tan-example (used to crash)

Percentage Accurate: 79.1% → 99.7%

Time: 47.3s

Alternatives: 12

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

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

FPCore

(FPCore (x y z a)
 :precision binary64
 (+ x (- (* (+ (tan y) (tan z)) (/ 1.0 (- 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 / (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 / (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 / (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 / (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(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 / (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[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.2%

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

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

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. Add Preprocessing

Alternative 2: 89.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan y + \tan z\\ \mathbf{if}\;\tan a \leq -0.002 \lor \neg \left(\tan a \leq 4 \cdot 10^{-7}\right):\\ \;\;\;\;x + \left(t\_0 - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{t\_0}{1 - \tan y \cdot \tan z} - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (+ (tan y) (tan z))))
   (if (or (<= (tan a) -0.002) (not (<= (tan a) 4e-7)))
     (+ x (- t_0 (tan a)))
     (+ x (- (/ t_0 (- 1.0 (* (tan y) (tan z)))) a)))))

C

double code(double x, double y, double z, double a) {
	double t_0 = tan(y) + tan(z);
	double tmp;
	if ((tan(a) <= -0.002) || !(tan(a) <= 4e-7)) {
		tmp = x + (t_0 - tan(a));
	} else {
		tmp = x + ((t_0 / (1.0 - (tan(y) * tan(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) :: t_0
    real(8) :: tmp
    t_0 = tan(y) + tan(z)
    if ((tan(a) <= (-0.002d0)) .or. (.not. (tan(a) <= 4d-7))) then
        tmp = x + (t_0 - tan(a))
    else
        tmp = x + ((t_0 / (1.0d0 - (tan(y) * tan(z)))) - a)
    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) <= -0.002) || !(Math.tan(a) <= 4e-7)) {
		tmp = x + (t_0 - Math.tan(a));
	} else {
		tmp = x + ((t_0 / (1.0 - (Math.tan(y) * Math.tan(z)))) - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	t_0 = math.tan(y) + math.tan(z)
	tmp = 0
	if (math.tan(a) <= -0.002) or not (math.tan(a) <= 4e-7):
		tmp = x + (t_0 - math.tan(a))
	else:
		tmp = x + ((t_0 / (1.0 - (math.tan(y) * math.tan(z)))) - a)
	return tmp

Julia

function code(x, y, z, a)
	t_0 = Float64(tan(y) + tan(z))
	tmp = 0.0
	if ((tan(a) <= -0.002) || !(tan(a) <= 4e-7))
		tmp = Float64(x + Float64(t_0 - tan(a)));
	else
		tmp = Float64(x + Float64(Float64(t_0 / Float64(1.0 - Float64(tan(y) * tan(z)))) - a));
	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) <= -0.002) || ~((tan(a) <= 4e-7)))
		tmp = x + (t_0 - tan(a));
	else
		tmp = x + ((t_0 / (1.0 - (tan(y) * tan(z)))) - a);
	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], -0.002], N[Not[LessEqual[N[Tan[a], $MachinePrecision], 4e-7]], $MachinePrecision]], N[(x + N[(t$95$0 - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t$95$0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (tan.f64 a) < -2e-3 or 3.9999999999999998e-7 < (tan.f64 a)

   1. Initial program 74.0%

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

      1. tan-sum 99.6%

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

      2. div-inv 99.6%

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

   4. Applied egg-rr 99.6%

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

      1. expm1-log1p-u 92.4%

         \[\leadsto x + \left(\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\tan y \cdot \tan z\right)\right)}} - \tan a\right) \]

      2. expm1-undefine 92.4%

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

      3. log1p-undefine 92.4%

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

      4. add-exp-log 99.6%

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

      5. +-commutative 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in y around 0 74.6%

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

   if -2e-3 < (tan.f64 a) < 3.9999999999999998e-7

   1. Initial program 78.8%

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

   3. Taylor expanded in a around 0 78.8%

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

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

      1. associate-*r/ 99.7%

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

      2. *-rgt-identity 99.7%

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

   7. Simplified 99.7%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.002 \lor \neg \left(\tan a \leq 4 \cdot 10^{-7}\right):\\ \;\;\;\;x + \left(\left(\tan y + \tan z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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 76.2%

