Example 2 from Robby

Percentage Accurate: 99.8% → 99.8%

Time: 17.0s

Alternatives: 9

Speedup: N/A×

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \tan^{-1} \left(\frac{\left(-eh\right) \cdot \tan t}{ew}\right)\\ \left|\left(ew \cdot \cos t\right) \cdot \cos t_1 - \left(eh \cdot \sin t\right) \cdot \sin t_1\right| \end{array} \end{array} \]

FPCore

(FPCore (eh ew t)
 :precision binary64
 (let* ((t_1 (atan (/ (* (- eh) (tan t)) ew))))
   (fabs (- (* (* ew (cos t)) (cos t_1)) (* (* eh (sin t)) (sin t_1))))))

C

double code(double eh, double ew, double t) {
	double t_1 = atan(((-eh * tan(t)) / ew));
	return fabs((((ew * cos(t)) * cos(t_1)) - ((eh * sin(t)) * sin(t_1))));
}

Fortran

real(8) function code(eh, ew, t)
    real(8), intent (in) :: eh
    real(8), intent (in) :: ew
    real(8), intent (in) :: t
    real(8) :: t_1
    t_1 = atan(((-eh * tan(t)) / ew))
    code = abs((((ew * cos(t)) * cos(t_1)) - ((eh * sin(t)) * sin(t_1))))
end function

Java

public static double code(double eh, double ew, double t) {
	double t_1 = Math.atan(((-eh * Math.tan(t)) / ew));
	return Math.abs((((ew * Math.cos(t)) * Math.cos(t_1)) - ((eh * Math.sin(t)) * Math.sin(t_1))));
}

Python

def code(eh, ew, t):
	t_1 = math.atan(((-eh * math.tan(t)) / ew))
	return math.fabs((((ew * math.cos(t)) * math.cos(t_1)) - ((eh * math.sin(t)) * math.sin(t_1))))

Julia

function code(eh, ew, t)
	t_1 = atan(Float64(Float64(Float64(-eh) * tan(t)) / ew))
	return abs(Float64(Float64(Float64(ew * cos(t)) * cos(t_1)) - Float64(Float64(eh * sin(t)) * sin(t_1))))
end

MATLAB

function tmp = code(eh, ew, t)
	t_1 = atan(((-eh * tan(t)) / ew));
	tmp = abs((((ew * cos(t)) * cos(t_1)) - ((eh * sin(t)) * sin(t_1))));
end

Wolfram

code[eh_, ew_, t_] := Block[{t$95$1 = N[ArcTan[N[(N[((-eh) * N[Tan[t], $MachinePrecision]), $MachinePrecision] / ew), $MachinePrecision]], $MachinePrecision]}, N[Abs[N[(N[(N[(ew * N[Cos[t], $MachinePrecision]), $MachinePrecision] * N[Cos[t$95$1], $MachinePrecision]), $MachinePrecision] - N[(N[(eh * N[Sin[t], $MachinePrecision]), $MachinePrecision] * N[Sin[t$95$1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \tan^{-1} \left(\frac{\left(-eh\right) \cdot \tan t}{ew}\right)\\ \left|\left(ew \cdot \cos t\right) \cdot \cos t_1 - \left(eh \cdot \sin t\right) \cdot \sin t_1\right| \end{array} \end{array} \]

FPCore

(FPCore (eh ew t)
 :precision binary64
 (let* ((t_1 (atan (/ (* (- eh) (tan t)) ew))))
   (fabs (- (* (* ew (cos t)) (cos t_1)) (* (* eh (sin t)) (sin t_1))))))

C

double code(double eh, double ew, double t) {
	double t_1 = atan(((-eh * tan(t)) / ew));
	return fabs((((ew * cos(t)) * cos(t_1)) - ((eh * sin(t)) * sin(t_1))));
}

Fortran

real(8) function code(eh, ew, t)
    real(8), intent (in) :: eh
    real(8), intent (in) :: ew
    real(8), intent (in) :: t
    real(8) :: t_1
    t_1 = atan(((-eh * tan(t)) / ew))
    code = abs((((ew * cos(t)) * cos(t_1)) - ((eh * sin(t)) * sin(t_1))))
end function

