tan-example (used to crash)

Percentage Accurate: 79.3% → 99.7%

Time: 31.5s

Alternatives: 14

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: 79.3% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.2%

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

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

4. Applied egg-rr 99.7%

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

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

6. Simplified 99.7%

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

Alternative 2: 89.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan y + \tan z\\ \mathbf{if}\;\tan a \leq -5 \cdot 10^{-5}:\\ \;\;\;\;\tan \left(y + z\right) + \left(x - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 5 \cdot 10^{-15}:\\ \;\;\;\;x - \left(a + \frac{t\_0}{-1 + \tan y \cdot \tan z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(t\_0, 1, -\tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (+ (tan y) (tan z))))
   (if (<= (tan a) -5e-5)
     (+ (tan (+ y z)) (- x (tan a)))
     (if (<= (tan a) 5e-15)
       (- x (+ a (/ t_0 (+ -1.0 (* (tan y) (tan z))))))
       (+ x (fma t_0 1.0 (- (tan a))))))))

C

double code(double x, double y, double z, double a) {
	double t_0 = tan(y) + tan(z);
	double tmp;
	if (tan(a) <= -5e-5) {
		tmp = tan((y + z)) + (x - tan(a));
	} else if (tan(a) <= 5e-15) {
		tmp = x - (a + (t_0 / (-1.0 + (tan(y) * tan(z)))));
	} else {
		tmp = x + fma(t_0, 1.0, -tan(a));
	}
	return tmp;
}

Julia

function code(x, y, z, a)
	t_0 = Float64(tan(y) + tan(z))
	tmp = 0.0
	if (tan(a) <= -5e-5)
		tmp = Float64(tan(Float64(y + z)) + Float64(x - tan(a)));
	elseif (tan(a) <= 5e-15)
		tmp = Float64(x - Float64(a + Float64(t_0 / Float64(-1.0 + Float64(tan(y) * tan(z))))));
	else
		tmp = Float64(x + fma(t_0, 1.0, Float64(-tan(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[LessEqual[N[Tan[a], $MachinePrecision], -5e-5], N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] + N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Tan[a], $MachinePrecision], 5e-15], N[(x - N[(a + N[(t$95$0 / N[(-1.0 + N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$0 * 1.0 + (-N[Tan[a], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (tan.f64 a) < -5.00000000000000024e-5

   1. Initial program 80.9%

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

      1. +-commutative 80.9%

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

      2. associate-+l- 81.0%

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

   4. Applied egg-rr 81.0%

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

   if -5.00000000000000024e-5 < (tan.f64 a) < 4.99999999999999999e-15

   1. Initial program 85.2%

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

   3. Taylor expanded in a around 0 85.2%

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

      1. tan-sum 99.8%

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

      2. div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. associate-*r/ 99.8%

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

      2. *-rgt-identity 99.8%

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

   7. Simplified 99.8%

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

   if 4.99999999999999999e-15 < (tan.f64 a)

   1. Initial program 81.9%

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

      1. tan-sum 99.5%

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

      2. div-inv 99.5%

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

      3. fma-neg 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in y around 0 82.5%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -5 \cdot 10^{-5}:\\ \;\;\;\;\tan \left(y + z\right) + \left(x - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 5 \cdot 10^{-15}:\\ \;\;\;\;x - \left(a + \frac{\tan y + \tan z}{-1 + \tan y \cdot \tan z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\tan y + \tan z, 1, -\tan a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -0.1 \lor \neg \left(\tan a \leq 0.0004\right):\\ \;\;\;\;x + \left(\sin y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= (tan a) -0.1) (not (<= (tan a) 0.0004)))
   (+ x (- (sin y) (tan a)))
   (- (+ x (tan (+ y z))) a)))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((tan(a) <= -0.1) || !(tan(a) <= 0.0004)) {
		tmp = x + (sin(y) - tan(a));
	} else {
		tmp = (x + tan((y + z))) - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((tan(a) <= (-0.1d0)) .or. (.not. (tan(a) <= 0.0004d0))) then
        tmp = x + (sin(y) - tan(a))
    else
        tmp = (x + tan((y + z))) - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((Math.tan(a) <= -0.1) || !(Math.tan(a) <= 0.0004)) {
		tmp = x + (Math.sin(y) - Math.tan(a));
	} else {
		tmp = (x + Math.tan((y + z))) - a;
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (math.tan(a) <= -0.1) or not (math.tan(a) <= 0.0004):
		tmp = x + (math.sin(y) - math.tan(a))
	else:
		tmp = (x + math.tan((y + z))) - a
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((tan(a) <= -0.1) || !(tan(a) <= 0.0004))
		tmp = Float64(x + Float64(sin(y) - tan(a)));
	else
		tmp = Float64(Float64(x + tan(Float64(y + z))) - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((tan(a) <= -0.1) || ~((tan(a) <= 0.0004)))
		tmp = x + (sin(y) - tan(a));
	else
		tmp = (x + tan((y + z))) - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[N[Tan[a], $MachinePrecision], -0.1], N[Not[LessEqual[N[Tan[a], $MachinePrecision], 0.0004]], $MachinePrecision]], N[(x + N[(N[Sin[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (tan.f64 a) < -0.10000000000000001 or 4.00000000000000019e-4 < (tan.f64 a)

