tan-example (used to crash)

Percentage Accurate: 79.9% → 99.7%

Time: 19.0s

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: 79.9% 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, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} t_0 := \mathsf{fma}\left(-\tan z, \tan y, 1\right)\\ x + \left(\frac{\tan z}{t\_0} + \left(\frac{\tan y}{t\_0} - \tan a\right)\right) \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (fma (- (tan z)) (tan y) 1.0)))
   (+ x (+ (/ (tan z) t_0) (- (/ (tan y) t_0) (tan a))))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double t_0 = fma(-tan(z), tan(y), 1.0);
	return x + ((tan(z) / t_0) + ((tan(y) / t_0) - tan(a)));
}

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	t_0 = fma(Float64(-tan(z)), tan(y), 1.0)
	return Float64(x + Float64(Float64(tan(z) / t_0) + Float64(Float64(tan(y) / t_0) - tan(a))))
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := Block[{t$95$0 = N[((-N[Tan[z], $MachinePrecision]) * N[Tan[y], $MachinePrecision] + 1.0), $MachinePrecision]}, N[(x + N[(N[(N[Tan[z], $MachinePrecision] / t$95$0), $MachinePrecision] + N[(N[(N[Tan[y], $MachinePrecision] / t$95$0), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 83.7%

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

   1. lift-tan.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. tan-sum N/A

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

   4. lower-/.f64 N/A

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

   5. +-commutative N/A

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

   6. lower-+.f64 N/A

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

   7. lower-tan.f64 N/A

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

   8. lower-tan.f64 N/A

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

   9. lower--.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 N/A

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

   12. lower-tan.f64 N/A

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

   13. lower-tan.f64 99.8

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

4. Applied rewrites 99.8%

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

   1. lift--.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. lift-+.f64 N/A

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

   4. div-add N/A

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

   5. associate--l+ N/A

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

   6. lower-+.f64 N/A

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

6. Applied rewrites 99.8%

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

Alternative 2: 99.7% accurate, 0.3× speedup

Math

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

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (+
  x
  (-
   (/ (+ (tan z) (tan y)) (- 1.0 (/ (* (sin y) (sin z)) (* (cos y) (cos z)))))
   (tan a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x + (((tan(z) + tan(y)) / (1.0 - ((sin(y) * sin(z)) / (cos(y) * cos(z))))) - tan(a));
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
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(y)) / (1.0d0 - ((sin(y) * sin(z)) / (cos(y) * cos(z))))) - tan(a))
end function

Java

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

Python

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

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + Float64(Float64(Float64(tan(z) + tan(y)) / Float64(1.0 - Float64(Float64(sin(y) * sin(z)) / Float64(cos(y) * cos(z))))) - tan(a)))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x + (((tan(z) + tan(y)) / (1.0 - ((sin(y) * sin(z)) / (cos(y) * cos(z))))) - tan(a));
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[(N[(N[Tan[z], $MachinePrecision] + N[Tan[y], $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(N[(N[Sin[y], $MachinePrecision] * N[Sin[z], $MachinePrecision]), $MachinePrecision] / N[(N[Cos[y], $MachinePrecision] * N[Cos[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.7%

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

   1. lift-tan.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. tan-sum N/A

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

   4. lower-/.f64 N/A

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

   5. +-commutative N/A

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

   6. lower-+.f64 N/A

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

   7. lower-tan.f64 N/A

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

   8. lower-tan.f64 N/A

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

   9. lower--.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 N/A

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

   12. lower-tan.f64 N/A

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

   13. lower-tan.f64 99.8

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

4. Applied rewrites 99.8%

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

   1. lift-*.f64 N/A

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

   2. lift-tan.f64 N/A

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

   3. tan-quot N/A

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

   4. lift-tan.f64 N/A

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

   5. tan-quot N/A

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

   6. lift-sin.f64 N/A

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

   7. lift-cos.f64 N/A

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

   8. frac-times N/A

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

   9. lift-sin.f64 N/A

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

   10. lift-cos.f64 N/A

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

   11. lower-/.f64 N/A

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

   12. lift-sin.f64 N/A

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

   13. *-commutative N/A

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

   14. lower-*.f64 N/A

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

   15. lower-sin.f64 N/A

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

   16. lift-cos.f64 N/A

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

   17. *-commutative N/A

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

   18. lower-*.f64 N/A

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

   19. lower-cos.f64 99.8

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

6. Applied rewrites 99.8%

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

Alternative 3: 99.7% accurate, 0.4× speedup

Math

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

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (+ x (- (/ (+ (tan z) (tan y)) (- 1.0 (* (tan z) (tan y)))) (tan a))))