Java

public static double code(double eh, double ew, double t) {
	double t_1 = Math.atan(((-eh * Math.tan(t)) / ew));
	return Math.abs((((ew * Math.cos(t)) * Math.cos(t_1)) - ((eh * Math.sin(t)) * Math.sin(t_1))));
}

Python

def code(eh, ew, t):
	t_1 = math.atan(((-eh * math.tan(t)) / ew))
	return math.fabs((((ew * math.cos(t)) * math.cos(t_1)) - ((eh * math.sin(t)) * math.sin(t_1))))

Julia

function code(eh, ew, t)
	t_1 = atan(Float64(Float64(Float64(-eh) * tan(t)) / ew))
	return abs(Float64(Float64(Float64(ew * cos(t)) * cos(t_1)) - Float64(Float64(eh * sin(t)) * sin(t_1))))
end

MATLAB

function tmp = code(eh, ew, t)
	t_1 = atan(((-eh * tan(t)) / ew));
	tmp = abs((((ew * cos(t)) * cos(t_1)) - ((eh * sin(t)) * sin(t_1))));
end

Wolfram

code[eh_, ew_, t_] := Block[{t$95$1 = N[ArcTan[N[(N[((-eh) * N[Tan[t], $MachinePrecision]), $MachinePrecision] / ew), $MachinePrecision]], $MachinePrecision]}, N[Abs[N[(N[(N[(ew * N[Cos[t], $MachinePrecision]), $MachinePrecision] * N[Cos[t$95$1], $MachinePrecision]), $MachinePrecision] - N[(N[(eh * N[Sin[t], $MachinePrecision]), $MachinePrecision] * N[Sin[t$95$1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Alternative 1: 99.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \left|\frac{1}{\mathsf{hypot}\left(1, \frac{\tan t}{\frac{ew}{eh}}\right)} \cdot \left(\cos t \cdot ew\right) - \left(eh \cdot \sin t\right) \cdot \sin \tan^{-1} \left(\frac{\tan t \cdot \left(-eh\right)}{ew}\right)\right| \end{array} \]

FPCore

(FPCore (eh ew t)
 :precision binary64
 (fabs
  (-
   (* (/ 1.0 (hypot 1.0 (/ (tan t) (/ ew eh)))) (* (cos t) ew))
   (* (* eh (sin t)) (sin (atan (/ (* (tan t) (- eh)) ew)))))))

C

double code(double eh, double ew, double t) {
	return fabs((((1.0 / hypot(1.0, (tan(t) / (ew / eh)))) * (cos(t) * ew)) - ((eh * sin(t)) * sin(atan(((tan(t) * -eh) / ew))))));
}

Java

public static double code(double eh, double ew, double t) {
	return Math.abs((((1.0 / Math.hypot(1.0, (Math.tan(t) / (ew / eh)))) * (Math.cos(t) * ew)) - ((eh * Math.sin(t)) * Math.sin(Math.atan(((Math.tan(t) * -eh) / ew))))));
}

Python

def code(eh, ew, t):
	return math.fabs((((1.0 / math.hypot(1.0, (math.tan(t) / (ew / eh)))) * (math.cos(t) * ew)) - ((eh * math.sin(t)) * math.sin(math.atan(((math.tan(t) * -eh) / ew))))))

Julia

function code(eh, ew, t)
	return abs(Float64(Float64(Float64(1.0 / hypot(1.0, Float64(tan(t) / Float64(ew / eh)))) * Float64(cos(t) * ew)) - Float64(Float64(eh * sin(t)) * sin(atan(Float64(Float64(tan(t) * Float64(-eh)) / ew))))))
end

MATLAB

function tmp = code(eh, ew, t)
	tmp = abs((((1.0 / hypot(1.0, (tan(t) / (ew / eh)))) * (cos(t) * ew)) - ((eh * sin(t)) * sin(atan(((tan(t) * -eh) / ew))))));
end

