tan-example (used to crash)

Percentage Accurate: 78.8% → 99.7%

Time: 57.0s

Alternatives: 6

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: 78.8% 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

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

FPCore

(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (/ 1.0 (- 1.0 (* (tan y) (tan z))))))
   (+ x (- (+ (* (tan z) t_0) (* (tan y) t_0)) (tan a)))))

C

double code(double x, double y, double z, double a) {
	double t_0 = 1.0 / (1.0 - (tan(y) * tan(z)));
	return x + (((tan(z) * t_0) + (tan(y) * t_0)) - 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
    real(8) :: t_0
    t_0 = 1.0d0 / (1.0d0 - (tan(y) * tan(z)))
    code = x + (((tan(z) * t_0) + (tan(y) * t_0)) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	double t_0 = 1.0 / (1.0 - (Math.tan(y) * Math.tan(z)));
	return x + (((Math.tan(z) * t_0) + (Math.tan(y) * t_0)) - Math.tan(a));
}

Python

def code(x, y, z, a):
	t_0 = 1.0 / (1.0 - (math.tan(y) * math.tan(z)))
	return x + (((math.tan(z) * t_0) + (math.tan(y) * t_0)) - math.tan(a))

Julia

function code(x, y, z, a)
	t_0 = Float64(1.0 / Float64(1.0 - Float64(tan(y) * tan(z))))
	return Float64(x + Float64(Float64(Float64(tan(z) * t_0) + Float64(tan(y) * t_0)) - tan(a)))
end

MATLAB

function tmp = code(x, y, z, a)
	t_0 = 1.0 / (1.0 - (tan(y) * tan(z)));
	tmp = x + (((tan(z) * t_0) + (tan(y) * t_0)) - tan(a));
end

Wolfram

code[x_, y_, z_, a_] := Block[{t$95$0 = N[(1.0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x + N[(N[(N[(N[Tan[z], $MachinePrecision] * t$95$0), $MachinePrecision] + N[(N[Tan[y], $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 79.0%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
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. *-commutative 99.7%

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

   2. +-commutative 99.7%

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

   3. distribute-lft-in 99.7%

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

6. Applied egg-rr 99.7%

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

7. Final simplification 99.7%

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

Alternative 2: 99.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double a) {
	return x + (((1.0 / (1.0 - (tan(y) * tan(z)))) * (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 + (((1.0d0 / (1.0d0 - (tan(y) * tan(z)))) * (tan(y) + tan(z))) - tan(a))
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, a)
	tmp = x + (((1.0 / (1.0 - (tan(y) * tan(z)))) * (tan(y) + tan(z))) - tan(a));
end

Wolfram

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

Derivation

1. Initial program 79.0%

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

   \[\leadsto x + \left(\frac{1}{1 - \tan y \cdot \tan z} \cdot \left(\tan y + \tan z\right) - \tan a\right) \]
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 79.0%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
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: 78.7% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z a)
 :precision binary64
 (+ x (- (/ 1.0 (/ (cos (+ y z)) (sin (+ y z)))) (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + ((1.0 / (cos((y + z)) / sin((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 + ((1.0d0 / (cos((y + z)) / sin((y + z)))) - tan(a))
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, a)
	tmp = x + ((1.0 / (cos((y + z)) / sin((y + z)))) - tan(a));
end

Wolfram

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

Derivation

1. Initial program 79.0%

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

   1. tan-quot 79.0%

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

   2. clear-num 79.0%

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

4. Applied egg-rr 79.0%

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

5. Final simplification 79.0%

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

Alternative 5: 78.8% 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 79.0%

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

3. Final simplification 79.0%

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

Alternative 6: 31.4% 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 79.0%

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

3. Taylor expanded in x around inf 31.6%

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

4. Final simplification 31.6%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024079 
(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))))