tan-example (used to crash)

Percentage Accurate: 79.0% → 99.7%

Time: 56.1s

Alternatives: 11

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, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.6%

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

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

Alternative 2: 88.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -5 \cdot 10^{-11}:\\ \;\;\;\;x + \left(\frac{1}{\frac{1}{\tan \left(y + z\right)}} - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 10^{-21}:\\ \;\;\;\;\left(x - a\right) + \left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\cos \left(y + z\right)} \cdot \sin \left(y + z\right) - \tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= (tan a) -5e-11)
   (+ x (- (/ 1.0 (/ 1.0 (tan (+ y z)))) (tan a)))
   (if (<= (tan a) 1e-21)
     (+ (- x a) (* (+ (tan y) (tan z)) (/ 1.0 (- 1.0 (* (tan y) (tan z))))))
     (+ x (- (* (/ 1.0 (cos (+ y z))) (sin (+ y z))) (tan a))))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (tan(a) <= -5e-11) {
		tmp = x + ((1.0 / (1.0 / tan((y + z)))) - tan(a));
	} else if (tan(a) <= 1e-21) {
		tmp = (x - a) + ((tan(y) + tan(z)) * (1.0 / (1.0 - (tan(y) * tan(z)))));
	} else {
		tmp = x + (((1.0 / cos((y + z))) * sin((y + z))) - tan(a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (tan(a) <= (-5d-11)) then
        tmp = x + ((1.0d0 / (1.0d0 / tan((y + z)))) - tan(a))
    else if (tan(a) <= 1d-21) then
        tmp = (x - a) + ((tan(y) + tan(z)) * (1.0d0 / (1.0d0 - (tan(y) * tan(z)))))
    else
        tmp = x + (((1.0d0 / cos((y + z))) * sin((y + z))) - tan(a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (Math.tan(a) <= -5e-11) {
		tmp = x + ((1.0 / (1.0 / Math.tan((y + z)))) - Math.tan(a));
	} else if (Math.tan(a) <= 1e-21) {
		tmp = (x - a) + ((Math.tan(y) + Math.tan(z)) * (1.0 / (1.0 - (Math.tan(y) * Math.tan(z)))));
	} else {
		tmp = x + (((1.0 / Math.cos((y + z))) * Math.sin((y + z))) - Math.tan(a));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if math.tan(a) <= -5e-11:
		tmp = x + ((1.0 / (1.0 / math.tan((y + z)))) - math.tan(a))
	elif math.tan(a) <= 1e-21:
		tmp = (x - a) + ((math.tan(y) + math.tan(z)) * (1.0 / (1.0 - (math.tan(y) * math.tan(z)))))
	else:
		tmp = x + (((1.0 / math.cos((y + z))) * math.sin((y + z))) - math.tan(a))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (tan(a) <= -5e-11)
		tmp = Float64(x + Float64(Float64(1.0 / Float64(1.0 / tan(Float64(y + z)))) - tan(a)));
	elseif (tan(a) <= 1e-21)
		tmp = Float64(Float64(x - a) + Float64(Float64(tan(y) + tan(z)) * Float64(1.0 / Float64(1.0 - Float64(tan(y) * tan(z))))));
	else
		tmp = Float64(x + Float64(Float64(Float64(1.0 / cos(Float64(y + z))) * sin(Float64(y + z))) - tan(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (tan(a) <= -5e-11)
		tmp = x + ((1.0 / (1.0 / tan((y + z)))) - tan(a));
	elseif (tan(a) <= 1e-21)
		tmp = (x - a) + ((tan(y) + tan(z)) * (1.0 / (1.0 - (tan(y) * tan(z)))));
	else
		tmp = x + (((1.0 / cos((y + z))) * sin((y + z))) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[N[Tan[a], $MachinePrecision], -5e-11], N[(x + N[(N[(1.0 / N[(1.0 / N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Tan[a], $MachinePrecision], 1e-21], N[(N[(x - a), $MachinePrecision] + 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[(N[(N[(1.0 / N[Cos[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Sin[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 86.0%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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. clear-num 99.7%

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

      3. clear-num 99.7%

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

      4. tan-sum 86.1%

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

   3. Applied egg-rr 86.1%

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

   if -5.00000000000000018e-11 < (tan.f64 a) < 9.99999999999999908e-22

   1. Initial program 80.5%

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

      1. associate-+r- 80.5%

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

      2. +-commutative 80.5%

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

      3. associate--l+ 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in a around 0 80.5%

