tan-example (used to crash)

Percentage Accurate: 79.1% → 99.7%

Time: 25.9s

Alternatives: 10

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: 79.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.4× 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 76.6%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
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: 88.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan y + \tan z\\ \mathbf{if}\;\tan a \leq -0.02 \lor \neg \left(\tan a \leq 10^{-20}\right):\\ \;\;\;\;\left(x + t_0\right) - \tan a\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t_0}{1 - \tan y \cdot \tan z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (+ (tan y) (tan z))))
   (if (or (<= (tan a) -0.02) (not (<= (tan a) 1e-20)))
     (- (+ x t_0) (tan a))
     (+ x (/ t_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 ((tan(a) <= -0.02) || !(tan(a) <= 1e-20)) {
		tmp = (x + t_0) - tan(a);
	} else {
		tmp = x + (t_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 ((tan(a) <= (-0.02d0)) .or. (.not. (tan(a) <= 1d-20))) then
        tmp = (x + t_0) - tan(a)
    else
        tmp = x + (t_0 / (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 ((Math.tan(a) <= -0.02) || !(Math.tan(a) <= 1e-20)) {
		tmp = (x + t_0) - Math.tan(a);
	} else {
		tmp = x + (t_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 (math.tan(a) <= -0.02) or not (math.tan(a) <= 1e-20):
		tmp = (x + t_0) - math.tan(a)
	else:
		tmp = x + (t_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 ((tan(a) <= -0.02) || !(tan(a) <= 1e-20))
		tmp = Float64(Float64(x + t_0) - tan(a));
	else
		tmp = Float64(x + Float64(t_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 ((tan(a) <= -0.02) || ~((tan(a) <= 1e-20)))
		tmp = (x + t_0) - tan(a);
	else
		tmp = x + (t_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[N[Tan[a], $MachinePrecision], -0.02], N[Not[LessEqual[N[Tan[a], $MachinePrecision], 1e-20]], $MachinePrecision]], N[(N[(x + t$95$0), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (tan.f64 a) < -0.0200000000000000004 or 9.99999999999999945e-21 < (tan.f64 a)

   1. Initial program 76.1%

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

      1. associate-+r- 75.9%

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

   3. Simplified 75.9%

      \[\leadsto \color{blue}{\left(x + \tan \left(y + z\right)\right) - \tan a} \]
   4. 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 99.7%

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

   5. Applied egg-rr 99.4%

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

   6. Taylor expanded in y around 0 76.5%

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

   if -0.0200000000000000004 < (tan.f64 a) < 9.99999999999999945e-21

   1. Initial program 77.1%

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

      1. +-commutative 77.1%

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

      2. associate-+l- 77.1%

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

   3. Applied egg-rr 77.1%

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

   4. Taylor expanded in a around 0 77.1%

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

      1. neg-mul-1 77.1%

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

   6. Simplified 77.1%

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

      1. sub-neg 77.1%

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

      2. add-sqr-sqrt 0.0%

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

      3. sqrt-unprod 3.2%

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

      4. sqr-neg 3.2%

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

      5. sqrt-unprod 3.2%

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

      6. add-sqr-sqrt 3.2%

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

      7. add-sqr-sqrt 0.0%

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

      8. sqrt-unprod 77.1%

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

      9. sqr-neg 77.1%

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

      10. sqrt-unprod 76.7%

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

      11. add-sqr-sqrt 77.1%

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

   8. Applied egg-rr 77.1%

      \[\leadsto \color{blue}{\tan \left(y + z\right) + x} \]
   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 99.6%

       \[\leadsto \color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} + x \]
   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 99.6%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.02 \lor \neg \left(\tan a \leq 10^{-20}\right):\\ \;\;\;\;\left(x + \left(\tan y + \tan z\right)\right) - \tan a\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}\\ \end{array} \]

