, 0.4× speedup

Math

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

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (+ x (- (* (+ (tan y) (tan z)) (/ 1.0 (- 1.0 (* (tan y) (tan z))))) (tan a))))

C

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

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
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 / (1.0d0 - (tan(y) * tan(z))))) - tan(a))
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x + (((tan(y) + tan(z)) * (1.0 / (1.0 - (tan(y) * tan(z))))) - tan(a));
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.8%

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

   1. tan-sum 99.7%

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

   2. div-inv 99.7%

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

3. Applied egg-rr 99.7%

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

4. Final simplification 99.7%

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

Alternative 7: 99.7% accurate, 0.4× speedup

Math

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

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (+ x (- (/ (+ (tan y) (tan z)) (- 1.0 (* (tan y) (tan z)))) (tan a))))

C

assert(x < y && y < z && z < a);
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

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
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

assert x < y && y < z && z < a;
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

[x, y, z, a] = sort([x, y, z, a])
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

x, y, z, a = sort([x, y, z, a])
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

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) - tan(a));
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.8%

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

   1. tan-sum 99.7%

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

   2. div-inv 99.7%

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

3. Applied egg-rr 99.7%

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

   1. associate-*r/ 99.7%

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

   2. *-rgt-identity 99.7%

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

5. Simplified 99.7%

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

6. Final simplification 99.7%

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

Alternative 8: 80.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x + \left(\log \left(e^{\tan \left(y + z\right)}\right) - \tan a\right) \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (+ x (- (log (exp (tan (+ y z)))) (tan a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x + (log(exp(tan((y + z)))) - tan(a));
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
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 + (log(exp(tan((y + z)))) - tan(a))
end function

Java

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

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return x + (math.log(math.exp(math.tan((y + z)))) - math.tan(a))

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + Float64(log(exp(tan(Float64(y + z)))) - tan(a)))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x + (log(exp(tan((y + z)))) - tan(a));
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[Log[N[Exp[N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.8%

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

   1. add-log-exp 79.9%

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

3. Applied egg-rr 79.9%

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

4. Final simplification 79.9%

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

Alternative 9: 60.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -0.12 \lor \neg \left(\tan a \leq 0.15\right):\\ \;\;\;\;x - \tan a\\ \mathbf{else}:\\ \;\;\;\;x + \tan \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (or (<= (tan a) -0.12) (not (<= (tan a) 0.15)))
   (- x (tan a))
   (+ x (tan (+ y z)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((tan(a) <= -0.12) || !(tan(a) <= 0.15)) {
		tmp = x - tan(a);
	} else {
		tmp = x + tan((y + z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
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) <= (-0.12d0)) .or. (.not. (tan(a) <= 0.15d0))) then
        tmp = x - tan(a)
    else
        tmp = x + tan((y + z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((Math.tan(a) <= -0.12) || !(Math.tan(a) <= 0.15)) {
		tmp = x - Math.tan(a);
	} else {
		tmp = x + Math.tan((y + z));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (math.tan(a) <= -0.12) or not (math.tan(a) <= 0.15):
		tmp = x - math.tan(a)
	else:
		tmp = x + math.tan((y + z))
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if ((tan(a) <= -0.12) || !(tan(a) <= 0.15))
		tmp = Float64(x - tan(a));
	else
		tmp = Float64(x + tan(Float64(y + z)));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((tan(a) <= -0.12) || ~((tan(a) <= 0.15)))
		tmp = x - tan(a);
	else
		tmp = x + tan((y + z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[Or[LessEqual[N[Tan[a], $MachinePrecision], -0.12], N[Not[LessEqual[N[Tan[a], $MachinePrecision], 0.15]], $MachinePrecision]], N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision], N[(x + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (tan.f64 a) < -0.12 or 0.149999999999999994 < (tan.f64 a)

   1. Initial program 82.1%

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

      1. add-cbrt-cube 81.6%

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

      2. pow3 81.6%

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

      3. +-commutative 81.6%

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

      4. associate-+l- 81.5%

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

   3. Applied egg-rr 81.5%

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

   4. Taylor expanded in y around 0 60.7%

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

   5. Taylor expanded in z around 0 40.8%

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

      1. rem-cbrt-cube 41.0%

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

      2. sub-neg 41.0%

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

      3. quot-tan 41.0%

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

   7. Applied egg-rr 41.0%

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

      1. sub-neg 41.0%

         \[\leadsto \color{blue}{x - \tan a} \]