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

      1. mul-1-neg 80.5%

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

      2. unsub-neg 80.5%

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

   6. Simplified 80.5%

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

      1. tan-sum 99.8%

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

      2. div-inv 99.8%

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

      3. *-commutative 99.8%

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

   8. Applied egg-rr 99.8%

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

   if 9.99999999999999908e-22 < (tan.f64 a)

   1. Initial program 83.4%

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

      1. tan-quot 83.5%

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

      2. div-inv 83.5%

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

      3. *-commutative 83.5%

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

   3. Applied egg-rr 83.5%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -5 \cdot 10^{-11}:\\ \;\;\;\;x + \left(\frac{1}{\frac{1}{\tan \left(y + z\right)}} - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 10^{-21}:\\ \;\;\;\;\left(x - a\right) + \left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\cos \left(y + z\right)} \cdot \sin \left(y + z\right) - \tan a\right)\\ \end{array} \]

Alternative 3: 88.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -5 \cdot 10^{-11}:\\ \;\;\;\;x + \left(\frac{1}{\frac{1}{\tan \left(y + z\right)}} - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 10^{-21}:\\ \;\;\;\;\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} + \left(x - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\cos \left(y + z\right)} \cdot \sin \left(y + z\right) - \tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= (tan a) -5e-11)
   (+ x (- (/ 1.0 (/ 1.0 (tan (+ y z)))) (tan a)))
   (if (<= (tan a) 1e-21)
     (+ (/ (+ (tan y) (tan z)) (- 1.0 (* (tan y) (tan z)))) (- x a))
     (+ x (- (* (/ 1.0 (cos (+ y z))) (sin (+ y z))) (tan a))))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (tan(a) <= -5e-11) {
		tmp = x + ((1.0 / (1.0 / tan((y + z)))) - tan(a));
	} else if (tan(a) <= 1e-21) {
		tmp = ((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) + (x - a);
	} else {
		tmp = x + (((1.0 / cos((y + z))) * sin((y + z))) - tan(a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (tan(a) <= (-5d-11)) then
        tmp = x + ((1.0d0 / (1.0d0 / tan((y + z)))) - tan(a))
    else if (tan(a) <= 1d-21) then
        tmp = ((tan(y) + tan(z)) / (1.0d0 - (tan(y) * tan(z)))) + (x - a)
    else
        tmp = x + (((1.0d0 / cos((y + z))) * sin((y + z))) - tan(a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (Math.tan(a) <= -5e-11) {
		tmp = x + ((1.0 / (1.0 / Math.tan((y + z)))) - Math.tan(a));
	} else if (Math.tan(a) <= 1e-21) {
		tmp = ((Math.tan(y) + Math.tan(z)) / (1.0 - (Math.tan(y) * Math.tan(z)))) + (x - a);
	} else {
		tmp = x + (((1.0 / Math.cos((y + z))) * Math.sin((y + z))) - Math.tan(a));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if math.tan(a) <= -5e-11:
		tmp = x + ((1.0 / (1.0 / math.tan((y + z)))) - math.tan(a))
	elif math.tan(a) <= 1e-21:
		tmp = ((math.tan(y) + math.tan(z)) / (1.0 - (math.tan(y) * math.tan(z)))) + (x - a)
	else:
		tmp = x + (((1.0 / math.cos((y + z))) * math.sin((y + z))) - math.tan(a))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (tan(a) <= -5e-11)
		tmp = Float64(x + Float64(Float64(1.0 / Float64(1.0 / tan(Float64(y + z)))) - tan(a)));
	elseif (tan(a) <= 1e-21)
		tmp = Float64(Float64(Float64(tan(y) + tan(z)) / Float64(1.0 - Float64(tan(y) * tan(z)))) + Float64(x - a));
	else
		tmp = Float64(x + Float64(Float64(Float64(1.0 / cos(Float64(y + z))) * sin(Float64(y + z))) - tan(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (tan(a) <= -5e-11)
		tmp = x + ((1.0 / (1.0 / tan((y + z)))) - tan(a));
	elseif (tan(a) <= 1e-21)
		tmp = ((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) + (x - a);
	else
		tmp = x + (((1.0 / cos((y + z))) * sin((y + z))) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[N[Tan[a], $MachinePrecision], -5e-11], N[(x + N[(N[(1.0 / N[(1.0 / N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Tan[a], $MachinePrecision], 1e-21], N[(N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(1.0 / N[Cos[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Sin[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 86.0%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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. clear-num 99.7%