Wolfram

code[eh_, ew_, t_] := N[Abs[N[(N[(N[(1.0 / N[Sqrt[1.0 ^ 2 + N[(N[Tan[t], $MachinePrecision] / N[(ew / eh), $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] * N[(N[Cos[t], $MachinePrecision] * ew), $MachinePrecision]), $MachinePrecision] - N[(N[(eh * N[Sin[t], $MachinePrecision]), $MachinePrecision] * N[Sin[N[ArcTan[N[(N[(N[Tan[t], $MachinePrecision] * (-eh)), $MachinePrecision] / ew), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 2: 99.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \left|\left(eh \cdot \sin t\right) \cdot \sin \tan^{-1} \left(\frac{t \cdot \left(-eh\right)}{ew}\right) - \frac{1}{\mathsf{hypot}\left(1, \frac{\tan t}{\frac{ew}{eh}}\right)} \cdot \left(\cos t \cdot ew\right)\right| \end{array} \]

FPCore

(FPCore (eh ew t)
 :precision binary64
 (fabs
  (-
   (* (* eh (sin t)) (sin (atan (/ (* t (- eh)) ew))))
   (* (/ 1.0 (hypot 1.0 (/ (tan t) (/ ew eh)))) (* (cos t) ew)))))

C

double code(double eh, double ew, double t) {
	return fabs((((eh * sin(t)) * sin(atan(((t * -eh) / ew)))) - ((1.0 / hypot(1.0, (tan(t) / (ew / eh)))) * (cos(t) * ew))));
}

Java

public static double code(double eh, double ew, double t) {
	return Math.abs((((eh * Math.sin(t)) * Math.sin(Math.atan(((t * -eh) / ew)))) - ((1.0 / Math.hypot(1.0, (Math.tan(t) / (ew / eh)))) * (Math.cos(t) * ew))));
}

Python

def code(eh, ew, t):
	return math.fabs((((eh * math.sin(t)) * math.sin(math.atan(((t * -eh) / ew)))) - ((1.0 / math.hypot(1.0, (math.tan(t) / (ew / eh)))) * (math.cos(t) * ew))))

Julia

function code(eh, ew, t)
	return abs(Float64(Float64(Float64(eh * sin(t)) * sin(atan(Float64(Float64(t * Float64(-eh)) / ew)))) - Float64(Float64(1.0 / hypot(1.0, Float64(tan(t) / Float64(ew / eh)))) * Float64(cos(t) * ew))))
end

MATLAB

function tmp = code(eh, ew, t)
	tmp = abs((((eh * sin(t)) * sin(atan(((t * -eh) / ew)))) - ((1.0 / hypot(1.0, (tan(t) / (ew / eh)))) * (cos(t) * ew))));
end

Wolfram

code[eh_, ew_, t_] := N[Abs[N[(N[(N[(eh * N[Sin[t], $MachinePrecision]), $MachinePrecision] * N[Sin[N[ArcTan[N[(N[(t * (-eh)), $MachinePrecision] / ew), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(N[(1.0 / N[Sqrt[1.0 ^ 2 + N[(N[Tan[t], $MachinePrecision] / N[(ew / eh), $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] * N[(N[Cos[t], $MachinePrecision] * ew), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 3: 98.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \left|\cos t \cdot ew - \left(eh \cdot \sin t\right) \cdot \sin \tan^{-1} \left(\frac{\tan t \cdot \left(-eh\right)}{ew}\right)\right| \end{array} \]

FPCore

(FPCore (eh ew t)
 :precision binary64
 (fabs
  (-
   (* (cos t) ew)
   (* (* eh (sin t)) (sin (atan (/ (* (tan t) (- eh)) ew)))))))

C

double code(double eh, double ew, double t) {
	return fabs(((cos(t) * ew) - ((eh * sin(t)) * sin(atan(((tan(t) * -eh) / ew))))));
}

Fortran

real(8) function code(eh, ew, t)
    real(8), intent (in) :: eh
    real(8), intent (in) :: ew
    real(8), intent (in) :: t
    code = abs(((cos(t) * ew) - ((eh * sin(t)) * sin(atan(((tan(t) * -eh) / ew))))))
end function

Java

public static double code(double eh, double ew, double t) {
	return Math.abs(((Math.cos(t) * ew) - ((eh * Math.sin(t)) * Math.sin(Math.atan(((Math.tan(t) * -eh) / ew))))));
}

Python

def code(eh, ew, t):
	return math.fabs(((math.cos(t) * ew) - ((eh * math.sin(t)) * math.sin(math.atan(((math.tan(t) * -eh) / ew))))))