   9. Simplified 41.0%

      \[\leadsto \color{blue}{x - \tan a} \]

   if -0.12 < (tan.f64 a) < 0.149999999999999994

   1. Initial program 78.0%

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

      1. +-commutative 78.0%

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

      2. associate-+l- 77.9%

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

   3. Applied egg-rr 77.9%

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

   4. Taylor expanded in a around 0 73.1%

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

      1. neg-mul-1 73.1%

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

   6. Simplified 73.1%

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

      1. sub-neg 73.1%

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

      2. +-commutative 73.1%

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

   8. Applied egg-rr 73.1%

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

      1. remove-double-neg 73.1%

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

      2. +-commutative 73.1%

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

   10. Simplified 73.1%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.12 \lor \neg \left(\tan a \leq 0.15\right):\\ \;\;\;\;x - \tan a\\ \mathbf{else}:\\ \;\;\;\;x + \tan \left(y + z\right)\\ \end{array} \]

Alternative 10: 70.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;y + z \leq -50:\\ \;\;\;\;x + \tan \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= (+ y z) -50.0) (+ x (tan (+ y z))) (+ x (- (tan z) (tan a)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -50.0) {
		tmp = x + tan((y + z));
	} else {
		tmp = x + (tan(z) - tan(a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
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) <= (-50.0d0)) then
        tmp = x + tan((y + z))
    else
        tmp = x + (tan(z) - tan(a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -50.0) {
		tmp = x + Math.tan((y + z));
	} else {
		tmp = x + (Math.tan(z) - Math.tan(a));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (y + z) <= -50.0:
		tmp = x + math.tan((y + z))
	else:
		tmp = x + (math.tan(z) - math.tan(a))
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (Float64(y + z) <= -50.0)
		tmp = Float64(x + tan(Float64(y + z)));
	else
		tmp = Float64(x + Float64(tan(z) - tan(a)));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((y + z) <= -50.0)
		tmp = x + tan((y + z));
	else
		tmp = x + (tan(z) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[N[(y + z), $MachinePrecision], -50.0], N[(x + N[Tan[N[(y + z), $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) < -50

   1. Initial program 71.0%

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

      1. +-commutative 71.0%

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

      2. associate-+l- 71.0%

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

   3. Applied egg-rr 71.0%

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

   4. Taylor expanded in a around 0 46.7%

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

      1. neg-mul-1 46.7%

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

   6. Simplified 46.7%

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

      1. sub-neg 46.7%

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

      2. +-commutative 46.7%

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

   8. Applied egg-rr 46.7%

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

      1. remove-double-neg 46.7%

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

      2. +-commutative 46.7%

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

   10. Simplified 46.7%

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

   if -50 < (+.f64 y z)

   1. Initial program 86.4%

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

      1. add-cbrt-cube 85.8%

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

      2. pow3 85.8%

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

      3. +-commutative 85.8%

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

      4. associate-+l- 85.8%

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

   3. Applied egg-rr 85.8%

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

   4. Taylor expanded in y around 0 69.2%

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

      1. rem-cbrt-cube 69.6%

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

      2. tan-quot 69.6%

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

      3. associate--r- 69.6%

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

   6. Applied egg-rr 69.6%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + z \leq -50:\\ \;\;\;\;x + \tan \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \]

Alternative 11: 70.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;y + z \leq -50:\\ \;\;\;\;x + \frac{\sin y}{\cos y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= (+ y z) -50.0) (+ x (/ (sin y) (cos y))) (+ x (- (tan z) (tan a)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -50.0) {
		tmp = x + (sin(y) / cos(y));
	} else {
		tmp = x + (tan(z) - tan(a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
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) <= (-50.0d0)) then
        tmp = x + (sin(y) / cos(y))
    else
        tmp = x + (tan(z) - tan(a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -50.0) {
		tmp = x + (Math.sin(y) / Math.cos(y));
	} else {
		tmp = x + (Math.tan(z) - Math.tan(a));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (y + z) <= -50.0:
		tmp = x + (math.sin(y) / math.cos(y))
	else:
		tmp = x + (math.tan(z) - math.tan(a))
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (Float64(y + z) <= -50.0)
		tmp = Float64(x + Float64(sin(y) / cos(y)));
	else
		tmp = Float64(x + Float64(tan(z) - tan(a)));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((y + z) <= -50.0)
		tmp = x + (sin(y) / cos(y));
	else
		tmp = x + (tan(z) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[N[(y + z), $MachinePrecision], -50.0], N[(x + N[(N[Sin[y], $MachinePrecision] / N[Cos[y], $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) < -50

   1. Initial program 71.0%

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

      1. +-commutative 71.0%

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

      2. associate-+l- 71.0%

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

   3. Applied egg-rr 71.0%

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

   4. Taylor expanded in a around 0 46.7%

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

      1. neg-mul-1 46.7%

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

   6. Simplified 46.7%

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

   7. Taylor expanded in z around 0 31.3%

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

      1. +-commutative 31.3%

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

   9. Simplified 31.3%

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

   if -50 < (+.f64 y z)

