Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2

Percentage Accurate: 85.9% → 99.4%

Time: 11.3s

Alternatives: 14

Speedup: 0.8×

• 23.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Python

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Python

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ (+ 2.0 (* (* 2.0 z) (- 1.0 t))) (* z t)))))
   (if (<= t_1 INFINITY) t_1 (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((2.0 + ((2.0 * z) * (1.0 - t))) / (z * t));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((2.0 + ((2.0 * z) * (1.0 - t))) / (z * t));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + ((2.0 + ((2.0 * z) * (1.0 - t))) / (z * t))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(2.0 * z) * Float64(1.0 - t))) / Float64(z * t)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + ((2.0 + ((2.0 * z) * (1.0 - t))) / (z * t));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(2.0 * z), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 x y) (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))) < +inf.0

   1. Initial program 99.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (/.f64 x y) (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)))

   1. Initial program 0.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Simplified 96.8%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} + \frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq \infty:\\ \;\;\;\;\frac{x}{y} + \frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(2, z, 2\right)}{z \cdot t}\\ t_2 := \frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t}\\ t_3 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+20}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (fma 2.0 z 2.0) (* z t)))
        (t_2 (/ (+ 2.0 (* (* 2.0 z) (- 1.0 t))) (* z t)))
        (t_3 (+ (/ x y) -2.0)))
   (if (<= t_2 -4e+30)
     t_1
     (if (<= t_2 2e+20) t_3 (if (<= t_2 INFINITY) t_1 t_3)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(2.0, z, 2.0) / (z * t);
	double t_2 = (2.0 + ((2.0 * z) * (1.0 - t))) / (z * t);
	double t_3 = (x / y) + -2.0;
	double tmp;
	if (t_2 <= -4e+30) {
		tmp = t_1;
	} else if (t_2 <= 2e+20) {
		tmp = t_3;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(2.0, z, 2.0) / Float64(z * t))
	t_2 = Float64(Float64(2.0 + Float64(Float64(2.0 * z) * Float64(1.0 - t))) / Float64(z * t))
	t_3 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t_2 <= -4e+30)
		tmp = t_1;
	elseif (t_2 <= 2e+20)
		tmp = t_3;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 * z + 2.0), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 + N[(N[(2.0 * z), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+30], t$95$1, If[LessEqual[t$95$2, 2e+20], t$95$3, If[LessEqual[t$95$2, Infinity], t$95$1, t$95$3]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -4.0000000000000001e30 or 2e20 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 99.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

   5. Simplified 83.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z}} \]

   if -4.0000000000000001e30 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2e20 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 73.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Simplified 97.3%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq -4 \cdot 10^{+30}:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, z, 2\right)}{z \cdot t}\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq 2 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;\frac{2 + \left(2 \cdot z\right) \cdot \left(1 - t\right)}{z \cdot t} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, z, 2\right)}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+198}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y} + -2, 2 + \frac{2}{z}\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, \frac{y}{z \cdot t}, x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+52)
   (+ (/ x y) (/ 2.0 (* z t)))
   (if (<= (/ x y) 2e+198)
     (/ (fma t (+ (/ x y) -2.0) (+ 2.0 (/ 2.0 z))) t)
     (/ (fma 2.0 (/ y (* z t)) x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+52) {
		tmp = (x / y) + (2.0 / (z * t));
	} else if ((x / y) <= 2e+198) {
		tmp = fma(t, ((x / y) + -2.0), (2.0 + (2.0 / z))) / t;
	} else {
		tmp = fma(2.0, (y / (z * t)), x) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+52)
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	elseif (Float64(x / y) <= 2e+198)
		tmp = Float64(fma(t, Float64(Float64(x / y) + -2.0), Float64(2.0 + Float64(2.0 / z))) / t);
	else
		tmp = Float64(fma(2.0, Float64(y / Float64(z * t)), x) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+52], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e+198], N[(N[(t * N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision] + N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(N[(2.0 * N[(y / N[(z * t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e52

   1. Initial program 85.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{2}{t \cdot z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \frac{x}{y} + \color{blue}{\frac{2}{t \cdot z}} \]

