tan-example (used to crash)

Percentage Accurate: 79.3% → 99.7%

Time: 48.7s

Alternatives: 7

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 78.1%

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

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

4. Applied egg-rr 99.8%

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

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

6. Simplified 99.8%

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

7. Final simplification 99.8%

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

Alternative 2: 36.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.6:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;e^{-\log \left(\frac{1}{x}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= z 2.6) (+ x (- z (tan a))) (exp (- (log (/ 1.0 x))))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= 2.6) {
		tmp = x + (z - tan(a));
	} else {
		tmp = exp(-log((1.0 / 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 (z <= 2.6d0) then
        tmp = x + (z - tan(a))
    else
        tmp = exp(-log((1.0d0 / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= 2.6) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = Math.exp(-Math.log((1.0 / x)));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if z <= 2.6:
		tmp = x + (z - math.tan(a))
	else:
		tmp = math.exp(-math.log((1.0 / x)))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (z <= 2.6)
		tmp = Float64(x + Float64(z - tan(a)));
	else
		tmp = exp(Float64(-log(Float64(1.0 / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (z <= 2.6)
		tmp = x + (z - tan(a));
	else
		tmp = exp(-log((1.0 / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[z, 2.6], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Exp[(-N[Log[N[(1.0 / x), $MachinePrecision]], $MachinePrecision])], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.60000000000000009

   1. Initial program 86.8%

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

      1. add-sqr-sqrt 42.1%

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

      2. sqrt-unprod 68.2%

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

      3. pow2 68.2%

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

   4. Applied egg-rr 68.2%

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

   5. Taylor expanded in y around 0 59.4%

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

   6. Taylor expanded in z around 0 45.1%

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

   if 2.60000000000000009 < z

   1. Initial program 51.3%

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

      1. add-exp-log 47.3%

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

      2. +-commutative 47.3%

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

      3. associate-+l- 47.3%

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

   4. Applied egg-rr 47.3%

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

   5. Taylor expanded in x around inf 22.3%

      \[\leadsto e^{\color{blue}{-1 \cdot \log \left(\frac{1}{x}\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.6:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;e^{-\log \left(\frac{1}{x}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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 78.1%

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

3. Final simplification 78.1%

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

Alternative 4: 36.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.6:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;e^{\log x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= z 2.6) (+ x (- z (tan a))) (exp (log x))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= 2.6) {
		tmp = x + (z - tan(a));
	} else {
		tmp = exp(log(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 (z <= 2.6d0) then
        tmp = x + (z - tan(a))
    else
        tmp = exp(log(x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= 2.6) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = Math.exp(Math.log(x));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if z <= 2.6:
		tmp = x + (z - math.tan(a))
	else:
		tmp = math.exp(math.log(x))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (z <= 2.6)
		tmp = Float64(x + Float64(z - tan(a)));
	else
		tmp = exp(log(x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (z <= 2.6)
		tmp = x + (z - tan(a));
	else
		tmp = exp(log(x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[z, 2.6], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Exp[N[Log[x], $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.60000000000000009

   1. Initial program 86.8%

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

      1. add-sqr-sqrt 42.1%

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

      2. sqrt-unprod 68.2%

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

      3. pow2 68.2%

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

   4. Applied egg-rr 68.2%

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

   5. Taylor expanded in y around 0 59.4%

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

   6. Taylor expanded in z around 0 45.1%

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

   if 2.60000000000000009 < z

   1. Initial program 51.3%

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

      1. add-exp-log 47.3%

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

      2. +-commutative 47.3%

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

      3. associate-+l- 47.3%

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

   4. Applied egg-rr 47.3%

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

   5. Taylor expanded in x around inf 22.3%

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

      1. mul-1-neg 22.3%

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

      2. log-rec 22.3%

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

      3. remove-double-neg 22.3%

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

   7. Simplified 22.3%

      \[\leadsto e^{\color{blue}{\log x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.6:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;e^{\log x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.1%

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

   1. add-sqr-sqrt 37.2%

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

   2. sqrt-unprod 59.8%

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

   3. pow2 59.8%

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

4. Applied egg-rr 59.8%

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

5. Taylor expanded in y around 0 53.3%

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

   1. tan-quot 53.3%

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

   2. sqrt-pow1 61.4%

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

   3. metadata-eval 61.4%

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

   4. pow1 61.4%

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

   5. expm1-log1p-u 54.1%

      \[\leadsto x + \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\tan z\right)\right)} - \tan a\right) \]

   6. expm1-udef 54.1%

      \[\leadsto x + \left(\color{blue}{\left(e^{\mathsf{log1p}\left(\tan z\right)} - 1\right)} - \tan a\right) \]

7. Applied egg-rr 54.1%

   \[\leadsto x + \left(\color{blue}{\left(e^{\mathsf{log1p}\left(\tan z\right)} - 1\right)} - \tan a\right) \]
8. Step-by-step derivation

   1. expm1-def 54.1%

      \[\leadsto x + \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\tan z\right)\right)} - \tan a\right) \]

   2. expm1-log1p 61.4%

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

9. Simplified 61.4%

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

10. Final simplification 61.4%

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

Alternative 6: 36.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.7:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 (if (<= z 2.7) (+ x (- z (tan a))) x))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= 2.7) {
		tmp = x + (z - tan(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 (z <= 2.7d0) then
        tmp = x + (z - tan(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 (z <= 2.7) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if z <= 2.7:
		tmp = x + (z - math.tan(a))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (z <= 2.7)
		tmp = Float64(x + Float64(z - tan(a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (z <= 2.7)
		tmp = x + (z - tan(a));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[z, 2.7], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < 2.7000000000000002

   1. Initial program 86.8%

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

      1. add-sqr-sqrt 42.1%

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

      2. sqrt-unprod 68.2%

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

      3. pow2 68.2%

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

   4. Applied egg-rr 68.2%

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

   5. Taylor expanded in y around 0 59.4%

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

   6. Taylor expanded in z around 0 45.1%

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

   if 2.7000000000000002 < z

   1. Initial program 51.3%

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

   3. Taylor expanded in x around inf 22.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.7:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 78.1%

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

3. Taylor expanded in x around inf 33.9%

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

4. Final simplification 33.9%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024026 
(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))))