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

      3. clear-num 99.7%

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

      4. tan-sum 86.1%

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

   3. Applied egg-rr 86.1%

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

   if -5.00000000000000018e-11 < (tan.f64 a) < 9.99999999999999908e-22

   1. Initial program 80.5%

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

      1. associate-+r- 80.5%

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

      2. +-commutative 80.5%

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

      3. associate--l+ 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in a around 0 80.5%

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

      1. mul-1-neg 80.5%

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

      2. unsub-neg 80.5%

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

   6. Simplified 80.5%

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

      1. tan-sum 99.8%

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

      2. div-inv 99.8%

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

   8. Applied egg-rr 99.8%

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

      1. associate-*r/ 99.8%

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

      2. *-rgt-identity 99.8%

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

   10. Simplified 99.8%

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

   if 9.99999999999999908e-22 < (tan.f64 a)

   1. Initial program 83.4%

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

      1. tan-quot 83.5%

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

      2. div-inv 83.5%

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

      3. *-commutative 83.5%

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

   3. Applied egg-rr 83.5%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -5 \cdot 10^{-11}:\\ \;\;\;\;x + \left(\frac{1}{\frac{1}{\tan \left(y + z\right)}} - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 10^{-21}:\\ \;\;\;\;\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} + \left(x - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\cos \left(y + z\right)} \cdot \sin \left(y + z\right) - \tan a\right)\\ \end{array} \]

Alternative 4: 88.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -0.001:\\ \;\;\;\;x + \left(\frac{1}{\frac{1}{\tan \left(y + z\right)}} - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 10^{-21}:\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\cos \left(y + z\right)} \cdot \sin \left(y + z\right) - \tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= (tan a) -0.001)
   (+ x (- (/ 1.0 (/ 1.0 (tan (+ y z)))) (tan a)))
   (if (<= (tan a) 1e-21)
     (+ x (- (/ (+ (tan y) (tan z)) (- 1.0 (* (tan y) (tan z)))) a))
     (+ x (- (* (/ 1.0 (cos (+ y z))) (sin (+ y z))) (tan a))))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (tan(a) <= -0.001) {
		tmp = x + ((1.0 / (1.0 / tan((y + z)))) - tan(a));
	} else if (tan(a) <= 1e-21) {
		tmp = x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) - a);
	} else {
		tmp = x + (((1.0 / cos((y + z))) * sin((y + z))) - tan(a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (tan(a) <= (-0.001d0)) then
        tmp = x + ((1.0d0 / (1.0d0 / tan((y + z)))) - tan(a))
    else if (tan(a) <= 1d-21) then
        tmp = x + (((tan(y) + tan(z)) / (1.0d0 - (tan(y) * tan(z)))) - a)
    else
        tmp = x + (((1.0d0 / cos((y + z))) * sin((y + z))) - tan(a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (Math.tan(a) <= -0.001) {
		tmp = x + ((1.0 / (1.0 / Math.tan((y + z)))) - Math.tan(a));
	} else if (Math.tan(a) <= 1e-21) {
		tmp = x + (((Math.tan(y) + Math.tan(z)) / (1.0 - (Math.tan(y) * Math.tan(z)))) - a);
	} else {
		tmp = x + (((1.0 / Math.cos((y + z))) * Math.sin((y + z))) - Math.tan(a));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if math.tan(a) <= -0.001:
		tmp = x + ((1.0 / (1.0 / math.tan((y + z)))) - math.tan(a))
	elif math.tan(a) <= 1e-21:
		tmp = x + (((math.tan(y) + math.tan(z)) / (1.0 - (math.tan(y) * math.tan(z)))) - a)
	else:
		tmp = x + (((1.0 / math.cos((y + z))) * math.sin((y + z))) - math.tan(a))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (tan(a) <= -0.001)
		tmp = Float64(x + Float64(Float64(1.0 / Float64(1.0 / tan(Float64(y + z)))) - tan(a)));
	elseif (tan(a) <= 1e-21)
		tmp = Float64(x + Float64(Float64(Float64(tan(y) + tan(z)) / Float64(1.0 - Float64(tan(y) * tan(z)))) - a));
	else
		tmp = Float64(x + Float64(Float64(Float64(1.0 / cos(Float64(y + z))) * sin(Float64(y + z))) - tan(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (tan(a) <= -0.001)
		tmp = x + ((1.0 / (1.0 / tan((y + z)))) - tan(a));
	elseif (tan(a) <= 1e-21)
		tmp = x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) - a);
	else
		tmp = x + (((1.0 / cos((y + z))) * sin((y + z))) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[N[Tan[a], $MachinePrecision], -0.001], N[(x + N[(N[(1.0 / N[(1.0 / N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Tan[a], $MachinePrecision], 1e-21], N[(x + N[(N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(1.0 / N[Cos[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Sin[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 85.6%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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. clear-num 99.7%