Julia

function code(eh, ew, t)
	return abs(Float64(Float64(cos(t) * ew) - Float64(Float64(eh * sin(t)) * sin(atan(Float64(Float64(tan(t) * Float64(-eh)) / ew))))))
end

MATLAB

function tmp = code(eh, ew, t)
	tmp = abs(((cos(t) * ew) - ((eh * sin(t)) * sin(atan(((tan(t) * -eh) / ew))))));
end

Wolfram

code[eh_, ew_, t_] := N[Abs[N[(N[(N[Cos[t], $MachinePrecision] * ew), $MachinePrecision] - N[(N[(eh * N[Sin[t], $MachinePrecision]), $MachinePrecision] * N[Sin[N[ArcTan[N[(N[(N[Tan[t], $MachinePrecision] * (-eh)), $MachinePrecision] / ew), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 4: 98.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \left|\cos t \cdot ew - \left(eh \cdot \sin t\right) \cdot \sin \tan^{-1} \left(\frac{\tan t \cdot eh}{ew}\right)\right| \end{array} \]

FPCore

(FPCore (eh ew t)
 :precision binary64
 (fabs
  (- (* (cos t) ew) (* (* eh (sin t)) (sin (atan (/ (* (tan t) eh) ew)))))))

C

double code(double eh, double ew, double t) {
	return fabs(((cos(t) * ew) - ((eh * sin(t)) * sin(atan(((tan(t) * eh) / ew))))));
}

Fortran

real(8) function code(eh, ew, t)
    real(8), intent (in) :: eh
    real(8), intent (in) :: ew
    real(8), intent (in) :: t
    code = abs(((cos(t) * ew) - ((eh * sin(t)) * sin(atan(((tan(t) * eh) / ew))))))
end function

Java

public static double code(double eh, double ew, double t) {
	return Math.abs(((Math.cos(t) * ew) - ((eh * Math.sin(t)) * Math.sin(Math.atan(((Math.tan(t) * eh) / ew))))));
}

Python

def code(eh, ew, t):
	return math.fabs(((math.cos(t) * ew) - ((eh * math.sin(t)) * math.sin(math.atan(((math.tan(t) * eh) / ew))))))

Julia

function code(eh, ew, t)
	return abs(Float64(Float64(cos(t) * ew) - Float64(Float64(eh * sin(t)) * sin(atan(Float64(Float64(tan(t) * eh) / ew))))))
end

MATLAB

function tmp = code(eh, ew, t)
	tmp = abs(((cos(t) * ew) - ((eh * sin(t)) * sin(atan(((tan(t) * eh) / ew))))));
end

Wolfram

code[eh_, ew_, t_] := N[Abs[N[(N[(N[Cos[t], $MachinePrecision] * ew), $MachinePrecision] - N[(N[(eh * N[Sin[t], $MachinePrecision]), $MachinePrecision] * N[Sin[N[ArcTan[N[(N[(N[Tan[t], $MachinePrecision] * eh), $MachinePrecision] / ew), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 5: 98.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \left|\cos t \cdot ew - \left(eh \cdot \sin t\right) \cdot \sin \tan^{-1} \left(\frac{t \cdot \left(-eh\right)}{ew}\right)\right| \end{array} \]

FPCore

(FPCore (eh ew t)
 :precision binary64
 (fabs (- (* (cos t) ew) (* (* eh (sin t)) (sin (atan (/ (* t (- eh)) ew)))))))

C

double code(double eh, double ew, double t) {
	return fabs(((cos(t) * ew) - ((eh * sin(t)) * sin(atan(((t * -eh) / ew))))));
}

Fortran

real(8) function code(eh, ew, t)
    real(8), intent (in) :: eh
    real(8), intent (in) :: ew
    real(8), intent (in) :: t
    code = abs(((cos(t) * ew) - ((eh * sin(t)) * sin(atan(((t * -eh) / ew))))))
end function

Java

public static double code(double eh, double ew, double t) {
	return Math.abs(((Math.cos(t) * ew) - ((eh * Math.sin(t)) * Math.sin(Math.atan(((t * -eh) / ew))))));
}

Python

def code(eh, ew, t):
	return math.fabs(((math.cos(t) * ew) - ((eh * math.sin(t)) * math.sin(math.atan(((t * -eh) / ew))))))