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

   1. +-commutative 76.2%

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

   2. sub-neg 76.2%

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

   3. associate-+l+ 76.1%

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

   4. tan-sum 99.5%

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

   5. div-inv 99.5%

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

   6. fma-define 99.5%

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

   7. neg-mul-1 99.5%

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

   8. fma-define 99.5%

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

4. Applied egg-rr 99.5%

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

   1. fma-undefine 99.5%

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

   2. fma-undefine 99.5%

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

   3. neg-mul-1 99.5%

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

   4. associate-+r+ 99.7%

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

   5. unsub-neg 99.7%

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

   6. associate-*r/ 99.6%

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

   7. *-rgt-identity 99.6%

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

6. Simplified 99.6%

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

7. Final simplification 99.6%

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

Alternative 4: 79.6% accurate, 0.7× speedup

Math

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

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(x + Float64(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[(x + N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.2%

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

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

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. expm1-log1p-u 92.6%

      \[\leadsto x + \left(\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\tan y \cdot \tan z\right)\right)}} - \tan a\right) \]

   2. expm1-undefine 92.6%

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

   3. log1p-undefine 92.6%

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

   4. add-exp-log 99.6%

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

   5. +-commutative 99.6%

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

6. Applied egg-rr 99.6%

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

7. Taylor expanded in y around 0 76.7%

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

8. Final simplification 76.7%

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

Alternative 5: 69.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-7} \lor \neg \left(a \leq 1.9\right):\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -1.8e-7) (not (<= a 1.9)))
   (+ x (- (tan y) (tan a)))
   (+ x (- (tan (+ y z)) a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -1.8e-7) || !(a <= 1.9)) {
		tmp = x + (tan(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 ((a <= (-1.8d-7)) .or. (.not. (a <= 1.9d0))) then
        tmp = x + (tan(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 ((a <= -1.8e-7) || !(a <= 1.9)) {
		tmp = x + (Math.tan(y) - Math.tan(a));
	} else {
		tmp = x + (Math.tan((y + z)) - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (a <= -1.8e-7) or not (a <= 1.9):
		tmp = x + (math.tan(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 ((a <= -1.8e-7) || !(a <= 1.9))
		tmp = Float64(x + Float64(tan(y) - tan(a)));
	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 <= -1.8e-7) || ~((a <= 1.9)))
		tmp = x + (tan(y) - tan(a));
	else
		tmp = x + (tan((y + z)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[a, -1.8e-7], N[Not[LessEqual[a, 1.9]], $MachinePrecision]], N[(x + N[(N[Tan[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.79999999999999997e-7 or 1.8999999999999999 < a

   1. Initial program 73.3%

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

   3. Taylor expanded in y around inf 56.9%

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

   if -1.79999999999999997e-7 < a < 1.8999999999999999

   1. Initial program 79.6%

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

   3. Taylor expanded in a around 0 78.9%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-7} \lor \neg \left(a \leq 1.9\right):\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.22 \cdot 10^{-6}:\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= z 1.22e-6) (+ x (- (tan y) (tan a))) (+ x (- (tan z) (tan a)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= 1.22e-6) {
		tmp = x + (tan(y) - tan(a));
	} 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 (z <= 1.22d-6) then
        tmp = x + (tan(y) - tan(a))
    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 (z <= 1.22e-6) {
		tmp = x + (Math.tan(y) - Math.tan(a));
	} else {
		tmp = x + (Math.tan(z) - Math.tan(a));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if z <= 1.22e-6:
		tmp = x + (math.tan(y) - math.tan(a))
	else:
		tmp = x + (math.tan(z) - math.tan(a))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (z <= 1.22e-6)
		tmp = Float64(x + Float64(tan(y) - tan(a)));
	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 (z <= 1.22e-6)
		tmp = x + (tan(y) - tan(a));
	else
		tmp = x + (tan(z) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[z, 1.22e-6], N[(x + N[(N[Tan[y], $MachinePrecision] - N[Tan[a], $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 z < 1.21999999999999997e-6

   1. Initial program 86.9%

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

   3. Taylor expanded in y around inf 69.7%

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

   if 1.21999999999999997e-6 < z

   1. Initial program 51.2%

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

   3. Taylor expanded in y around 0 51.6%

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

Alternative 7: 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 76.2%

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

Alternative 8: 55.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.88 \lor \neg \left(a \leq 7.2\right):\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -0.88) (not (<= a 7.2)))
   (+ x (- z (tan a)))
   (+ x (- (tan (+ y z)) a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -0.88) || !(a <= 7.2)) {
		tmp = x + (z - 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 ((a <= (-0.88d0)) .or. (.not. (a <= 7.2d0))) then
        tmp = x + (z - 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 ((a <= -0.88) || !(a <= 7.2)) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = x + (Math.tan((y + z)) - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (a <= -0.88) or not (a <= 7.2):
		tmp = x + (z - math.tan(a))
	else:
		tmp = x + (math.tan((y + z)) - a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -0.88) || !(a <= 7.2))
		tmp = Float64(x + Float64(z - tan(a)));
	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 <= -0.88) || ~((a <= 7.2)))
		tmp = x + (z - tan(a));
	else
		tmp = x + (tan((y + z)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[a, -0.88], N[Not[LessEqual[a, 7.2]], $MachinePrecision]], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.880000000000000004 or 7.20000000000000018 < a