   1. Initial program 81.0%

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

      1. tan-quot 81.0%

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

      2. clear-num 81.0%

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

   4. Applied egg-rr 81.0%

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

   5. Taylor expanded in y around 0 59.4%

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

   6. Taylor expanded in z around 0 44.0%

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

   if -0.10000000000000001 < (tan.f64 a) < 4.00000000000000019e-4

   1. Initial program 85.5%

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

   3. Taylor expanded in a around 0 85.3%

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

      1. associate-+r- 85.3%

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

   5. Applied egg-rr 85.3%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.1 \lor \neg \left(\tan a \leq 0.0004\right):\\ \;\;\;\;x + \left(\sin y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -0.1:\\ \;\;\;\;x + \left(\sin z - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 0.0004:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \mathbf{else}:\\ \;\;\;\;x + \left(\sin y - \tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= (tan a) -0.1)
   (+ x (- (sin z) (tan a)))
   (if (<= (tan a) 0.0004)
     (- (+ x (tan (+ y z))) a)
     (+ x (- (sin y) (tan a))))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (tan(a) <= -0.1) {
		tmp = x + (sin(z) - tan(a));
	} else if (tan(a) <= 0.0004) {
		tmp = (x + tan((y + z))) - a;
	} else {
		tmp = x + (sin(y) - 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) <= (-0.1d0)) then
        tmp = x + (sin(z) - tan(a))
    else if (tan(a) <= 0.0004d0) then
        tmp = (x + tan((y + z))) - a
    else
        tmp = x + (sin(y) - 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) <= -0.1) {
		tmp = x + (Math.sin(z) - Math.tan(a));
	} else if (Math.tan(a) <= 0.0004) {
		tmp = (x + Math.tan((y + z))) - a;
	} else {
		tmp = x + (Math.sin(y) - Math.tan(a));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if math.tan(a) <= -0.1:
		tmp = x + (math.sin(z) - math.tan(a))
	elif math.tan(a) <= 0.0004:
		tmp = (x + math.tan((y + z))) - a
	else:
		tmp = x + (math.sin(y) - math.tan(a))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (tan(a) <= -0.1)
		tmp = Float64(x + Float64(sin(z) - tan(a)));
	elseif (tan(a) <= 0.0004)
		tmp = Float64(Float64(x + tan(Float64(y + z))) - a);
	else
		tmp = Float64(x + Float64(sin(y) - tan(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (tan(a) <= -0.1)
		tmp = x + (sin(z) - tan(a));
	elseif (tan(a) <= 0.0004)
		tmp = (x + tan((y + z))) - a;
	else
		tmp = x + (sin(y) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[N[Tan[a], $MachinePrecision], -0.1], N[(x + N[(N[Sin[z], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Tan[a], $MachinePrecision], 0.0004], N[(N[(x + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision], N[(x + N[(N[Sin[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (tan.f64 a) < -0.10000000000000001

   1. Initial program 80.3%

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

      1. tan-quot 80.4%

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

      2. clear-num 80.4%

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

   4. Applied egg-rr 80.4%

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

   5. Taylor expanded in z around 0 63.1%

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

   6. Taylor expanded in y around 0 42.9%

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

   if -0.10000000000000001 < (tan.f64 a) < 4.00000000000000019e-4

   1. Initial program 85.5%

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

   3. Taylor expanded in a around 0 85.3%

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

      1. associate-+r- 85.3%

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

   5. Applied egg-rr 85.3%

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

   if 4.00000000000000019e-4 < (tan.f64 a)