      2. *-lowering-*.f64 98.1

         \[\leadsto \frac{x}{y} + \frac{2}{\color{blue}{t \cdot z}} \]

   5. Simplified 98.1%

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{2}{t \cdot z}} \]

   if -2e52 < (/.f64 x y) < 2.00000000000000004e198

   1. Initial program 89.3%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]

      2. associate-+r+ N/A

         \[\leadsto \frac{\color{blue}{\left(2 + 2 \cdot \frac{1}{z}\right) + t \cdot \left(\frac{x}{y} - 2\right)}}{t} \]

      3. +-commutative N/A

         \[\leadsto \frac{\color{blue}{t \cdot \left(\frac{x}{y} - 2\right) + \left(2 + 2 \cdot \frac{1}{z}\right)}}{t} \]

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(t, \frac{x}{y} - 2, 2 + 2 \cdot \frac{1}{z}\right)}}{t} \]

      5. sub-neg N/A

         \[\leadsto \frac{\mathsf{fma}\left(t, \color{blue}{\frac{x}{y} + \left(\mathsf{neg}\left(2\right)\right)}, 2 + 2 \cdot \frac{1}{z}\right)}{t} \]

      6. metadata-eval N/A

         \[\leadsto \frac{\mathsf{fma}\left(t, \frac{x}{y} + \color{blue}{-2}, 2 + 2 \cdot \frac{1}{z}\right)}{t} \]

      7. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(t, \color{blue}{-2 + \frac{x}{y}}, 2 + 2 \cdot \frac{1}{z}\right)}{t} \]

      8. *-lft-identity N/A

         \[\leadsto \frac{\mathsf{fma}\left(t, -2 + \frac{\color{blue}{1 \cdot x}}{y}, 2 + 2 \cdot \frac{1}{z}\right)}{t} \]

      9. associate-*l/ N/A

         \[\leadsto \frac{\mathsf{fma}\left(t, -2 + \color{blue}{\frac{1}{y} \cdot x}, 2 + 2 \cdot \frac{1}{z}\right)}{t} \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t, \color{blue}{-2 + \frac{1}{y} \cdot x}, 2 + 2 \cdot \frac{1}{z}\right)}{t} \]

      11. associate-*l/ N/A

          \[\leadsto \frac{\mathsf{fma}\left(t, -2 + \color{blue}{\frac{1 \cdot x}{y}}, 2 + 2 \cdot \frac{1}{z}\right)}{t} \]

      12. *-lft-identity N/A

          \[\leadsto \frac{\mathsf{fma}\left(t, -2 + \frac{\color{blue}{x}}{y}, 2 + 2 \cdot \frac{1}{z}\right)}{t} \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t, -2 + \color{blue}{\frac{x}{y}}, 2 + 2 \cdot \frac{1}{z}\right)}{t} \]

      14. +-lowering-+.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(t, -2 + \frac{x}{y}, \color{blue}{2 + 2 \cdot \frac{1}{z}}\right)}{t} \]

      15. associate-*r/ N/A

          \[\leadsto \frac{\mathsf{fma}\left(t, -2 + \frac{x}{y}, 2 + \color{blue}{\frac{2 \cdot 1}{z}}\right)}{t} \]

      16. metadata-eval N/A

          \[\leadsto \frac{\mathsf{fma}\left(t, -2 + \frac{x}{y}, 2 + \frac{\color{blue}{2}}{z}\right)}{t} \]

      17. /-lowering-/.f64 99.3

          \[\leadsto \frac{\mathsf{fma}\left(t, -2 + \frac{x}{y}, 2 + \color{blue}{\frac{2}{z}}\right)}{t} \]

   5. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, -2 + \frac{x}{y}, 2 + \frac{2}{z}\right)}{t}} \]

   if 2.00000000000000004e198 < (/.f64 x y)

   1. Initial program 82.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{2}{t \cdot z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \frac{x}{y} + \color{blue}{\frac{2}{t \cdot z}} \]

      2. *-lowering-*.f64 96.6

         \[\leadsto \frac{x}{y} + \frac{2}{\color{blue}{t \cdot z}} \]