Alternative 3: 79.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.6%

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

   1. associate-+r- 76.5%

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

3. Simplified 76.5%

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

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

5. Applied egg-rr 99.6%

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

6. Taylor expanded in y around 0 77.0%

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

7. Final simplification 77.0%

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

Alternative 4: 59.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + z \leq -0.0002:\\ \;\;\;\;x + \tan \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= (+ y z) -0.0002) (+ x (tan (+ y z))) (+ x (- (tan z) (tan a)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -0.0002) {
		tmp = x + tan((y + z));
	} else {
		tmp = x + (tan(z) - tan(a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y + z) <= (-0.0002d0)) then
        tmp = x + tan((y + z))
    else
        tmp = x + (tan(z) - tan(a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -0.0002) {
		tmp = x + Math.tan((y + z));
	} else {
		tmp = x + (Math.tan(z) - Math.tan(a));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (y + z) <= -0.0002:
		tmp = x + math.tan((y + z))
	else:
		tmp = x + (math.tan(z) - math.tan(a))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (Float64(y + z) <= -0.0002)
		tmp = Float64(x + tan(Float64(y + z)));
	else
		tmp = Float64(x + Float64(tan(z) - tan(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((y + z) <= -0.0002)
		tmp = x + tan((y + z));
	else
		tmp = x + (tan(z) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[N[(y + z), $MachinePrecision], -0.0002], N[(x + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[z], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 y z) < -2.0000000000000001e-4

   1. Initial program 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-+l- 71.8%

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

   3. Applied egg-rr 71.8%

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

   4. Taylor expanded in a around 0 46.5%

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

      1. neg-mul-1 46.5%

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

   6. Simplified 46.5%

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

      1. sub-neg 46.5%

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

      2. add-sqr-sqrt 0.0%

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

      3. sqrt-unprod 3.8%

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

      4. sqr-neg 3.8%

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

      5. sqrt-unprod 3.8%

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

      6. add-sqr-sqrt 3.8%

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

      7. add-sqr-sqrt 0.0%

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

      8. sqrt-unprod 46.5%

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

      9. sqr-neg 46.5%

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

      10. sqrt-unprod 46.4%

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

      11. add-sqr-sqrt 46.5%

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

   8. Applied egg-rr 46.5%

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

   if -2.0000000000000001e-4 < (+.f64 y z)

   1. Initial program 79.3%

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

      1. +-commutative 79.3%

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

      2. associate-+l- 79.3%

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

   3. Applied egg-rr 79.3%

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

   4. Taylor expanded in y around 0 64.2%

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

      1. tan-quot 64.2%

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

      2. associate--r- 64.2%

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

   6. Applied egg-rr 64.2%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + z \leq -0.0002:\\ \;\;\;\;x + \tan \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \]

Alternative 5: 54.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + z \leq -0.0002:\\ \;\;\;\;x + \frac{\sin y}{\cos y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= (+ y z) -0.0002) (+ x (/ (sin y) (cos y))) (+ x (- (tan z) (tan a)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -0.0002) {
		tmp = x + (sin(y) / cos(y));
	} else {
		tmp = x + (tan(z) - tan(a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y + z) <= (-0.0002d0)) then
        tmp = x + (sin(y) / cos(y))
    else
        tmp = x + (tan(z) - tan(a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -0.0002) {
		tmp = x + (Math.sin(y) / Math.cos(y));
	} else {
		tmp = x + (Math.tan(z) - Math.tan(a));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (y + z) <= -0.0002:
		tmp = x + (math.sin(y) / math.cos(y))
	else:
		tmp = x + (math.tan(z) - math.tan(a))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (Float64(y + z) <= -0.0002)
		tmp = Float64(x + Float64(sin(y) / cos(y)));
	else
		tmp = Float64(x + Float64(tan(z) - tan(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((y + z) <= -0.0002)
		tmp = x + (sin(y) / cos(y));
	else
		tmp = x + (tan(z) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[N[(y + z), $MachinePrecision], -0.0002], N[(x + N[(N[Sin[y], $MachinePrecision] / N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[z], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 y z) < -2.0000000000000001e-4