   1. Initial program 81.6%

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

      1. tan-quot 81.6%

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

      2. clear-num 81.6%

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

   4. Applied egg-rr 81.6%

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

   5. Taylor expanded in y around 0 58.0%

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

   6. Taylor expanded in z around 0 46.0%

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

Alternative 5: 79.3% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.2%

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

   1. tan-quot 83.2%

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

   2. clear-num 83.2%

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

4. Applied egg-rr 83.2%

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

Alternative 6: 79.3% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.2%

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

3. Taylor expanded in a around inf 83.2%

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

Alternative 7: 50.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65:\\ \;\;\;\;e^{\log x}\\ \mathbf{elif}\;a \leq 1.56:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(\frac{1}{x}\right)}^{-3}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= a -1.65)
   (exp (log x))
   (if (<= a 1.56) (- (+ x (tan (+ y z))) a) (cbrt (pow (/ 1.0 x) -3.0)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.65) {
		tmp = exp(log(x));
	} else if (a <= 1.56) {
		tmp = (x + tan((y + z))) - a;
	} else {
		tmp = cbrt(pow((1.0 / x), -3.0));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.65) {
		tmp = Math.exp(Math.log(x));
	} else if (a <= 1.56) {
		tmp = (x + Math.tan((y + z))) - a;
	} else {
		tmp = Math.cbrt(Math.pow((1.0 / x), -3.0));
	}
	return tmp;
}

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (a <= -1.65)
		tmp = exp(log(x));
	elseif (a <= 1.56)
		tmp = Float64(Float64(x + tan(Float64(y + z))) - a);
	else
		tmp = cbrt((Float64(1.0 / x) ^ -3.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[a, -1.65], N[Exp[N[Log[x], $MachinePrecision]], $MachinePrecision], If[LessEqual[a, 1.56], N[(N[(x + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision], N[Power[N[Power[N[(1.0 / x), $MachinePrecision], -3.0], $MachinePrecision], 1/3], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.6499999999999999

   1. Initial program 77.8%

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

      1. add-cbrt-cube 77.4%

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

      2. pow3 77.3%

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

      3. +-commutative 77.3%

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

      4. associate-+l- 77.4%

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

   4. Applied egg-rr 77.4%

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

      1. add-exp-log 70.0%

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

      2. log-pow 69.8%

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

      3. associate--r- 69.8%

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

      4. tan-sum 87.3%

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

      5. +-commutative 87.3%

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

      6. tan-sum 69.8%

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

      7. sub-neg 69.8%

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

      8. add-sqr-sqrt 39.3%

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

      9. sqrt-unprod 49.0%

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

      10. sqr-neg 49.0%

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

      11. sqrt-unprod 9.7%

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

      12. add-sqr-sqrt 19.0%

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

   6. Applied egg-rr 19.0%

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

   7. Taylor expanded in x around inf 22.0%

      \[\leadsto \sqrt[3]{e^{\color{blue}{-3 \cdot \log \left(\frac{1}{x}\right)}}} \]
   8. Step-by-step derivation

      1. *-un-lft-identity 22.0%

         \[\leadsto \color{blue}{1 \cdot \sqrt[3]{e^{-3 \cdot \log \left(\frac{1}{x}\right)}}} \]

      2. *-commutative 22.0%

         \[\leadsto 1 \cdot \sqrt[3]{e^{\color{blue}{\log \left(\frac{1}{x}\right) \cdot -3}}} \]

      3. exp-to-pow 22.0%

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

   9. Applied egg-rr 22.0%

      \[\leadsto \color{blue}{1 \cdot \sqrt[3]{{\left(\frac{1}{x}\right)}^{-3}}} \]
   10. Step-by-step derivation

       1. *-lft-identity 22.0%

          \[\leadsto \color{blue}{\sqrt[3]{{\left(\frac{1}{x}\right)}^{-3}}} \]

       2. unpow1/3 22.0%

          \[\leadsto \color{blue}{{\left({\left(\frac{1}{x}\right)}^{-3}\right)}^{0.3333333333333333}} \]