   5. Simplified 96.6%

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{2}{t \cdot z}} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x + 2 \cdot \frac{y}{t \cdot z}}{y}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x + 2 \cdot \frac{y}{t \cdot z}}{y}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{y}{t \cdot z} + x}}{y} \]

      3. accelerator-lowering-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(2, \frac{y}{t \cdot z}, x\right)}}{y} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(2, \color{blue}{\frac{y}{t \cdot z}}, x\right)}{y} \]

      5. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(2, \frac{y}{\color{blue}{z \cdot t}}, x\right)}{y} \]

      6. *-lowering-*.f64 100.0

         \[\leadsto \frac{\mathsf{fma}\left(2, \frac{y}{\color{blue}{z \cdot t}}, x\right)}{y} \]

   8. Simplified 100.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+198}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, \frac{x}{y} + -2, 2 + \frac{2}{z}\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, \frac{y}{z \cdot t}, x\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 200:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{2}{t}}{z}, z + 1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ 2.0 (* z t)))))
   (if (<= (/ x y) -2e+52)
     t_1
     (if (<= (/ x y) 200.0) (fma (/ (/ 2.0 t) z) (+ z 1.0) -2.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / (z * t));
	double tmp;
	if ((x / y) <= -2e+52) {
		tmp = t_1;
	} else if ((x / y) <= 200.0) {
		tmp = fma(((2.0 / t) / z), (z + 1.0), -2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)))
	tmp = 0.0
	if (Float64(x / y) <= -2e+52)
		tmp = t_1;
	elseif (Float64(x / y) <= 200.0)
		tmp = fma(Float64(Float64(2.0 / t) / z), Float64(z + 1.0), -2.0);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+52], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 200.0], N[(N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision] * N[(z + 1.0), $MachinePrecision] + -2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e52 or 200 < (/.f64 x y)

   1. Initial program 86.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{2}{t \cdot z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \frac{x}{y} + \color{blue}{\frac{2}{t \cdot z}} \]

      2. *-lowering-*.f64 95.1

         \[\leadsto \frac{x}{y} + \frac{2}{\color{blue}{t \cdot z}} \]

   5. Simplified 95.1%

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{2}{t \cdot z}} \]

   if -2e52 < (/.f64 x y) < 200

   1. Initial program 88.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]

   5. Simplified 98.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2}{t \cdot z}, z + 1, -2\right)} \]
   6. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\frac{2}{t}}{z}}, z + 1, -2\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\frac{2}{t}}{z}}, z + 1, -2\right) \]

      3. /-lowering-/.f64 98.5

         \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\frac{2}{t}}}{z}, z + 1, -2\right) \]

   7. Applied egg-rr 98.5%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 200:\\ \;\;\;\;\mathsf{fma}\left(\frac{\frac{2}{t}}{z}, z + 1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z \cdot t}\\ t_2 := \frac{x}{y} + t\_1\\ \mathbf{if}\;\frac{x}{y} \leq -3.8 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 520:\\ \;\;\;\;\mathsf{fma}\left(t\_1, z + 1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* z t))) (t_2 (+ (/ x y) t_1)))
   (if (<= (/ x y) -3.8e+48)
     t_2
     (if (<= (/ x y) 520.0) (fma t_1 (+ z 1.0) -2.0) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (z * t);
	double t_2 = (x / y) + t_1;
	double tmp;
	if ((x / y) <= -3.8e+48) {
		tmp = t_2;
	} else if ((x / y) <= 520.0) {
		tmp = fma(t_1, (z + 1.0), -2.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(z * t))
	t_2 = Float64(Float64(x / y) + t_1)
	tmp = 0.0
	if (Float64(x / y) <= -3.8e+48)
		tmp = t_2;
	elseif (Float64(x / y) <= 520.0)
		tmp = fma(t_1, Float64(z + 1.0), -2.0);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -3.8e+48], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 520.0], N[(t$95$1 * N[(z + 1.0), $MachinePrecision] + -2.0), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3.8e48 or 520 < (/.f64 x y)

   1. Initial program 86.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{2}{t \cdot z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \frac{x}{y} + \color{blue}{\frac{2}{t \cdot z}} \]