C

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

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
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(y)) / (1.0d0 - (tan(z) * tan(y)))) - tan(a))
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x + (((tan(z) + tan(y)) / (1.0 - (tan(z) * tan(y)))) - tan(a));
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[(N[(N[Tan[z], $MachinePrecision] + N[Tan[y], $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(N[Tan[z], $MachinePrecision] * N[Tan[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.7%

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

   1. lift-tan.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. tan-sum N/A

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

   4. lower-/.f64 N/A

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

   5. +-commutative N/A

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

   6. lower-+.f64 N/A

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

   7. lower-tan.f64 N/A

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

   8. lower-tan.f64 N/A

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

   9. lower--.f64 N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 N/A

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

   12. lower-tan.f64 N/A

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

   13. lower-tan.f64 99.8

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

4. Applied rewrites 99.8%

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

Alternative 4: 88.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{-13} \lor \neg \left(a \leq 4 \cdot 10^{-79}\right):\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan y + \tan z}{\mathsf{fma}\left(\tan y, -\tan z, 1\right)} - \left(-x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -8.8e-13) (not (<= a 4e-79)))
   (+ x (- (tan (+ y z)) (tan a)))
   (- (/ (+ (tan y) (tan z)) (fma (tan y) (- (tan z)) 1.0)) (- x))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -8.8e-13) || !(a <= 4e-79)) {
		tmp = x + (tan((y + z)) - tan(a));
	} else {
		tmp = ((tan(y) + tan(z)) / fma(tan(y), -tan(z), 1.0)) - -x;
	}
	return tmp;
}

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -8.8e-13) || !(a <= 4e-79))
		tmp = Float64(x + Float64(tan(Float64(y + z)) - tan(a)));
	else
		tmp = Float64(Float64(Float64(tan(y) + tan(z)) / fma(tan(y), Float64(-tan(z)), 1.0)) - Float64(-x));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[Or[LessEqual[a, -8.8e-13], N[Not[LessEqual[a, 4e-79]], $MachinePrecision]], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] / N[(N[Tan[y], $MachinePrecision] * (-N[Tan[z], $MachinePrecision]) + 1.0), $MachinePrecision]), $MachinePrecision] - (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.79999999999999986e-13 or 4e-79 < a

   1. Initial program 82.6%

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

   if -8.79999999999999986e-13 < a < 4e-79

   1. Initial program 84.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. lower--.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 84.8

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

   4. Applied rewrites 84.8%

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

   5. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 84.8

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

   7. Applied rewrites 84.8%

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

      1. lift-tan.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. tan-sum N/A

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

      4. lift-tan.f64 N/A

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

      5. lift-tan.f64 N/A

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

      6. fp-cancel-sub-sign-inv N/A

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

      7. lift-neg.f64 N/A

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

      8. +-commutative N/A

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

      9. lift-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift-tan.f64 N/A

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

      12. lift-tan.f64 N/A

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

      13. +-commutative N/A

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

      14. lower-+.f64 99.8

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

      15. lift-fma.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 99.8

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

   9. Applied rewrites 99.8%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{-13} \lor \neg \left(a \leq 4 \cdot 10^{-79}\right):\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan y + \tan z}{\mathsf{fma}\left(\tan y, -\tan z, 1\right)} - \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{-15}:\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\tan \left(z \cdot \left(\frac{y}{z} - -1\right)\right) - \left(-x\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= z 1.7e-15)
   (+ x (- (tan y) (tan a)))
   (- (tan (* z (- (/ y z) -1.0))) (- x))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= 1.7e-15) {
		tmp = x + (tan(y) - tan(a));
	} else {
		tmp = tan((z * ((y / z) - -1.0))) - -x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
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 <= 1.7d-15) then
        tmp = x + (tan(y) - tan(a))
    else
        tmp = tan((z * ((y / z) - (-1.0d0)))) - -x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= 1.7e-15) {
		tmp = x + (Math.tan(y) - Math.tan(a));
	} else {
		tmp = Math.tan((z * ((y / z) - -1.0))) - -x;
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if z <= 1.7e-15:
		tmp = x + (math.tan(y) - math.tan(a))
	else:
		tmp = math.tan((z * ((y / z) - -1.0))) - -x
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (z <= 1.7e-15)
		tmp = Float64(x + Float64(tan(y) - tan(a)));
	else
		tmp = Float64(tan(Float64(z * Float64(Float64(y / z) - -1.0))) - Float64(-x));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (z <= 1.7e-15)
		tmp = x + (tan(y) - tan(a));
	else
		tmp = tan((z * ((y / z) - -1.0))) - -x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[z, 1.7e-15], N[(x + N[(N[Tan[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Tan[N[(z * N[(N[(y / z), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.7e-15