       3. rem-exp-log 22.0%

          \[\leadsto {\left({\color{blue}{\left(e^{\log \left(\frac{1}{x}\right)}\right)}}^{-3}\right)}^{0.3333333333333333} \]

       4. log-rec 22.0%

          \[\leadsto {\left({\left(e^{\color{blue}{-\log x}}\right)}^{-3}\right)}^{0.3333333333333333} \]

       5. exp-prod 22.0%

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

       6. *-commutative 22.0%

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

       7. exp-prod 22.0%

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

       8. *-commutative 22.0%

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

       9. associate-*r* 22.0%

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

       10. metadata-eval 22.0%

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

       11. neg-mul-1 22.0%

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

       12. associate-*r* 22.0%

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

       13. metadata-eval 22.0%

           \[\leadsto e^{\color{blue}{1} \cdot \log x} \]

       14. *-lft-identity 22.0%

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

   11. Simplified 22.0%

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

   if -1.6499999999999999 < a < 1.5600000000000001

   1. Initial program 85.5%

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

   3. Taylor expanded in a around 0 85.3%

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

      1. associate-+r- 85.3%

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

   5. Applied egg-rr 85.3%

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

   if 1.5600000000000001 < a

   1. Initial program 84.6%

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

      1. add-cbrt-cube 84.3%

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

      2. pow3 84.4%

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

      3. +-commutative 84.4%

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

      4. associate-+l- 84.4%

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

   4. Applied egg-rr 84.4%

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

      1. add-exp-log 72.9%

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

      2. log-pow 72.8%

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

      3. associate--r- 72.7%

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

      4. tan-sum 87.4%

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

      5. +-commutative 87.4%

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

      6. tan-sum 72.7%

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

      7. sub-neg 72.7%

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

      8. add-sqr-sqrt 39.2%

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

      9. sqrt-unprod 49.2%

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

      10. sqr-neg 49.2%

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

      11. sqrt-unprod 10.0%

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

      12. add-sqr-sqrt 20.5%

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

   6. Applied egg-rr 20.5%

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

   7. Taylor expanded in x around inf 21.4%

      \[\leadsto \sqrt[3]{e^{\color{blue}{-3 \cdot \log \left(\frac{1}{x}\right)}}} \]
   8. Step-by-step derivation

      1. *-commutative 21.4%

         \[\leadsto \sqrt[3]{e^{\color{blue}{\log \left(\frac{1}{x}\right) \cdot -3}}} \]

      2. exp-to-pow 21.4%

         \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{1}{x}\right)}^{-3}}} \]

   9. Applied egg-rr 21.4%

      \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{1}{x}\right)}^{-3}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 50.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9:\\ \;\;\;\;e^{\log x}\\ \mathbf{elif}\;a \leq 1.56:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \mathbf{else}:\\ \;\;\;\;{\left(\sqrt{x}\right)}^{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= a -1.9)
   (exp (log x))
   (if (<= a 1.56) (- (+ x (tan (+ y z))) a) (pow (sqrt x) 2.0))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.9) {
		tmp = exp(log(x));
	} else if (a <= 1.56) {
		tmp = (x + tan((y + z))) - a;
	} else {
		tmp = pow(sqrt(x), 2.0);
	}
	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 <= (-1.9d0)) then
        tmp = exp(log(x))
    else if (a <= 1.56d0) then
        tmp = (x + tan((y + z))) - a
    else
        tmp = sqrt(x) ** 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.9) {
		tmp = Math.exp(Math.log(x));
	} else if (a <= 1.56) {
		tmp = (x + Math.tan((y + z))) - a;
	} else {
		tmp = Math.pow(Math.sqrt(x), 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if a <= -1.9:
		tmp = math.exp(math.log(x))
	elif a <= 1.56:
		tmp = (x + math.tan((y + z))) - a
	else:
		tmp = math.pow(math.sqrt(x), 2.0)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (a <= -1.9)
		tmp = exp(log(x));
	elseif (a <= 1.56)
		tmp = Float64(Float64(x + tan(Float64(y + z))) - a);
	else
		tmp = sqrt(x) ^ 2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -1.9)
		tmp = exp(log(x));
	elseif (a <= 1.56)
		tmp = (x + tan((y + z))) - a;
	else
		tmp = sqrt(x) ^ 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[a, -1.9], N[Exp[N[Log[x], $MachinePrecision]], $MachinePrecision], If[LessEqual[a, 1.56], N[(N[(x + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision], N[Power[N[Sqrt[x], $MachinePrecision], 2.0], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8999999999999999