      2. *-lowering-*.f64 95.1

         \[\leadsto \frac{x}{y} + \frac{2}{\color{blue}{t \cdot z}} \]

   5. Simplified 95.1%

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{2}{t \cdot z}} \]

   if -3.8e48 < (/.f64 x y) < 520

   1. Initial program 88.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]

   5. Simplified 98.5%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.8 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 520:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5.4 \cdot 10^{-45}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 6.5 \cdot 10^{+14}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -4.2e+48)
   (/ x y)
   (if (<= (/ x y) -5.4e-45)
     (/ 2.0 t)
     (if (<= (/ x y) 6.5e+14) -2.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4.2e+48) {
		tmp = x / y;
	} else if ((x / y) <= -5.4e-45) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 6.5e+14) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-4.2d+48)) then
        tmp = x / y
    else if ((x / y) <= (-5.4d-45)) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 6.5d+14) then
        tmp = -2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4.2e+48) {
		tmp = x / y;
	} else if ((x / y) <= -5.4e-45) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 6.5e+14) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -4.2e+48:
		tmp = x / y
	elif (x / y) <= -5.4e-45:
		tmp = 2.0 / t
	elif (x / y) <= 6.5e+14:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -4.2e+48)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -5.4e-45)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 6.5e+14)
		tmp = -2.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -4.2e+48)
		tmp = x / y;
	elseif ((x / y) <= -5.4e-45)
		tmp = 2.0 / t;
	elseif ((x / y) <= 6.5e+14)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -4.2e+48], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -5.4e-45], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 6.5e+14], -2.0, N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.1999999999999997e48 or 6.5e14 < (/.f64 x y)

   1. Initial program 86.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 70.6

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

   5. Simplified 70.6%

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

   if -4.1999999999999997e48 < (/.f64 x y) < -5.3999999999999997e-45

   1. Initial program 93.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]

   5. Simplified 89.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2}{t \cdot z}, z + 1, -2\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \frac{1}{t} - 2} \]
   7. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right)} \]

      2. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t} + \color{blue}{-2} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + -2} \]

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{2 \cdot 1}{t}} + -2 \]

      5. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{2}}{t} + -2 \]

      6. /-lowering-/.f64 70.9

         \[\leadsto \color{blue}{\frac{2}{t}} + -2 \]

   8. Simplified 70.9%

      \[\leadsto \color{blue}{\frac{2}{t} + -2} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2}{t}} \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 51.6

          \[\leadsto \color{blue}{\frac{2}{t}} \]

   11. Simplified 51.6%

       \[\leadsto \color{blue}{\frac{2}{t}} \]

   if -5.3999999999999997e-45 < (/.f64 x y) < 6.5e14

   1. Initial program 88.2%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]

   5. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2}{t \cdot z}, z + 1, -2\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-2} \]
   7. Step-by-step derivation

   8. Simplified 38.9%

      \[\leadsto \color{blue}{-2} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.4 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -4.2e+58)
   (/ x y)
   (if (<= (/ x y) 2.4e+100)
     (fma (/ 2.0 (* z t)) (+ z 1.0) -2.0)
     (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4.2e+58) {
		tmp = x / y;
	} else if ((x / y) <= 2.4e+100) {
		tmp = fma((2.0 / (z * t)), (z + 1.0), -2.0);
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -4.2e+58)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 2.4e+100)
		tmp = fma(Float64(2.0 / Float64(z * t)), Float64(z + 1.0), -2.0);
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -4.2e+58], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.4e+100], N[(N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(z + 1.0), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.20000000000000024e58

   1. Initial program 86.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 80.0

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

   5. Simplified 80.0%

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

   if -4.20000000000000024e58 < (/.f64 x y) < 2.40000000000000012e100

   1. Initial program 89.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]

   5. Simplified 95.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2}{t \cdot z}, z + 1, -2\right)} \]

   if 2.40000000000000012e100 < (/.f64 x y)