   1. Initial program 88.3%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-sin.f64 N/A

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

      6. lower-cos.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-sin.f64 N/A

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

      9. lower-cos.f64 75.9

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

   5. Applied rewrites 75.9%

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

   7. Applied rewrites 76.0%

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

   if 1.7e-15 < z

   1. Initial program 70.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift--.f64 N/A

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

      4. associate-+l- N/A

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

      5. lower--.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower--.f64 70.0

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

   4. Applied rewrites 70.0%

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

   5. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 52.0

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

   7. Applied rewrites 52.0%

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

   8. Taylor expanded in z around -inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

      6. associate-*r/ N/A

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

      7. mul-1-neg N/A

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

      8. lower-/.f64 N/A

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

      9. lower-neg.f64 52.0

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

   10. Applied rewrites 52.0%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{-15}:\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\tan \left(z \cdot \left(\frac{y}{z} - -1\right)\right) - \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.9% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))

C

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

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
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

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

Python

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

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + Float64(tan(Float64(y + z)) - tan(a)))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x + (tan((y + z)) - tan(a));
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.7%

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

Alternative 7: 50.6% accurate, 1.9× speedup

Math

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

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a) :precision binary64 (- (tan (+ z y)) (- x)))

C

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

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
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 = tan((z + y)) - -x
end function

Java

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

Python

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

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(tan(Float64(z + y)) - Float64(-x))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = tan((z + y)) - -x;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision] - (-x)), $MachinePrecision]

Derivation

1. Initial program 83.7%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift--.f64 N/A

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

   4. associate-+l- N/A

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

   5. lower--.f64 N/A

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

   6. lift-+.f64 N/A

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

   7. +-commutative N/A

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

   8. lower-+.f64 N/A

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

   9. lower--.f64 83.6

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

4. Applied rewrites 83.6%

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

5. Taylor expanded in x around inf

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 56.1

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

7. Applied rewrites 56.1%

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

Alternative 8: 32.1% accurate, 26.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ -1 \cdot \left(-x\right) \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a) :precision binary64 (* -1.0 (- x)))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return -1.0 * -x;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
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 = (-1.0d0) * -x
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	return -1.0 * -x;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return -1.0 * -x

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(-1.0 * Float64(-x))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = -1.0 * -x;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(-1.0 * (-x)), $MachinePrecision]

Derivation

1. Initial program 83.7%

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

   1. lift--.f64 N/A

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

   2. lift-tan.f64 N/A

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

   3. tan-quot N/A

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

   4. lift-tan.f64 N/A

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

   5. tan-quot N/A

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

   6. frac-2neg N/A

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

   7. frac-sub N/A

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

   8. lower-/.f64 N/A

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

4. Applied rewrites 83.6%

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

5. Taylor expanded in x around -inf

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

   1. mul-1-neg N/A

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

   2. *-commutative N/A

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

   3. distribute-rgt-neg-in N/A

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

   4. mul-1-neg N/A

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

   5. lower-*.f64 N/A

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

7. Applied rewrites 83.4%

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

8. Taylor expanded in x around inf

   \[\leadsto -1 \cdot \left(-\color{blue}{x}\right) \]
9. Step-by-step derivation

10. Applied rewrites 36.1%

    \[\leadsto -1 \cdot \left(-\color{blue}{x}\right) \]
11. Add Preprocessing

Alternative 9: 22.6% accurate, 35.0× speedup

Math

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

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a) :precision binary64 (+ x (- a)))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x + -a;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
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 + -a
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	return x + -a;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return x + -a

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + Float64(-a))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x + -a;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + (-a)), $MachinePrecision]

Derivation

1. Initial program 83.7%

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

3. Taylor expanded in a around 0

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

   1. +-commutative N/A

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

   2. fp-cancel-sign-sub-inv N/A

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

   3. metadata-eval N/A

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

   4. *-lft-identity N/A

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

   5. lower--.f64 N/A

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

   6. lower-/.f64 N/A

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

   7. lower-sin.f64 N/A

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

   8. +-commutative N/A

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

   9. lower-+.f64 N/A

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

   10. lower-cos.f64 N/A

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

   11. +-commutative N/A

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

   12. lower-+.f64 47.5

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

5. Applied rewrites 47.5%

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

6. Taylor expanded in a around inf

   \[\leadsto x + -1 \cdot \color{blue}{a} \]
7. Step-by-step derivation

8. Applied rewrites 27.5%

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

Reproduce

herbie shell --seed 2024337 
(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))))