   1. Initial program 73.6%

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

   3. Taylor expanded in y around 0 56.3%

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

   4. Taylor expanded in z around 0 29.5%

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

   if -0.880000000000000004 < a < 7.20000000000000018

   1. Initial program 79.2%

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

   3. Taylor expanded in a around 0 78.5%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.88 \lor \neg \left(a \leq 7.2\right):\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 45.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.044 \lor \neg \left(a \leq 1.9\right):\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan y - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -0.044) (not (<= a 1.9)))
   (+ x (- z (tan a)))
   (+ x (- (tan y) a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -0.044) || !(a <= 1.9)) {
		tmp = x + (z - tan(a));
	} else {
		tmp = x + (tan(y) - 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 <= (-0.044d0)) .or. (.not. (a <= 1.9d0))) then
        tmp = x + (z - tan(a))
    else
        tmp = x + (tan(y) - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -0.044) || !(a <= 1.9)) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = x + (Math.tan(y) - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (a <= -0.044) or not (a <= 1.9):
		tmp = x + (z - math.tan(a))
	else:
		tmp = x + (math.tan(y) - a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -0.044) || !(a <= 1.9))
		tmp = Float64(x + Float64(z - tan(a)));
	else
		tmp = Float64(x + Float64(tan(y) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -0.044) || ~((a <= 1.9)))
		tmp = x + (z - tan(a));
	else
		tmp = x + (tan(y) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[a, -0.044], N[Not[LessEqual[a, 1.9]], $MachinePrecision]], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[y], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.043999999999999997 or 1.8999999999999999 < a

   1. Initial program 73.6%

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

   3. Taylor expanded in y around 0 56.3%

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

   4. Taylor expanded in z around 0 29.5%

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

   if -0.043999999999999997 < a < 1.8999999999999999

   1. Initial program 79.2%

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

   3. Taylor expanded in a around 0 78.5%

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

   4. Taylor expanded in y around inf 52.6%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.044 \lor \neg \left(a \leq 1.9\right):\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan y - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 0.019:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= z 0.019) (+ x (- z (tan a))) (+ x (- (tan z) a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= 0.019) {
		tmp = x + (z - tan(a));
	} else {
		tmp = x + (tan(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 (z <= 0.019d0) then
        tmp = x + (z - tan(a))
    else
        tmp = x + (tan(z) - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= 0.019) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = x + (Math.tan(z) - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if z <= 0.019:
		tmp = x + (z - math.tan(a))
	else:
		tmp = x + (math.tan(z) - a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (z <= 0.019)
		tmp = Float64(x + Float64(z - tan(a)));
	else
		tmp = Float64(x + Float64(tan(z) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (z <= 0.019)
		tmp = x + (z - tan(a));
	else
		tmp = x + (tan(z) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[z, 0.019], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[z], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 0.0189999999999999995

   1. Initial program 86.9%

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

   3. Taylor expanded in y around 0 60.1%

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

   4. Taylor expanded in z around 0 34.9%

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

   if 0.0189999999999999995 < z

   1. Initial program 51.2%

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

   3. Taylor expanded in a around 0 34.7%

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

   4. Taylor expanded in y around 0 34.6%

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

Alternative 11: 36.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.35:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 (if (<= z 1.35) (+ x (- z (tan a))) x))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= 1.35) {
		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 <= 1.35d0) 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 <= 1.35) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if z <= 1.35:
		tmp = x + (z - math.tan(a))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (z <= 1.35)
		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 <= 1.35)
		tmp = x + (z - tan(a));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[z, 1.35], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < 1.3500000000000001

   1. Initial program 86.7%

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

   3. Taylor expanded in y around 0 60.4%

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

   4. Taylor expanded in z around 0 34.9%

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

   if 1.3500000000000001 < z

   1. Initial program 50.3%

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

   3. Taylor expanded in x around inf 22.3%

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

Alternative 12: 31.6% 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 76.2%

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

3. Taylor expanded in x around inf 26.9%

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

Reproduce

herbie shell --seed 2024135 
(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))))