tan-example (used to crash)

Percentage Accurate: 79.5% → 99.7%

Time: 26.0s

Alternatives: 9

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: 79.5% 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 76.3%

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

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

Alternative 2: 89.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan y + \tan z\\ \mathbf{if}\;\tan a \leq -0.005 \lor \neg \left(\tan a \leq 10^{-11}\right):\\ \;\;\;\;\mathsf{fma}\left(t_0, 1, x - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{1 - \tan y \cdot \tan z} + \left(x - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (+ (tan y) (tan z))))
   (if (or (<= (tan a) -0.005) (not (<= (tan a) 1e-11)))
     (fma t_0 1.0 (- x (tan a)))
     (+ (/ t_0 (- 1.0 (* (tan y) (tan z)))) (- x a)))))

C

double code(double x, double y, double z, double a) {
	double t_0 = tan(y) + tan(z);
	double tmp;
	if ((tan(a) <= -0.005) || !(tan(a) <= 1e-11)) {
		tmp = fma(t_0, 1.0, (x - tan(a)));
	} else {
		tmp = (t_0 / (1.0 - (tan(y) * tan(z)))) + (x - a);
	}
	return tmp;
}

Julia

function code(x, y, z, a)
	t_0 = Float64(tan(y) + tan(z))
	tmp = 0.0
	if ((tan(a) <= -0.005) || !(tan(a) <= 1e-11))
		tmp = fma(t_0, 1.0, Float64(x - tan(a)));
	else
		tmp = Float64(Float64(t_0 / Float64(1.0 - Float64(tan(y) * tan(z)))) + Float64(x - a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, a_] := Block[{t$95$0 = N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[Tan[a], $MachinePrecision], -0.005], N[Not[LessEqual[N[Tan[a], $MachinePrecision], 1e-11]], $MachinePrecision]], N[(t$95$0 * 1.0 + N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (tan.f64 a) < -0.0050000000000000001 or 9.99999999999999939e-12 < (tan.f64 a)

   1. Initial program 76.7%

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

      1. associate-+r- 76.6%

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

      2. +-commutative 76.6%

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

      3. associate-+r- 76.5%

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

      4. tan-sum 99.5%

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

      5. div-inv 99.4%

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

      6. fma-def 99.4%

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

   3. Applied egg-rr 99.4%

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

   4. Taylor expanded in y around 0 77.3%

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

   if -0.0050000000000000001 < (tan.f64 a) < 9.99999999999999939e-12

   1. Initial program 75.9%

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

      1. associate-+r- 75.9%

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

      2. +-commutative 75.9%

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

      3. associate--l+ 75.9%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in a around 0 75.9%

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

      1. mul-1-neg 75.9%

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

      2. unsub-neg 75.9%

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

   6. Simplified 75.9%

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

      1. tan-sum 99.8%

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

      2. div-inv 99.8%

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

   8. Applied egg-rr 99.7%

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

      1. associate-*r/ 99.8%

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

      2. *-rgt-identity 99.8%

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

   10. Simplified 99.8%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.005 \lor \neg \left(\tan a \leq 10^{-11}\right):\\ \;\;\;\;\mathsf{fma}\left(\tan y + \tan z, 1, x - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} + \left(x - a\right)\\ \end{array} \]