   1. Initial program 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-+l- 71.8%

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

   3. Applied egg-rr 71.8%

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

   4. Taylor expanded in a around 0 46.5%

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

      1. neg-mul-1 46.5%

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

   6. Simplified 46.5%

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

   7. Taylor expanded in z around 0 34.6%

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

   if -2.0000000000000001e-4 < (+.f64 y z)

   1. Initial program 79.3%

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

      1. +-commutative 79.3%

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

      2. associate-+l- 79.3%

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

   3. Applied egg-rr 79.3%

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

   4. Taylor expanded in y around 0 64.2%

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

      1. tan-quot 64.2%

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

      2. associate--r- 64.2%

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

   6. Applied egg-rr 64.2%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + z \leq -0.0002:\\ \;\;\;\;x + \frac{\sin y}{\cos y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \]

Alternative 6: 79.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.6%

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

2. Final simplification 76.6%

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

Alternative 7: 54.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + z \leq -0.0002:\\ \;\;\;\;x + \tan \left(y + z\right)\\ \mathbf{elif}\;y + z \leq 2 \cdot 10^{-5}:\\ \;\;\;\;z + \left(x - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \tan z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= (+ y z) -0.0002)
   (+ x (tan (+ y z)))
   (if (<= (+ y z) 2e-5) (+ z (- x (tan a))) (+ x (tan z)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -0.0002) {
		tmp = x + tan((y + z));
	} else if ((y + z) <= 2e-5) {
		tmp = z + (x - tan(a));
	} else {
		tmp = x + 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) :: tmp
    if ((y + z) <= (-0.0002d0)) then
        tmp = x + tan((y + z))
    else if ((y + z) <= 2d-5) then
        tmp = z + (x - tan(a))
    else
        tmp = x + tan(z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -0.0002) {
		tmp = x + Math.tan((y + z));
	} else if ((y + z) <= 2e-5) {
		tmp = z + (x - Math.tan(a));
	} else {
		tmp = x + Math.tan(z);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (y + z) <= -0.0002:
		tmp = x + math.tan((y + z))
	elif (y + z) <= 2e-5:
		tmp = z + (x - math.tan(a))
	else:
		tmp = x + math.tan(z)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (Float64(y + z) <= -0.0002)
		tmp = Float64(x + tan(Float64(y + z)));
	elseif (Float64(y + z) <= 2e-5)
		tmp = Float64(z + Float64(x - tan(a)));
	else
		tmp = Float64(x + tan(z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((y + z) <= -0.0002)
		tmp = x + tan((y + z));
	elseif ((y + z) <= 2e-5)
		tmp = z + (x - tan(a));
	else
		tmp = x + tan(z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[N[(y + z), $MachinePrecision], -0.0002], N[(x + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y + z), $MachinePrecision], 2e-5], N[(z + N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Tan[z], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 y z) < -2.0000000000000001e-4

   1. Initial program 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-+l- 71.8%

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

   3. Applied egg-rr 71.8%

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

   4. Taylor expanded in a around 0 46.5%

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

      1. neg-mul-1 46.5%

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

   6. Simplified 46.5%

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

      1. sub-neg 46.5%

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

      2. add-sqr-sqrt 0.0%

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

      3. sqrt-unprod 3.8%

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

      4. sqr-neg 3.8%

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

      5. sqrt-unprod 3.8%

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

      6. add-sqr-sqrt 3.8%

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

      7. add-sqr-sqrt 0.0%

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

      8. sqrt-unprod 46.5%

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

      9. sqr-neg 46.5%

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

      10. sqrt-unprod 46.4%

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

      11. add-sqr-sqrt 46.5%

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

   8. Applied egg-rr 46.5%

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

   if -2.0000000000000001e-4 < (+.f64 y z) < 2.00000000000000016e-5

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+l- 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in y around 0 98.2%

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

   5. Taylor expanded in z around 0 98.2%

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

   if 2.00000000000000016e-5 < (+.f64 y z)