   1. Initial program 77.8%

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

      1. add-cbrt-cube 77.4%

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

      2. pow3 77.3%

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

      3. +-commutative 77.3%

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

      4. associate-+l- 77.4%

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

   4. Applied egg-rr 77.4%

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

      1. add-exp-log 70.0%

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

      2. log-pow 69.8%

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

      3. associate--r- 69.8%

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

      4. tan-sum 87.3%

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

      5. +-commutative 87.3%

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

      6. tan-sum 69.8%

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

      7. sub-neg 69.8%

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

      8. add-sqr-sqrt 39.3%

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

      9. sqrt-unprod 49.0%

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

      10. sqr-neg 49.0%

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

      11. sqrt-unprod 9.7%

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

      12. add-sqr-sqrt 19.0%

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

   6. Applied egg-rr 19.0%

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

   7. Taylor expanded in x around inf 22.0%

      \[\leadsto \sqrt[3]{e^{\color{blue}{-3 \cdot \log \left(\frac{1}{x}\right)}}} \]
   8. Step-by-step derivation

      1. *-un-lft-identity 22.0%

         \[\leadsto \color{blue}{1 \cdot \sqrt[3]{e^{-3 \cdot \log \left(\frac{1}{x}\right)}}} \]

      2. *-commutative 22.0%

         \[\leadsto 1 \cdot \sqrt[3]{e^{\color{blue}{\log \left(\frac{1}{x}\right) \cdot -3}}} \]

      3. exp-to-pow 22.0%

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

   9. Applied egg-rr 22.0%

      \[\leadsto \color{blue}{1 \cdot \sqrt[3]{{\left(\frac{1}{x}\right)}^{-3}}} \]
   10. Step-by-step derivation

       1. *-lft-identity 22.0%

          \[\leadsto \color{blue}{\sqrt[3]{{\left(\frac{1}{x}\right)}^{-3}}} \]

       2. unpow1/3 22.0%

          \[\leadsto \color{blue}{{\left({\left(\frac{1}{x}\right)}^{-3}\right)}^{0.3333333333333333}} \]

       3. rem-exp-log 22.0%

          \[\leadsto {\left({\color{blue}{\left(e^{\log \left(\frac{1}{x}\right)}\right)}}^{-3}\right)}^{0.3333333333333333} \]

       4. log-rec 22.0%

          \[\leadsto {\left({\left(e^{\color{blue}{-\log x}}\right)}^{-3}\right)}^{0.3333333333333333} \]

       5. exp-prod 22.0%

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

       6. *-commutative 22.0%

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

       7. exp-prod 22.0%

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

       8. *-commutative 22.0%

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

       9. associate-*r* 22.0%

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

       10. metadata-eval 22.0%

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

       11. neg-mul-1 22.0%

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

       12. associate-*r* 22.0%

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

       13. metadata-eval 22.0%

           \[\leadsto e^{\color{blue}{1} \cdot \log x} \]

       14. *-lft-identity 22.0%

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

   11. Simplified 22.0%

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

   if -1.8999999999999999 < a < 1.5600000000000001

   1. Initial program 85.5%

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

   3. Taylor expanded in a around 0 85.3%

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

      1. associate-+r- 85.3%

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

   5. Applied egg-rr 85.3%

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

   if 1.5600000000000001 < a

   1. Initial program 84.6%

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

      1. add-sqr-sqrt 72.9%

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

      2. pow2 72.9%

         \[\leadsto \color{blue}{{\left(\sqrt{x + \left(\tan \left(y + z\right) - \tan a\right)}\right)}^{2}} \]

      3. +-commutative 72.9%

         \[\leadsto {\left(\sqrt{\color{blue}{\left(\tan \left(y + z\right) - \tan a\right) + x}}\right)}^{2} \]

      4. associate-+l- 73.0%

         \[\leadsto {\left(\sqrt{\color{blue}{\tan \left(y + z\right) - \left(\tan a - x\right)}}\right)}^{2} \]

   4. Applied egg-rr 73.0%

      \[\leadsto \color{blue}{{\left(\sqrt{\tan \left(y + z\right) - \left(\tan a - x\right)}\right)}^{2}} \]