Julia

function code(eh, ew, t)
	return abs(Float64(Float64(cos(t) * ew) - Float64(Float64(eh * sin(t)) * sin(atan(Float64(Float64(t * Float64(-eh)) / ew))))))
end

MATLAB

function tmp = code(eh, ew, t)
	tmp = abs(((cos(t) * ew) - ((eh * sin(t)) * sin(atan(((t * -eh) / ew))))));
end

Wolfram

code[eh_, ew_, t_] := N[Abs[N[(N[(N[Cos[t], $MachinePrecision] * ew), $MachinePrecision] - N[(N[(eh * N[Sin[t], $MachinePrecision]), $MachinePrecision] * N[Sin[N[ArcTan[N[(N[(t * (-eh)), $MachinePrecision] / ew), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 6: 79.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \left|ew - \left(eh \cdot \sin t\right) \cdot \sin \tan^{-1} \left(\frac{\tan t \cdot \left(-eh\right)}{ew}\right)\right| \end{array} \]

FPCore

(FPCore (eh ew t)
 :precision binary64
 (fabs (- ew (* (* eh (sin t)) (sin (atan (/ (* (tan t) (- eh)) ew)))))))

C

double code(double eh, double ew, double t) {
	return fabs((ew - ((eh * sin(t)) * sin(atan(((tan(t) * -eh) / ew))))));
}

Fortran

real(8) function code(eh, ew, t)
    real(8), intent (in) :: eh
    real(8), intent (in) :: ew
    real(8), intent (in) :: t
    code = abs((ew - ((eh * sin(t)) * sin(atan(((tan(t) * -eh) / ew))))))
end function

Java

public static double code(double eh, double ew, double t) {
	return Math.abs((ew - ((eh * Math.sin(t)) * Math.sin(Math.atan(((Math.tan(t) * -eh) / ew))))));
}

Python

def code(eh, ew, t):
	return math.fabs((ew - ((eh * math.sin(t)) * math.sin(math.atan(((math.tan(t) * -eh) / ew))))))

Julia

function code(eh, ew, t)
	return abs(Float64(ew - Float64(Float64(eh * sin(t)) * sin(atan(Float64(Float64(tan(t) * Float64(-eh)) / ew))))))
end

MATLAB

function tmp = code(eh, ew, t)
	tmp = abs((ew - ((eh * sin(t)) * sin(atan(((tan(t) * -eh) / ew))))));
end

Wolfram

code[eh_, ew_, t_] := N[Abs[N[(ew - N[(N[(eh * N[Sin[t], $MachinePrecision]), $MachinePrecision] * N[Sin[N[ArcTan[N[(N[(N[Tan[t], $MachinePrecision] * (-eh)), $MachinePrecision] / ew), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 7: 79.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \left|ew - \left(eh \cdot \sin t\right) \cdot \sin \tan^{-1} \left(\frac{\tan t \cdot eh}{ew}\right)\right| \end{array} \]

FPCore

(FPCore (eh ew t)
 :precision binary64
 (fabs (- ew (* (* eh (sin t)) (sin (atan (/ (* (tan t) eh) ew)))))))

C

double code(double eh, double ew, double t) {
	return fabs((ew - ((eh * sin(t)) * sin(atan(((tan(t) * eh) / ew))))));
}

Fortran

real(8) function code(eh, ew, t)
    real(8), intent (in) :: eh
    real(8), intent (in) :: ew
    real(8), intent (in) :: t
    code = abs((ew - ((eh * sin(t)) * sin(atan(((tan(t) * eh) / ew))))))
end function

Java

public static double code(double eh, double ew, double t) {
	return Math.abs((ew - ((eh * Math.sin(t)) * Math.sin(Math.atan(((Math.tan(t) * eh) / ew))))));
}

Python

def code(eh, ew, t):
	return math.fabs((ew - ((eh * math.sin(t)) * math.sin(math.atan(((math.tan(t) * eh) / ew))))))

Julia

function code(eh, ew, t)
	return abs(Float64(ew - Float64(Float64(eh * sin(t)) * sin(atan(Float64(Float64(tan(t) * eh) / ew))))))
end

MATLAB

function tmp = code(eh, ew, t)
	tmp = abs((ew - ((eh * sin(t)) * sin(atan(((tan(t) * eh) / ew))))));
end