   1. Initial program 65.4%

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

      1. +-commutative 65.4%

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

      2. associate-+l- 65.4%

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

   3. Applied egg-rr 65.4%

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

   4. Taylor expanded in y around 0 41.3%

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

      1. tan-quot 41.3%

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

      2. add-sqr-sqrt 23.8%

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

      3. sqrt-unprod 33.1%

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

      4. pow2 33.1%

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

   6. Applied egg-rr 33.1%

      \[\leadsto \color{blue}{\sqrt{{\tan z}^{2}}} - \left(\tan a - x\right) \]
   7. Step-by-step derivation

      1. unpow2 33.1%

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

      2. rem-sqrt-square 33.1%

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

   8. Simplified 33.1%

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

   9. Taylor expanded in a around 0 27.7%

      \[\leadsto \color{blue}{x + \left|\tan z\right|} \]
   10. Step-by-step derivation

       1. rem-square-sqrt 18.9%

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

       2. fabs-sqr 18.9%

          \[\leadsto x + \color{blue}{\sqrt{\tan z} \cdot \sqrt{\tan z}} \]

       3. rem-square-sqrt 34.5%

          \[\leadsto x + \color{blue}{\tan z} \]

   11. Simplified 34.5%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + z \leq -0.0002:\\ \;\;\;\;x + \tan \left(y + z\right)\\ \mathbf{elif}\;y + z \leq 2 \cdot 10^{-5}:\\ \;\;\;\;z + \left(x - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \tan z\\ \end{array} \]

Alternative 8: 50.1% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.6%

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

   1. +-commutative 76.6%

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

   2. associate-+l- 76.6%

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

3. Applied egg-rr 76.6%

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

4. Taylor expanded in a around 0 50.8%

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

   1. neg-mul-1 50.8%

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

6. Simplified 50.8%

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

   1. sub-neg 50.8%

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

   2. add-sqr-sqrt 0.0%

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

   3. sqrt-unprod 3.5%

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

   4. sqr-neg 3.5%

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

   5. sqrt-unprod 3.5%

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

   6. add-sqr-sqrt 3.5%

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

   7. add-sqr-sqrt 0.0%

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

   8. sqrt-unprod 50.8%

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

   9. sqr-neg 50.8%

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

   10. sqrt-unprod 50.6%

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

   11. add-sqr-sqrt 50.8%

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

8. Applied egg-rr 50.8%

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

9. Final simplification 50.8%

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

Alternative 9: 40.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ x + \tan z \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.6%

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

   1. +-commutative 76.6%

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

   2. associate-+l- 76.6%

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

3. Applied egg-rr 76.6%

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

4. Taylor expanded in y around 0 57.9%

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

   1. tan-quot 57.9%

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

   2. add-sqr-sqrt 31.1%

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

   3. sqrt-unprod 51.1%

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

   4. pow2 51.1%

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

6. Applied egg-rr 51.1%

   \[\leadsto \color{blue}{\sqrt{{\tan z}^{2}}} - \left(\tan a - x\right) \]
7. Step-by-step derivation

   1. unpow2 51.1%

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

   2. rem-sqrt-square 51.1%

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

8. Simplified 51.1%

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

9. Taylor expanded in a around 0 36.8%

   \[\leadsto \color{blue}{x + \left|\tan z\right|} \]
10. Step-by-step derivation

    1. rem-square-sqrt 20.8%

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

    2. fabs-sqr 20.8%

       \[\leadsto x + \color{blue}{\sqrt{\tan z} \cdot \sqrt{\tan z}} \]

    3. rem-square-sqrt 41.5%

       \[\leadsto x + \color{blue}{\tan z} \]

11. Simplified 41.5%

    \[\leadsto \color{blue}{x + \tan z} \]

12. Final simplification 41.5%

    \[\leadsto x + \tan z \]

Alternative 10: 31.1% 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 76.6%

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

2. Taylor expanded in x around inf 32.7%

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

3. Final simplification 32.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023200 
(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))))