Alternative 3: 79.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 76.3%

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

   1. associate-+r- 76.2%

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

   2. +-commutative 76.2%

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

   3. associate-+r- 76.2%

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

   4. tan-sum 99.6%

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

   5. div-inv 99.6%

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

   6. fma-def 99.6%

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

3. Applied egg-rr 99.6%

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

4. Taylor expanded in y around 0 76.7%

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

5. Final simplification 76.7%

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

Alternative 4: 69.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.0008 \lor \neg \left(a \leq 250000\right):\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - a\right) + \tan \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -0.0008) (not (<= a 250000.0)))
   (+ x (- (tan z) (tan a)))
   (+ (- x a) (tan (+ y z)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -0.0008) || !(a <= 250000.0)) {
		tmp = x + (tan(z) - tan(a));
	} else {
		tmp = (x - a) + tan((y + 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 ((a <= (-0.0008d0)) .or. (.not. (a <= 250000.0d0))) then
        tmp = x + (tan(z) - tan(a))
    else
        tmp = (x - a) + tan((y + z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -0.0008) || !(a <= 250000.0)) {
		tmp = x + (Math.tan(z) - Math.tan(a));
	} else {
		tmp = (x - a) + Math.tan((y + z));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (a <= -0.0008) or not (a <= 250000.0):
		tmp = x + (math.tan(z) - math.tan(a))
	else:
		tmp = (x - a) + math.tan((y + z))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -0.0008) || !(a <= 250000.0))
		tmp = Float64(x + Float64(tan(z) - tan(a)));
	else
		tmp = Float64(Float64(x - a) + tan(Float64(y + z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -0.0008) || ~((a <= 250000.0)))
		tmp = x + (tan(z) - tan(a));
	else
		tmp = (x - a) + tan((y + z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[a, -0.0008], N[Not[LessEqual[a, 250000.0]], $MachinePrecision]], N[(x + N[(N[Tan[z], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - a), $MachinePrecision] + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.00000000000000038e-4 or 2.5e5 < a

   1. Initial program 76.7%

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

   2. Taylor expanded in y around 0 60.8%

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

      1. tan-quot 60.8%

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

      2. tan-quot 60.8%

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

      3. associate--l+ 60.9%

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

   4. Applied egg-rr 60.9%

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

   if -8.00000000000000038e-4 < a < 2.5e5

   1. Initial program 75.9%

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

      1. associate-+r- 75.8%

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

      2. +-commutative 75.8%

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

      3. associate--l+ 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in a around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

   6. Simplified 75.5%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0008 \lor \neg \left(a \leq 250000\right):\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - a\right) + \tan \left(y + z\right)\\ \end{array} \]

Alternative 5: 69.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.00059:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \mathbf{elif}\;a \leq 250000:\\ \;\;\;\;\left(x - a\right) + \tan \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \tan z\right) - \tan a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= a -0.00059)
   (+ x (- (tan z) (tan a)))
   (if (<= a 250000.0) (+ (- x a) (tan (+ y z))) (- (+ x (tan z)) (tan a)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -0.00059) {
		tmp = x + (tan(z) - tan(a));
	} else if (a <= 250000.0) {
		tmp = (x - a) + 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 (a <= (-0.00059d0)) then
        tmp = x + (tan(z) - tan(a))
    else if (a <= 250000.0d0) then
        tmp = (x - a) + 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 (a <= -0.00059) {
		tmp = x + (Math.tan(z) - Math.tan(a));
	} else if (a <= 250000.0) {
		tmp = (x - a) + 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 a <= -0.00059:
		tmp = x + (math.tan(z) - math.tan(a))
	elif a <= 250000.0:
		tmp = (x - a) + 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 (a <= -0.00059)
		tmp = Float64(x + Float64(tan(z) - tan(a)));
	elseif (a <= 250000.0)
		tmp = Float64(Float64(x - a) + tan(Float64(y + z)));
	else
		tmp = Float64(Float64(x + tan(z)) - tan(a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -0.00059)
		tmp = x + (tan(z) - tan(a));
	elseif (a <= 250000.0)
		tmp = (x - a) + tan((y + z));
	else
		tmp = (x + tan(z)) - tan(a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[a, -0.00059], N[(x + N[(N[Tan[z], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 250000.0], N[(N[(x - a), $MachinePrecision] + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Tan[z], $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.9000000000000003e-4

   1. Initial program 83.6%

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

   2. Taylor expanded in y around 0 64.4%

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

      1. tan-quot 64.4%

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

      2. tan-quot 64.5%

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

      3. associate--l+ 64.6%

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

   4. Applied egg-rr 64.6%

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

   if -5.9000000000000003e-4 < a < 2.5e5

   1. Initial program 75.9%

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

      1. associate-+r- 75.8%

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

      2. +-commutative 75.8%

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

      3. associate--l+ 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in a around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

   6. Simplified 75.5%

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

   if 2.5e5 < a

   1. Initial program 67.9%

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

   2. Taylor expanded in y around 0 56.1%

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

      1. tan-quot 56.1%

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

      2. sub-neg 56.1%

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

      3. tan-quot 56.1%

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

      4. +-commutative 56.1%

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

   4. Applied egg-rr 56.1%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.00059:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \mathbf{elif}\;a \leq 250000:\\ \;\;\;\;\left(x - a\right) + \tan \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \tan z\right) - \tan a\\ \end{array} \]