Wolfram

code[eh_, ew_, t_] := N[Abs[N[(ew - N[(N[(eh * N[Sin[t], $MachinePrecision]), $MachinePrecision] * N[Sin[N[ArcTan[N[(N[(N[Tan[t], $MachinePrecision] * eh), $MachinePrecision] / ew), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 8: 55.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \left|ew - t \cdot \left(eh \cdot \sin \tan^{-1} \left(\frac{eh}{ew} \cdot \left(-\tan t\right)\right)\right)\right| \end{array} \]

FPCore

(FPCore (eh ew t)
 :precision binary64
 (fabs (- ew (* t (* eh (sin (atan (* (/ eh ew) (- (tan t))))))))))

C

double code(double eh, double ew, double t) {
	return fabs((ew - (t * (eh * sin(atan(((eh / ew) * -tan(t))))))));
}

Fortran

real(8) function code(eh, ew, t)
    real(8), intent (in) :: eh
    real(8), intent (in) :: ew
    real(8), intent (in) :: t
    code = abs((ew - (t * (eh * sin(atan(((eh / ew) * -tan(t))))))))
end function

Java

public static double code(double eh, double ew, double t) {
	return Math.abs((ew - (t * (eh * Math.sin(Math.atan(((eh / ew) * -Math.tan(t))))))));
}

Python

def code(eh, ew, t):
	return math.fabs((ew - (t * (eh * math.sin(math.atan(((eh / ew) * -math.tan(t))))))))

Julia

function code(eh, ew, t)
	return abs(Float64(ew - Float64(t * Float64(eh * sin(atan(Float64(Float64(eh / ew) * Float64(-tan(t)))))))))
end

MATLAB

function tmp = code(eh, ew, t)
	tmp = abs((ew - (t * (eh * sin(atan(((eh / ew) * -tan(t))))))));
end

Wolfram

code[eh_, ew_, t_] := N[Abs[N[(ew - N[(t * N[(eh * N[Sin[N[ArcTan[N[(N[(eh / ew), $MachinePrecision] * (-N[Tan[t], $MachinePrecision])), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 9: 79.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \left|ew - \left(eh \cdot \sin t\right) \cdot \sin \tan^{-1} \left(\frac{t \cdot \left(-eh\right)}{ew}\right)\right| \end{array} \]

FPCore

(FPCore (eh ew t)
 :precision binary64
 (fabs (- ew (* (* eh (sin t)) (sin (atan (/ (* t (- eh)) ew)))))))

C

double code(double eh, double ew, double t) {
	return fabs((ew - ((eh * sin(t)) * sin(atan(((t * -eh) / ew))))));
}

Fortran

real(8) function code(eh, ew, t)
    real(8), intent (in) :: eh
    real(8), intent (in) :: ew
    real(8), intent (in) :: t
    code = abs((ew - ((eh * sin(t)) * sin(atan(((t * -eh) / ew))))))
end function

Java

public static double code(double eh, double ew, double t) {
	return Math.abs((ew - ((eh * Math.sin(t)) * Math.sin(Math.atan(((t * -eh) / ew))))));
}

Python

def code(eh, ew, t):
	return math.fabs((ew - ((eh * math.sin(t)) * math.sin(math.atan(((t * -eh) / ew))))))

Julia

function code(eh, ew, t)
	return abs(Float64(ew - Float64(Float64(eh * sin(t)) * sin(atan(Float64(Float64(t * Float64(-eh)) / ew))))))
end

MATLAB

function tmp = code(eh, ew, t)
	tmp = abs((ew - ((eh * sin(t)) * sin(atan(((t * -eh) / ew))))));
end

Wolfram

code[eh_, ew_, t_] := N[Abs[N[(ew - N[(N[(eh * N[Sin[t], $MachinePrecision]), $MachinePrecision] * N[Sin[N[ArcTan[N[(N[(t * (-eh)), $MachinePrecision] / ew), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2023343 
(FPCore (eh ew t)
  :name "Example 2 from Robby"
  :precision binary64
  (fabs (- (* (* ew (cos t)) (cos (atan (/ (* (- eh) (tan t)) ew)))) (* (* eh (sin t)) (sin (atan (/ (* (- eh) (tan t)) ew)))))))