   5. Taylor expanded in x around inf 21.4%

      \[\leadsto {\color{blue}{\left(\sqrt{x}\right)}}^{2} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 50.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2:\\ \;\;\;\;e^{\log x}\\ \mathbf{elif}\;a \leq 1.46:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{x}^{3}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= a -2.2)
   (exp (log x))
   (if (<= a 1.46) (- (+ x (tan (+ y z))) a) (cbrt (pow x 3.0)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -2.2) {
		tmp = exp(log(x));
	} else if (a <= 1.46) {
		tmp = (x + tan((y + z))) - a;
	} else {
		tmp = cbrt(pow(x, 3.0));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -2.2) {
		tmp = Math.exp(Math.log(x));
	} else if (a <= 1.46) {
		tmp = (x + Math.tan((y + z))) - a;
	} else {
		tmp = Math.cbrt(Math.pow(x, 3.0));
	}
	return tmp;
}

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (a <= -2.2)
		tmp = exp(log(x));
	elseif (a <= 1.46)
		tmp = Float64(Float64(x + tan(Float64(y + z))) - a);
	else
		tmp = cbrt((x ^ 3.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[a, -2.2], N[Exp[N[Log[x], $MachinePrecision]], $MachinePrecision], If[LessEqual[a, 1.46], N[(N[(x + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision], N[Power[N[Power[x, 3.0], $MachinePrecision], 1/3], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.2000000000000002

   1. Initial program 77.8%

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

      1. add-cbrt-cube 77.4%

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

      2. pow3 77.3%

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

      3. +-commutative 77.3%

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

      4. associate-+l- 77.4%

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

   4. Applied egg-rr 77.4%

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

      1. add-exp-log 70.0%

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

      2. log-pow 69.8%

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

      3. associate--r- 69.8%

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

      4. tan-sum 87.3%

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

      5. +-commutative 87.3%

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

      6. tan-sum 69.8%

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

      7. sub-neg 69.8%

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

      8. add-sqr-sqrt 39.3%

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

      9. sqrt-unprod 49.0%

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

      10. sqr-neg 49.0%

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

      11. sqrt-unprod 9.7%

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

      12. add-sqr-sqrt 19.0%

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

   6. Applied egg-rr 19.0%

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

   7. Taylor expanded in x around inf 22.0%

      \[\leadsto \sqrt[3]{e^{\color{blue}{-3 \cdot \log \left(\frac{1}{x}\right)}}} \]
   8. Step-by-step derivation

      1. *-un-lft-identity 22.0%

         \[\leadsto \color{blue}{1 \cdot \sqrt[3]{e^{-3 \cdot \log \left(\frac{1}{x}\right)}}} \]

      2. *-commutative 22.0%

         \[\leadsto 1 \cdot \sqrt[3]{e^{\color{blue}{\log \left(\frac{1}{x}\right) \cdot -3}}} \]

      3. exp-to-pow 22.0%

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

   9. Applied egg-rr 22.0%

      \[\leadsto \color{blue}{1 \cdot \sqrt[3]{{\left(\frac{1}{x}\right)}^{-3}}} \]
   10. Step-by-step derivation

       1. *-lft-identity 22.0%

          \[\leadsto \color{blue}{\sqrt[3]{{\left(\frac{1}{x}\right)}^{-3}}} \]

       2. unpow1/3 22.0%

          \[\leadsto \color{blue}{{\left({\left(\frac{1}{x}\right)}^{-3}\right)}^{0.3333333333333333}} \]

       3. rem-exp-log 22.0%

          \[\leadsto {\left({\color{blue}{\left(e^{\log \left(\frac{1}{x}\right)}\right)}}^{-3}\right)}^{0.3333333333333333} \]

       4. log-rec 22.0%

          \[\leadsto {\left({\left(e^{\color{blue}{-\log x}}\right)}^{-3}\right)}^{0.3333333333333333} \]

       5. exp-prod 22.0%

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

       6. *-commutative 22.0%

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

       7. exp-prod 22.0%

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

       8. *-commutative 22.0%

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

       9. associate-*r* 22.0%

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

       10. metadata-eval 22.0%

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

       11. neg-mul-1 22.0%

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

       12. associate-*r* 22.0%

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

       13. metadata-eval 22.0%

           \[\leadsto e^{\color{blue}{1} \cdot \log x} \]