   1. Initial program 86.4%

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

      1. add-cbrt-cube 85.8%

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

      2. pow3 85.8%

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

      3. +-commutative 85.8%

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

      4. associate-+l- 85.8%

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

   3. Applied egg-rr 85.8%

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

   4. Taylor expanded in y around 0 69.2%

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

      1. rem-cbrt-cube 69.6%

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

      2. tan-quot 69.6%

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

      3. associate--r- 69.6%

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

   6. Applied egg-rr 69.6%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + z \leq -50:\\ \;\;\;\;x + \frac{\sin y}{\cos y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \]

Alternative 12: 80.1% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))

C

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

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
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

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

Python

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

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + Float64(tan(Float64(y + z)) - tan(a)))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x + (tan((y + z)) - tan(a));
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
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 79.8%

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

2. Final simplification 79.8%

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

Alternative 13: 60.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+30} \lor \neg \left(a \leq 0.08\right):\\ \;\;\;\;x - \tan a\\ \mathbf{else}:\\ \;\;\;\;\tan \left(y + z\right) + \left(x - a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -7e+30) (not (<= a 0.08)))
   (- x (tan a))
   (+ (tan (+ y z)) (- x a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -7e+30) || !(a <= 0.08)) {
		tmp = x - tan(a);
	} else {
		tmp = tan((y + z)) + (x - a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
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 <= (-7d+30)) .or. (.not. (a <= 0.08d0))) then
        tmp = x - tan(a)
    else
        tmp = tan((y + z)) + (x - a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -7e+30) || !(a <= 0.08)) {
		tmp = x - Math.tan(a);
	} else {
		tmp = Math.tan((y + z)) + (x - a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (a <= -7e+30) or not (a <= 0.08):
		tmp = x - math.tan(a)
	else:
		tmp = math.tan((y + z)) + (x - a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -7e+30) || !(a <= 0.08))
		tmp = Float64(x - tan(a));
	else
		tmp = Float64(tan(Float64(y + z)) + Float64(x - a));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -7e+30) || ~((a <= 0.08)))
		tmp = x - tan(a);
	else
		tmp = tan((y + z)) + (x - a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[Or[LessEqual[a, -7e+30], N[Not[LessEqual[a, 0.08]], $MachinePrecision]], N[(x - N[Tan[a], $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 < -7.00000000000000042e30 or 0.0800000000000000017 < a

   1. Initial program 82.5%

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

      1. add-cbrt-cube 82.0%

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

      2. pow3 82.0%

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

      3. +-commutative 82.0%

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

      4. associate-+l- 81.9%

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

   3. Applied egg-rr 81.9%

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

   4. Taylor expanded in y around 0 59.0%

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

   5. Taylor expanded in z around 0 40.0%

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

      1. rem-cbrt-cube 40.1%

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

      2. sub-neg 40.1%

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

      3. quot-tan 40.1%

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

   7. Applied egg-rr 40.1%

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

      1. sub-neg 40.1%

         \[\leadsto \color{blue}{x - \tan a} \]

   9. Simplified 40.1%

      \[\leadsto \color{blue}{x - \tan a} \]

   if -7.00000000000000042e30 < a < 0.0800000000000000017

   1. Initial program 77.4%

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

      1. +-commutative 77.4%

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

      2. associate-+l- 77.4%

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

   3. Applied egg-rr 77.4%

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

   4. Taylor expanded in a around 0 75.9%

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

      1. neg-mul-1 75.9%

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

      2. unsub-neg 75.9%

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

   6. Simplified 75.9%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+30} \lor \neg \left(a \leq 0.08\right):\\ \;\;\;\;x - \tan a\\ \mathbf{else}:\\ \;\;\;\;\tan \left(y + z\right) + \left(x - a\right)\\ \end{array} \]

Alternative 14: 41.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x - \tan a \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a) :precision binary64 (- x (tan a)))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x - tan(a);
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x - tan(a)
end function

Java

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

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return x - math.tan(a)

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x - tan(a))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x - tan(a);
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.8%

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

   1. add-cbrt-cube 79.3%

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

   2. pow3 79.3%

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

   3. +-commutative 79.3%

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

   4. associate-+l- 79.3%

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

3. Applied egg-rr 79.3%

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

4. Taylor expanded in y around 0 59.6%

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

5. Taylor expanded in z around 0 38.2%

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

   1. rem-cbrt-cube 38.4%

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

   2. sub-neg 38.4%

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

   3. quot-tan 38.4%

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

7. Applied egg-rr 38.4%

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

   1. sub-neg 38.4%

      \[\leadsto \color{blue}{x - \tan a} \]

9. Simplified 38.4%

   \[\leadsto \color{blue}{x - \tan a} \]

10. Final simplification 38.4%

    \[\leadsto x - \tan a \]

Alternative 15: 31.6% accurate, 207.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a) :precision binary64 x)

C

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

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
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

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

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return x

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return x
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := x

Derivation

1. Initial program 79.8%

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

2. Taylor expanded in x around inf 29.5%

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

3. Final simplification 29.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023322 
(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))))