tan-example (used to crash)

Percentage Accurate: 79.5% → 99.7%

Time: 41.0s

Alternatives: 11

Speedup: 1.0×

• could not determine a ground truth

  1. x = 1.888306998962487
  2. y = 5.872377098175464e-213
  3. z = -6.770498703728799e+204
  4. a = -3.6896843099920073e-150

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, 0.3× speedup

Math

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

FPCore

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

C

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

Julia

function code(x, y, z, a)
	return Float64(x + Float64(Float64(Float64(tan(y) + tan(z)) * Float64(-1.0 / fma(tan(y), tan(z), -1.0))) - 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] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.9%

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

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

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 91.9%

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

   2. expm1-undefine 91.8%

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

   3. log1p-undefine 91.8%

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

   4. add-exp-log 99.7%

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

6. Applied egg-rr 99.7%

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

   1. associate--l+ 99.7%

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

   2. fma-neg 99.7%

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

   3. metadata-eval 99.7%

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

8. Simplified 99.7%

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

   1. *-un-lft-identity 99.7%

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

   2. associate--r+ 99.7%

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

   3. metadata-eval 99.7%

      \[\leadsto x + \left(\left(\tan y + \tan z\right) \cdot \left(1 \cdot \frac{1}{\color{blue}{0} - \mathsf{fma}\left(\tan y, \tan z, -1\right)}\right) - \tan a\right) \]

   4. sub0-neg 99.7%

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

10. Applied egg-rr 99.7%

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

    1. *-lft-identity 99.7%

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

    2. metadata-eval 99.7%

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

    3. distribute-neg-frac 99.7%

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

    4. distribute-neg-frac2 99.7%

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

    5. remove-double-neg 99.7%

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

12. Simplified 99.7%

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

13. Final simplification 99.7%

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

Alternative 2: 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 76.9%

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

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

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. Final simplification 99.7%

   \[\leadsto x + \left(\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z} - \tan a\right) \]
6. 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 76.9%

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

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

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. 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%

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

6. Simplified 99.7%

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

7. Final simplification 99.7%

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

Alternative 4: 80.0% 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 76.9%

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

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

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 91.9%

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

   2. expm1-undefine 91.8%

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

   3. log1p-undefine 91.8%

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

   4. add-exp-log 99.7%

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

6. Applied egg-rr 99.7%

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

   1. associate--l+ 99.7%

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

   2. fma-neg 99.7%

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

   3. metadata-eval 99.7%

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

8. Simplified 99.7%

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

9. Taylor expanded in y around 0 77.6%

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

10. Final simplification 77.6%

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

Alternative 5: 41.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left({x}^{3}\right)}^{0.3333333333333333}\\ \mathbf{if}\;z \leq -1.35:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.00065:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (pow (pow x 3.0) 0.3333333333333333)))
   (if (<= z -1.35) t_0 (if (<= z 0.00065) (+ x (- z (tan a))) t_0))))

C

double code(double x, double y, double z, double a) {
	double t_0 = pow(pow(x, 3.0), 0.3333333333333333);
	double tmp;
	if (z <= -1.35) {
		tmp = t_0;
	} else if (z <= 0.00065) {
		tmp = x + (z - tan(a));
	} else {
		tmp = t_0;
	}
	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 = (x ** 3.0d0) ** 0.3333333333333333d0
    if (z <= (-1.35d0)) then
        tmp = t_0
    else if (z <= 0.00065d0) then
        tmp = x + (z - tan(a))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double t_0 = Math.pow(Math.pow(x, 3.0), 0.3333333333333333);
	double tmp;
	if (z <= -1.35) {
		tmp = t_0;
	} else if (z <= 0.00065) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z, a):
	t_0 = math.pow(math.pow(x, 3.0), 0.3333333333333333)
	tmp = 0
	if z <= -1.35:
		tmp = t_0
	elif z <= 0.00065:
		tmp = x + (z - math.tan(a))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z, a)
	t_0 = (x ^ 3.0) ^ 0.3333333333333333
	tmp = 0.0
	if (z <= -1.35)
		tmp = t_0;
	elseif (z <= 0.00065)
		tmp = Float64(x + Float64(z - tan(a)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	t_0 = (x ^ 3.0) ^ 0.3333333333333333;
	tmp = 0.0;
	if (z <= -1.35)
		tmp = t_0;
	elseif (z <= 0.00065)
		tmp = x + (z - tan(a));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := Block[{t$95$0 = N[Power[N[Power[x, 3.0], $MachinePrecision], 0.3333333333333333], $MachinePrecision]}, If[LessEqual[z, -1.35], t$95$0, If[LessEqual[z, 0.00065], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3500000000000001 or 6.4999999999999997e-4 < z

   1. Initial program 58.3%

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

      1. add-cbrt-cube 58.0%

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

      2. pow1/3 50.8%

         \[\leadsto \color{blue}{{\left(\left(\left(x + \left(\tan \left(y + z\right) - \tan a\right)\right) \cdot \left(x + \left(\tan \left(y + z\right) - \tan a\right)\right)\right) \cdot \left(x + \left(\tan \left(y + z\right) - \tan a\right)\right)\right)}^{0.3333333333333333}} \]

      3. pow3 50.8%

         \[\leadsto {\color{blue}{\left({\left(x + \left(\tan \left(y + z\right) - \tan a\right)\right)}^{3}\right)}}^{0.3333333333333333} \]

      4. +-commutative 50.8%

         \[\leadsto {\left({\color{blue}{\left(\left(\tan \left(y + z\right) - \tan a\right) + x\right)}}^{3}\right)}^{0.3333333333333333} \]

      5. associate-+l- 50.8%

         \[\leadsto {\left({\color{blue}{\left(\tan \left(y + z\right) - \left(\tan a - x\right)\right)}}^{3}\right)}^{0.3333333333333333} \]