       14. *-lft-identity 22.0%

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

   11. Simplified 22.0%

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

   if -2.2000000000000002 < a < 1.46

   1. Initial program 85.5%

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

   3. Taylor expanded in a around 0 85.3%

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

      1. associate-+r- 85.3%

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

   5. Applied egg-rr 85.3%

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

   if 1.46 < a

   1. Initial program 84.6%

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

      1. add-cbrt-cube 84.3%

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

      2. pow3 84.4%

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

      3. +-commutative 84.4%

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

      4. associate-+l- 84.4%

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

   4. Applied egg-rr 84.4%

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

   5. Taylor expanded in x around inf 21.4%

      \[\leadsto \sqrt[3]{\color{blue}{{x}^{3}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 79.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.2%

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

Alternative 11: 50.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7:\\ \;\;\;\;e^{\log x}\\ \mathbf{elif}\;a \leq 1.56:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= a -1.7) (exp (log x)) (if (<= a 1.56) (- (+ x (tan (+ y z))) a) x)))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.7) {
		tmp = exp(log(x));
	} else if (a <= 1.56) {
		tmp = (x + tan((y + z))) - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.7d0)) then
        tmp = exp(log(x))
    else if (a <= 1.56d0) then
        tmp = (x + tan((y + z))) - a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.7) {
		tmp = Math.exp(Math.log(x));
	} else if (a <= 1.56) {
		tmp = (x + Math.tan((y + z))) - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if a <= -1.7:
		tmp = math.exp(math.log(x))
	elif a <= 1.56:
		tmp = (x + math.tan((y + z))) - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (a <= -1.7)
		tmp = exp(log(x));
	elseif (a <= 1.56)
		tmp = Float64(Float64(x + tan(Float64(y + z))) - a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -1.7)
		tmp = exp(log(x));
	elseif (a <= 1.56)
		tmp = (x + tan((y + z))) - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[a, -1.7], N[Exp[N[Log[x], $MachinePrecision]], $MachinePrecision], If[LessEqual[a, 1.56], N[(N[(x + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if a < -1.69999999999999996

   1. Initial program 77.8%

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

      1. add-cbrt-cube 77.4%

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

      2. pow3 77.3%

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

      3. +-commutative 77.3%

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

      4. associate-+l- 77.4%

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

   4. Applied egg-rr 77.4%

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

      1. add-exp-log 70.0%

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

      2. log-pow 69.8%

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

      3. associate--r- 69.8%

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

      4. tan-sum 87.3%

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

      5. +-commutative 87.3%

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

      6. tan-sum 69.8%

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

      7. sub-neg 69.8%

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

      8. add-sqr-sqrt 39.3%

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

      9. sqrt-unprod 49.0%

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

      10. sqr-neg 49.0%

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

      11. sqrt-unprod 9.7%

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

      12. add-sqr-sqrt 19.0%

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

   6. Applied egg-rr 19.0%

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

   7. Taylor expanded in x around inf 22.0%

      \[\leadsto \sqrt[3]{e^{\color{blue}{-3 \cdot \log \left(\frac{1}{x}\right)}}} \]
   8. Step-by-step derivation

      1. *-un-lft-identity 22.0%

         \[\leadsto \color{blue}{1 \cdot \sqrt[3]{e^{-3 \cdot \log \left(\frac{1}{x}\right)}}} \]

      2. *-commutative 22.0%

         \[\leadsto 1 \cdot \sqrt[3]{e^{\color{blue}{\log \left(\frac{1}{x}\right) \cdot -3}}} \]

      3. exp-to-pow 22.0%

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

   9. Applied egg-rr 22.0%

      \[\leadsto \color{blue}{1 \cdot \sqrt[3]{{\left(\frac{1}{x}\right)}^{-3}}} \]
   10. Step-by-step derivation

       1. *-lft-identity 22.0%

          \[\leadsto \color{blue}{\sqrt[3]{{\left(\frac{1}{x}\right)}^{-3}}} \]

       2. unpow1/3 22.0%

          \[\leadsto \color{blue}{{\left({\left(\frac{1}{x}\right)}^{-3}\right)}^{0.3333333333333333}} \]