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

      3. clear-num 99.7%

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

      4. tan-sum 85.6%

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

   3. Applied egg-rr 85.6%

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

   if -1e-3 < (tan.f64 a) < 9.99999999999999908e-22

   1. Initial program 80.8%

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

      1. associate-+r- 80.8%

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

      2. +-commutative 80.8%

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

      3. associate--l+ 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in a around 0 80.8%

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

      1. mul-1-neg 80.8%

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

      2. unsub-neg 80.8%

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

   6. Simplified 80.8%

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

      1. +-commutative 80.8%

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

      2. associate-+l- 80.8%

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

   8. Applied egg-rr 80.8%

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

      1. tan-sum 99.8%

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

      2. div-inv 99.8%

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

   10. Applied egg-rr 99.8%

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

       1. associate-*r/ 99.8%

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

       2. *-rgt-identity 99.8%

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

   12. Simplified 99.8%

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

   if 9.99999999999999908e-22 < (tan.f64 a)

   1. Initial program 83.4%

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

      1. tan-quot 83.5%

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

      2. div-inv 83.5%

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

      3. *-commutative 83.5%

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

   3. Applied egg-rr 83.5%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.001:\\ \;\;\;\;x + \left(\frac{1}{\frac{1}{\tan \left(y + z\right)}} - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 10^{-21}:\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\cos \left(y + z\right)} \cdot \sin \left(y + z\right) - \tan a\right)\\ \end{array} \]

Alternative 5: 88.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan y + \tan z\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{-11} \lor \neg \left(a \leq 8.5 \cdot 10^{-50}\right):\\ \;\;\;\;x + \left(\frac{t_0}{1 - \frac{\tan y}{z \cdot -0.3333333333333333 + \frac{1}{z}}} - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{\mathsf{fma}\left(\tan y, -\tan z, 1\right)} + \left(x - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (+ (tan y) (tan z))))
   (if (or (<= a -5.8e-11) (not (<= a 8.5e-50)))
     (+
      x
      (-
       (/ t_0 (- 1.0 (/ (tan y) (+ (* z -0.3333333333333333) (/ 1.0 z)))))
       (tan a)))
     (+ (/ t_0 (fma (tan y) (- (tan z)) 1.0)) (- x a)))))

C

double code(double x, double y, double z, double a) {
	double t_0 = tan(y) + tan(z);
	double tmp;
	if ((a <= -5.8e-11) || !(a <= 8.5e-50)) {
		tmp = x + ((t_0 / (1.0 - (tan(y) / ((z * -0.3333333333333333) + (1.0 / z))))) - tan(a));
	} else {
		tmp = (t_0 / fma(tan(y), -tan(z), 1.0)) + (x - a);
	}
	return tmp;
}

Julia

function code(x, y, z, a)
	t_0 = Float64(tan(y) + tan(z))
	tmp = 0.0
	if ((a <= -5.8e-11) || !(a <= 8.5e-50))
		tmp = Float64(x + Float64(Float64(t_0 / Float64(1.0 - Float64(tan(y) / Float64(Float64(z * -0.3333333333333333) + Float64(1.0 / z))))) - tan(a)));
	else
		tmp = Float64(Float64(t_0 / fma(tan(y), Float64(-tan(z)), 1.0)) + Float64(x - a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, a_] := Block[{t$95$0 = N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -5.8e-11], N[Not[LessEqual[a, 8.5e-50]], $MachinePrecision]], N[(x + N[(N[(t$95$0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] / N[(N[(z * -0.3333333333333333), $MachinePrecision] + N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$0 / N[(N[Tan[y], $MachinePrecision] * (-N[Tan[z], $MachinePrecision]) + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.8e-11 or 8.50000000000000012e-50 < a