   4. Applied egg-rr 50.8%

      \[\leadsto \color{blue}{{\left({\left(\tan \left(y + z\right) - \left(\tan a - x\right)\right)}^{3}\right)}^{0.3333333333333333}} \]

   5. Taylor expanded in x around inf 21.4%

      \[\leadsto {\left({\color{blue}{x}}^{3}\right)}^{0.3333333333333333} \]

   if -1.3500000000000001 < z < 6.4999999999999997e-4

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 60.0%

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

   4. Taylor expanded in z around 0 60.0%

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

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35:\\ \;\;\;\;{\left({x}^{3}\right)}^{0.3333333333333333}\\ \mathbf{elif}\;z \leq 0.00065:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;{\left({x}^{3}\right)}^{0.3333333333333333}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.98:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00065:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{expm1}\left(\mathsf{log1p}\left(x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= z -0.98) x (if (<= z 0.00065) (+ x (- z (tan a))) (expm1 (log1p x)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= -0.98) {
		tmp = x;
	} else if (z <= 0.00065) {
		tmp = x + (z - tan(a));
	} else {
		tmp = expm1(log1p(x));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= -0.98) {
		tmp = x;
	} else if (z <= 0.00065) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = Math.expm1(Math.log1p(x));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if z <= -0.98:
		tmp = x
	elif z <= 0.00065:
		tmp = x + (z - math.tan(a))
	else:
		tmp = math.expm1(math.log1p(x))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (z <= -0.98)
		tmp = x;
	elseif (z <= 0.00065)
		tmp = Float64(x + Float64(z - tan(a)));
	else
		tmp = expm1(log1p(x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[z, -0.98], x, If[LessEqual[z, 0.00065], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(Exp[N[Log[1 + x], $MachinePrecision]] - 1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.97999999999999998

   1. Initial program 61.2%

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

   3. Taylor expanded in x around inf 20.7%

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

   if -0.97999999999999998 < z < 6.4999999999999997e-4

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 60.0%

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

   4. Taylor expanded in z around 0 60.0%

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

   if 6.4999999999999997e-4 < z

   1. Initial program 55.4%

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

      1. tan-sum 99.5%

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

      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. *-un-lft-identity 99.6%

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

      2. un-div-inv 99.5%

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

      3. tan-sum 55.4%

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

      4. +-commutative 55.4%

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

      5. +-commutative 55.4%

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

      6. associate-+l- 55.4%

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

      7. +-commutative 55.4%

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

      8. tan-sum 99.5%

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

      9. un-div-inv 99.6%

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

      10. sub-neg 99.6%

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

      11. add-sqr-sqrt 96.1%

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

      12. sqrt-unprod 96.8%

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

      13. sqr-neg 96.8%

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

   6. Applied egg-rr 4.1%

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

      1. *-lft-identity 4.1%

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

   8. Simplified 4.1%

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

   9. Taylor expanded in x around inf 3.3%

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

       1. neg-mul-1 3.3%

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

   11. Simplified 3.3%

       \[\leadsto \color{blue}{-x} \]
   12. Step-by-step derivation

       1. add-sqr-sqrt 0.0%

          \[\leadsto \color{blue}{\sqrt{-x} \cdot \sqrt{-x}} \]

       2. sqrt-unprod 22.1%

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

       3. sqr-neg 22.1%

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

       4. sqrt-unprod 22.1%

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

       5. add-sqr-sqrt 22.1%

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

       6. expm1-log1p-u 22.1%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x\right)\right)} \]

       7. expm1-undefine 22.1%

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

   13. Applied egg-rr 22.1%

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

       1. expm1-define 22.1%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x\right)\right)} \]

   15. Simplified 22.1%

       \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.98:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00065:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{expm1}\left(\mathsf{log1p}\left(x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 76.9%

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

3. Final simplification 76.9%

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

Alternative 8: 60.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.9%

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

3. Taylor expanded in y around 0 58.9%

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

   1. tan-quot 58.9%

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

   2. *-un-lft-identity 58.9%

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

5. Applied egg-rr 58.9%

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

   1. *-lft-identity 58.9%

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

7. Simplified 58.9%

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

8. Final simplification 58.9%

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

Alternative 9: 60.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.9%

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

3. Taylor expanded in y around 0 58.9%

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

   1. tan-quot 58.9%

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

   2. associate-+r- 58.9%

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

5. Applied egg-rr 58.9%

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

6. Final simplification 58.9%

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

Alternative 10: 41.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00065:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= z -1.8) x (if (<= z 0.00065) (+ x (- z (tan a))) x)))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= -1.8) {
		tmp = x;
	} else if (z <= 0.00065) {
		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 <= (-1.8d0)) then
        tmp = x
    else if (z <= 0.00065d0) 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 <= -1.8) {
		tmp = x;
	} else if (z <= 0.00065) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if z <= -1.8:
		tmp = x
	elif z <= 0.00065:
		tmp = x + (z - math.tan(a))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (z <= -1.8)
		tmp = x;
	elseif (z <= 0.00065)
		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 <= -1.8)
		tmp = x;
	elseif (z <= 0.00065)
		tmp = x + (z - tan(a));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[z, -1.8], x, If[LessEqual[z, 0.00065], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.80000000000000004 or 6.4999999999999997e-4 < z

   1. Initial program 58.3%

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

   3. Taylor expanded in x around inf 21.4%

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

   if -1.80000000000000004 < z < 6.4999999999999997e-4

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 60.0%

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

   4. Taylor expanded in z around 0 60.0%

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

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00065:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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 76.9%

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

3. Taylor expanded in x around inf 30.7%

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

4. Final simplification 30.7%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024046 
(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))))