       3. rem-exp-log 22.0%

          \[\leadsto {\left({\color{blue}{\left(e^{\log \left(\frac{1}{x}\right)}\right)}}^{-3}\right)}^{0.3333333333333333} \]

       4. log-rec 22.0%

          \[\leadsto {\left({\left(e^{\color{blue}{-\log x}}\right)}^{-3}\right)}^{0.3333333333333333} \]

       5. exp-prod 22.0%

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

       6. *-commutative 22.0%

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

       7. exp-prod 22.0%

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

       8. *-commutative 22.0%

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

       9. associate-*r* 22.0%

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

       10. metadata-eval 22.0%

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

       11. neg-mul-1 22.0%

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

       12. associate-*r* 22.0%

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

       13. metadata-eval 22.0%

           \[\leadsto e^{\color{blue}{1} \cdot \log x} \]

       14. *-lft-identity 22.0%

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

   11. Simplified 22.0%

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

   if -1.69999999999999996 < a < 1.5600000000000001

   1. Initial program 85.5%

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

   3. Taylor expanded in a around 0 85.3%

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

      1. associate-+r- 85.3%

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

   5. Applied egg-rr 85.3%

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

   if 1.5600000000000001 < a

   1. Initial program 84.6%

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

   3. Taylor expanded in x around inf 21.4%

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

Alternative 12: 50.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \lor \neg \left(a \leq 1.56\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -1.95) (not (<= a 1.56))) x (- (+ x (tan (+ y z))) a)))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -1.95) || !(a <= 1.56)) {
		tmp = x;
	} else {
		tmp = (x + tan((y + z))) - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.95d0)) .or. (.not. (a <= 1.56d0))) then
        tmp = x
    else
        tmp = (x + tan((y + z))) - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -1.95) || !(a <= 1.56)) {
		tmp = x;
	} else {
		tmp = (x + Math.tan((y + z))) - a;
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (a <= -1.95) or not (a <= 1.56):
		tmp = x
	else:
		tmp = (x + math.tan((y + z))) - a
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -1.95) || !(a <= 1.56))
		tmp = x;
	else
		tmp = Float64(Float64(x + tan(Float64(y + z))) - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -1.95) || ~((a <= 1.56)))
		tmp = x;
	else
		tmp = (x + tan((y + z))) - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[a, -1.95], N[Not[LessEqual[a, 1.56]], $MachinePrecision]], x, N[(N[(x + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.94999999999999996 or 1.5600000000000001 < a

   1. Initial program 81.0%

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

   3. Taylor expanded in x around inf 21.7%

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

   if -1.94999999999999996 < a < 1.5600000000000001

   1. Initial program 85.5%

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

   3. Taylor expanded in a around 0 85.3%

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

      1. associate-+r- 85.3%

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

   5. Applied egg-rr 85.3%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \lor \neg \left(a \leq 1.56\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \lor \neg \left(a \leq 1.56\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -1.9) (not (<= a 1.56))) x (+ x (- (tan (+ y z)) a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -1.9) || !(a <= 1.56)) {
		tmp = x;
	} else {
		tmp = x + (tan((y + z)) - a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.9d0)) .or. (.not. (a <= 1.56d0))) then
        tmp = x
    else
        tmp = x + (tan((y + z)) - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -1.9) || !(a <= 1.56)) {
		tmp = x;
	} else {
		tmp = x + (Math.tan((y + z)) - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (a <= -1.9) or not (a <= 1.56):
		tmp = x
	else:
		tmp = x + (math.tan((y + z)) - a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -1.9) || !(a <= 1.56))
		tmp = x;
	else
		tmp = Float64(x + Float64(tan(Float64(y + z)) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -1.9) || ~((a <= 1.56)))
		tmp = x;
	else
		tmp = x + (tan((y + z)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[a, -1.9], N[Not[LessEqual[a, 1.56]], $MachinePrecision]], x, N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8999999999999999 or 1.5600000000000001 < a

   1. Initial program 81.0%

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

   3. Taylor expanded in x around inf 21.7%

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

   if -1.8999999999999999 < a < 1.5600000000000001

   1. Initial program 85.5%

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

   3. Taylor expanded in a around 0 85.3%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \lor \neg \left(a \leq 1.56\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.7% 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 83.2%

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

3. Taylor expanded in x around inf 32.8%

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

Reproduce

herbie shell --seed 2024096 
(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))))