   1. Initial program 85.2%

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

      1. tan-sum 99.6%

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

      2. div-inv 99.6%

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

   3. Applied egg-rr 99.6%

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

      1. associate-*r/ 99.6%

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

      2. *-rgt-identity 99.6%

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

   5. Simplified 99.6%

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

      1. tan-quot 99.6%

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

      2. clear-num 99.6%

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

      3. un-div-inv 99.6%

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

      4. clear-num 99.6%

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

      5. tan-quot 99.6%

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

   7. Applied egg-rr 99.6%

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

   8. Taylor expanded in z around 0 85.5%

      \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \frac{\tan y}{\color{blue}{-0.3333333333333333 \cdot z + \frac{1}{z}}}} - \tan a\right) \]

   if -5.8e-11 < a < 8.50000000000000012e-50

   1. Initial program 79.7%

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

      1. associate-+r- 79.7%

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

      2. +-commutative 79.7%

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

      3. associate--l+ 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in a around 0 79.7%

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

      1. mul-1-neg 79.7%

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

      2. unsub-neg 79.7%

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

   6. Simplified 79.7%

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

      1. tan-sum 99.8%

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

      2. div-inv 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. fma-def 99.8%

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

   8. Applied egg-rr 99.8%

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

      1. fma-udef 99.8%

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

      2. associate-*r/ 99.8%

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

      3. *-rgt-identity 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-11} \lor \neg \left(a \leq 8.5 \cdot 10^{-50}\right):\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 - \frac{\tan y}{z \cdot -0.3333333333333333 + \frac{1}{z}}} - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan y + \tan z}{\mathsf{fma}\left(\tan y, -\tan z, 1\right)} + \left(x - a\right)\\ \end{array} \]

Alternative 6: 88.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan y + \tan z\\ \mathbf{if}\;a \leq -5.8 \cdot 10^{-11} \lor \neg \left(a \leq 8 \cdot 10^{-50}\right):\\ \;\;\;\;x + \left(\frac{t_0}{1 - \frac{\tan y}{z \cdot -0.3333333333333333 + \frac{1}{z}}} - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - a\right) + t_0 \cdot \frac{1}{1 - \tan y \cdot \tan z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (+ (tan y) (tan z))))
   (if (or (<= a -5.8e-11) (not (<= a 8e-50)))
     (+
      x
      (-
       (/ t_0 (- 1.0 (/ (tan y) (+ (* z -0.3333333333333333) (/ 1.0 z)))))
       (tan a)))
     (+ (- x a) (* t_0 (/ 1.0 (- 1.0 (* (tan y) (tan z)))))))))

C

double code(double x, double y, double z, double a) {
	double t_0 = tan(y) + tan(z);
	double tmp;
	if ((a <= -5.8e-11) || !(a <= 8e-50)) {
		tmp = x + ((t_0 / (1.0 - (tan(y) / ((z * -0.3333333333333333) + (1.0 / z))))) - tan(a));
	} else {
		tmp = (x - a) + (t_0 * (1.0 / (1.0 - (tan(y) * tan(z)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: t_0
    real(8) :: tmp
    t_0 = tan(y) + tan(z)
    if ((a <= (-5.8d-11)) .or. (.not. (a <= 8d-50))) then
        tmp = x + ((t_0 / (1.0d0 - (tan(y) / ((z * (-0.3333333333333333d0)) + (1.0d0 / z))))) - tan(a))
    else
        tmp = (x - a) + (t_0 * (1.0d0 / (1.0d0 - (tan(y) * tan(z)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double t_0 = Math.tan(y) + Math.tan(z);
	double tmp;
	if ((a <= -5.8e-11) || !(a <= 8e-50)) {
		tmp = x + ((t_0 / (1.0 - (Math.tan(y) / ((z * -0.3333333333333333) + (1.0 / z))))) - Math.tan(a));
	} else {
		tmp = (x - a) + (t_0 * (1.0 / (1.0 - (Math.tan(y) * Math.tan(z)))));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	t_0 = math.tan(y) + math.tan(z)
	tmp = 0
	if (a <= -5.8e-11) or not (a <= 8e-50):
		tmp = x + ((t_0 / (1.0 - (math.tan(y) / ((z * -0.3333333333333333) + (1.0 / z))))) - math.tan(a))
	else:
		tmp = (x - a) + (t_0 * (1.0 / (1.0 - (math.tan(y) * math.tan(z)))))
	return tmp