Alternative 6: 79.5% 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 76.3%

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

2. Final simplification 76.3%

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

Alternative 7: 50.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 250000:\\ \;\;\;\;\left(x - a\right) + \tan \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{x}^{3}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= a -1.4)
   x
   (if (<= a 250000.0) (+ (- x a) (tan (+ y z))) (cbrt (pow x 3.0)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.4) {
		tmp = x;
	} else if (a <= 250000.0) {
		tmp = (x - a) + tan((y + z));
	} else {
		tmp = cbrt(pow(x, 3.0));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.4) {
		tmp = x;
	} else if (a <= 250000.0) {
		tmp = (x - a) + Math.tan((y + z));
	} else {
		tmp = Math.cbrt(Math.pow(x, 3.0));
	}
	return tmp;
}

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (a <= -1.4)
		tmp = x;
	elseif (a <= 250000.0)
		tmp = Float64(Float64(x - a) + tan(Float64(y + z)));
	else
		tmp = cbrt((x ^ 3.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[a, -1.4], x, If[LessEqual[a, 250000.0], N[(N[(x - a), $MachinePrecision] + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Power[N[Power[x, 3.0], $MachinePrecision], 1/3], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.3999999999999999

   1. Initial program 83.6%

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

   2. Taylor expanded in x around inf 20.7%

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

   if -1.3999999999999999 < a < 2.5e5

   1. Initial program 75.9%

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

      1. associate-+r- 75.8%

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

      2. +-commutative 75.8%

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

      3. associate--l+ 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in a around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

   6. Simplified 75.5%

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

   if 2.5e5 < a

   1. Initial program 67.9%

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

      1. associate-+r- 67.8%

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

      2. +-commutative 67.8%

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

      3. associate--l+ 67.8%

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

   3. Simplified 67.8%

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

   4. Taylor expanded in a around 0 1.1%

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

      1. mul-1-neg 1.1%

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

      2. unsub-neg 1.1%

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

   6. Simplified 1.1%

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

      1. add-cbrt-cube 0.9%

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

      2. pow3 0.9%

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

   8. Applied egg-rr 0.9%

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

   9. Taylor expanded in x around inf 22.6%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 250000:\\ \;\;\;\;\left(x - a\right) + \tan \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{x}^{3}}\\ \end{array} \]

Alternative 8: 50.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 250000:\\ \;\;\;\;\left(x - a\right) + \tan \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= a -1.0) x (if (<= a 250000.0) (+ (- x a) (tan (+ y z))) x)))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.0) {
		tmp = x;
	} else if (a <= 250000.0) {
		tmp = (x - a) + tan((y + z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.0d0)) then
        tmp = x
    else if (a <= 250000.0d0) then
        tmp = (x - a) + tan((y + z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.0) {
		tmp = x;
	} else if (a <= 250000.0) {
		tmp = (x - a) + Math.tan((y + z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if a <= -1.0:
		tmp = x
	elif a <= 250000.0:
		tmp = (x - a) + math.tan((y + z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (a <= -1.0)
		tmp = x;
	elseif (a <= 250000.0)
		tmp = Float64(Float64(x - a) + tan(Float64(y + z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -1.0)
		tmp = x;
	elseif (a <= 250000.0)
		tmp = (x - a) + tan((y + z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[a, -1.0], x, If[LessEqual[a, 250000.0], N[(N[(x - a), $MachinePrecision] + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1 or 2.5e5 < a

   1. Initial program 76.7%

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

   2. Taylor expanded in x around inf 21.5%

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

   if -1 < a < 2.5e5

   1. Initial program 75.9%

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

      1. associate-+r- 75.8%

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

      2. +-commutative 75.8%

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

      3. associate--l+ 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in a around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

   6. Simplified 75.5%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 250000:\\ \;\;\;\;\left(x - a\right) + \tan \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 31.8% 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 76.3%

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

2. Taylor expanded in x around inf 29.0%

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

3. Final simplification 29.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023271 
(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))))