Julia

function code(x, y, z, a)
	t_0 = Float64(tan(y) + tan(z))
	tmp = 0.0
	if ((a <= -5.8e-11) || !(a <= 8e-50))
		tmp = Float64(x + Float64(Float64(t_0 / Float64(1.0 - Float64(tan(y) / Float64(Float64(z * -0.3333333333333333) + Float64(1.0 / z))))) - tan(a)));
	else
		tmp = Float64(Float64(x - a) + Float64(t_0 * Float64(1.0 / Float64(1.0 - Float64(tan(y) * tan(z))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	t_0 = tan(y) + tan(z);
	tmp = 0.0;
	if ((a <= -5.8e-11) || ~((a <= 8e-50)))
		tmp = x + ((t_0 / (1.0 - (tan(y) / ((z * -0.3333333333333333) + (1.0 / z))))) - tan(a));
	else
		tmp = (x - a) + (t_0 * (1.0 / (1.0 - (tan(y) * tan(z)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := Block[{t$95$0 = N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -5.8e-11], N[Not[LessEqual[a, 8e-50]], $MachinePrecision]], N[(x + N[(N[(t$95$0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] / N[(N[(z * -0.3333333333333333), $MachinePrecision] + N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - a), $MachinePrecision] + N[(t$95$0 * N[(1.0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.8e-11 or 8.00000000000000006e-50 < a

   1. Initial program 85.2%

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

      1. tan-sum 99.6%

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

      2. div-inv 99.6%

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

   3. Applied egg-rr 99.6%

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

      1. associate-*r/ 99.6%

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

      2. *-rgt-identity 99.6%

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

   5. Simplified 99.6%

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

      1. tan-quot 99.6%

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

      2. clear-num 99.6%

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

      3. un-div-inv 99.6%

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

      4. clear-num 99.6%

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

      5. tan-quot 99.6%

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

   7. Applied egg-rr 99.6%

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

   8. Taylor expanded in z around 0 85.5%

      \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \frac{\tan y}{\color{blue}{-0.3333333333333333 \cdot z + \frac{1}{z}}}} - \tan a\right) \]

   if -5.8e-11 < a < 8.00000000000000006e-50

   1. Initial program 79.7%

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

      1. associate-+r- 79.7%

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

      2. +-commutative 79.7%

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

      3. associate--l+ 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in a around 0 79.7%

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

      1. mul-1-neg 79.7%

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

      2. unsub-neg 79.7%

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

   6. Simplified 79.7%

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

      1. tan-sum 99.8%

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

      2. div-inv 99.8%

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

      3. *-commutative 99.8%

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

   8. Applied egg-rr 99.8%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-11} \lor \neg \left(a \leq 8 \cdot 10^{-50}\right):\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 - \frac{\tan y}{z \cdot -0.3333333333333333 + \frac{1}{z}}} - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - a\right) + \left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}\\ \end{array} \]

Alternative 7: 79.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.6%

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

2. Final simplification 82.6%

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

Alternative 8: 50.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5:\\ \;\;\;\;e^{-\log \left(\frac{1}{x}\right)}\\ \mathbf{elif}\;a \leq 1.55:\\ \;\;\;\;x - \left(a - \tan \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= a -1.5)
   (exp (- (log (/ 1.0 x))))
   (if (<= a 1.55) (- x (- a (tan (+ y z)))) x)))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.5) {
		tmp = exp(-log((1.0 / x)));
	} else if (a <= 1.55) {
		tmp = x - (a - tan((y + z)));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.5d0)) then
        tmp = exp(-log((1.0d0 / x)))
    else if (a <= 1.55d0) then
        tmp = x - (a - tan((y + z)))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.5) {
		tmp = Math.exp(-Math.log((1.0 / x)));
	} else if (a <= 1.55) {
		tmp = x - (a - Math.tan((y + z)));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if a <= -1.5:
		tmp = math.exp(-math.log((1.0 / x)))
	elif a <= 1.55:
		tmp = x - (a - math.tan((y + z)))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (a <= -1.5)
		tmp = exp(Float64(-log(Float64(1.0 / x))));
	elseif (a <= 1.55)
		tmp = Float64(x - Float64(a - tan(Float64(y + z))));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -1.5)
		tmp = exp(-log((1.0 / x)));
	elseif (a <= 1.55)
		tmp = x - (a - tan((y + z)));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[a, -1.5], N[Exp[(-N[Log[N[(1.0 / x), $MachinePrecision]], $MachinePrecision])], $MachinePrecision], If[LessEqual[a, 1.55], N[(x - N[(a - N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if a < -1.5

   1. Initial program 83.2%

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

      1. associate-+r- 83.2%

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

      2. +-commutative 83.2%

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

      3. associate--l+ 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in a around 0 5.5%

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

      1. mul-1-neg 5.5%

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

      2. unsub-neg 5.5%

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

   6. Simplified 5.5%

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

      1. add-exp-log_binary64 5.5%

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

   8. Applied rewrite-once 5.5%

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

   9. Taylor expanded in x around inf 20.9%

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

   if -1.5 < a < 1.55000000000000004

   1. Initial program 81.8%

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

      1. associate-+r- 81.8%

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

      2. +-commutative 81.8%

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

      3. associate--l+ 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in a around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. unsub-neg 81.2%

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

   6. Simplified 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-+l- 81.3%

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

   8. Applied egg-rr 81.3%

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

   if 1.55000000000000004 < a

   1. Initial program 83.8%

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

   2. Taylor expanded in x around inf 22.0%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5:\\ \;\;\;\;e^{-\log \left(\frac{1}{x}\right)}\\ \mathbf{elif}\;a \leq 1.55:\\ \;\;\;\;x - \left(a - \tan \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 50.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.55:\\ \;\;\;\;\left(x - a\right) + \tan \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= a -1.6) x (if (<= a 1.55) (+ (- x a) (tan (+ y z))) x)))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.6) {
		tmp = x;
	} else if (a <= 1.55) {
		tmp = (x - a) + tan((y + z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.6d0)) then
        tmp = x
    else if (a <= 1.55d0) then
        tmp = (x - a) + tan((y + z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.6) {
		tmp = x;
	} else if (a <= 1.55) {
		tmp = (x - a) + Math.tan((y + z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if a <= -1.6:
		tmp = x
	elif a <= 1.55:
		tmp = (x - a) + math.tan((y + z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (a <= -1.6)
		tmp = x;
	elseif (a <= 1.55)
		tmp = Float64(Float64(x - a) + tan(Float64(y + z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -1.6)
		tmp = x;
	elseif (a <= 1.55)
		tmp = (x - a) + tan((y + z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[a, -1.6], x, If[LessEqual[a, 1.55], N[(N[(x - a), $MachinePrecision] + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6000000000000001 or 1.55000000000000004 < a

   1. Initial program 83.5%

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

   2. Taylor expanded in x around inf 21.5%

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

   if -1.6000000000000001 < a < 1.55000000000000004

   1. Initial program 81.8%

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

      1. associate-+r- 81.8%

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

      2. +-commutative 81.8%

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

      3. associate--l+ 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in a around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. unsub-neg 81.2%

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

   6. Simplified 81.2%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.55:\\ \;\;\;\;\left(x - a\right) + \tan \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 50.3% accurate, 1.9× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.55) {
		tmp = x;
	} else if (a <= 1.55) {
		tmp = x - (a - tan((y + z)));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.55d0)) then
        tmp = x
    else if (a <= 1.55d0) then
        tmp = x - (a - tan((y + z)))
    else
        tmp = x
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if a < -1.55000000000000004 or 1.55000000000000004 < a

   1. Initial program 83.5%

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

   2. Taylor expanded in x around inf 21.5%

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

   if -1.55000000000000004 < a < 1.55000000000000004

   1. Initial program 81.8%

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

      1. associate-+r- 81.8%

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

      2. +-commutative 81.8%

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

      3. associate--l+ 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in a around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. unsub-neg 81.2%

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

   6. Simplified 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-+l- 81.3%

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

   8. Applied egg-rr 81.3%

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

4. Final simplification 52.8%

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

Alternative 11: 31.4% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x
end function

Java

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

Python

def code(x, y, z, a):
	return x

Julia

function code(x, y, z, a)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, a_] := x

Derivation

1. Initial program 82.6%

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

2. Taylor expanded in x around inf 31.9%

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

3. Final simplification 31.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023297 
(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))))