   1. Initial program 84.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Simplified 76.4%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.4 \cdot 10^{+100}:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{z \cdot t}, z + 1, -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.8 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 6 \cdot 10^{+17}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -3.8e+48)
   (/ x y)
   (if (<= (/ x y) 6e+17) (+ -2.0 (/ 2.0 t)) (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -3.8e+48) {
		tmp = x / y;
	} else if ((x / y) <= 6e+17) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-3.8d+48)) then
        tmp = x / y
    else if ((x / y) <= 6d+17) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else
        tmp = (x / y) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -3.8e+48) {
		tmp = x / y;
	} else if ((x / y) <= 6e+17) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -3.8e+48:
		tmp = x / y
	elif (x / y) <= 6e+17:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -3.8e+48)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 6e+17)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -3.8e+48)
		tmp = x / y;
	elseif ((x / y) <= 6e+17)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -3.8e+48], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 6e+17], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -3.8e48

   1. Initial program 85.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 78.9

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

   5. Simplified 78.9%

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

   if -3.8e48 < (/.f64 x y) < 6e17

   1. Initial program 88.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]

   5. Simplified 98.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2}{t \cdot z}, z + 1, -2\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \frac{1}{t} - 2} \]
   7. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right)} \]

      2. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t} + \color{blue}{-2} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + -2} \]

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{2 \cdot 1}{t}} + -2 \]

      5. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{2}}{t} + -2 \]

      6. /-lowering-/.f64 64.1

         \[\leadsto \color{blue}{\frac{2}{t}} + -2 \]

   8. Simplified 64.1%

      \[\leadsto \color{blue}{\frac{2}{t} + -2} \]

   if 6e17 < (/.f64 x y)

   1. Initial program 87.2%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Simplified 63.2%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.8 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 6 \cdot 10^{+17}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 6.5 \cdot 10^{+14}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+48)
   (/ x y)
   (if (<= (/ x y) 6.5e+14) (+ -2.0 (/ 2.0 t)) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+48) {
		tmp = x / y;
	} else if ((x / y) <= 6.5e+14) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5d+48)) then
        tmp = x / y
    else if ((x / y) <= 6.5d+14) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+48) {
		tmp = x / y;
	} else if ((x / y) <= 6.5e+14) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+48:
		tmp = x / y
	elif (x / y) <= 6.5e+14:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+48)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 6.5e+14)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e+48)
		tmp = x / y;
	elseif ((x / y) <= 6.5e+14)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+48], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 6.5e+14], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.99999999999999973e48 or 6.5e14 < (/.f64 x y)

   1. Initial program 86.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 70.6

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

   5. Simplified 70.6%

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

   if -4.99999999999999973e48 < (/.f64 x y) < 6.5e14

   1. Initial program 88.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]

   5. Simplified 98.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2}{t \cdot z}, z + 1, -2\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \frac{1}{t} - 2} \]
   7. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right)} \]

      2. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t} + \color{blue}{-2} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + -2} \]

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{2 \cdot 1}{t}} + -2 \]

      5. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{2}}{t} + -2 \]

      6. /-lowering-/.f64 64.1

         \[\leadsto \color{blue}{\frac{2}{t}} + -2 \]

   8. Simplified 64.1%

      \[\leadsto \color{blue}{\frac{2}{t} + -2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 6.5 \cdot 10^{+14}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-147}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (+ -2.0 (/ 2.0 t)))))
   (if (<= z -3.1e-131)
     t_1
     (if (<= z 6.2e-147) (+ -2.0 (/ 2.0 (* z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if (z <= -3.1e-131) {
		tmp = t_1;
	} else if (z <= 6.2e-147) {
		tmp = -2.0 + (2.0 / (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + ((-2.0d0) + (2.0d0 / t))
    if (z <= (-3.1d-131)) then
        tmp = t_1
    else if (z <= 6.2d-147) then
        tmp = (-2.0d0) + (2.0d0 / (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if (z <= -3.1e-131) {
		tmp = t_1;
	} else if (z <= 6.2e-147) {
		tmp = -2.0 + (2.0 / (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (-2.0 + (2.0 / t))
	tmp = 0
	if z <= -3.1e-131:
		tmp = t_1
	elif z <= 6.2e-147:
		tmp = -2.0 + (2.0 / (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)))
	tmp = 0.0
	if (z <= -3.1e-131)
		tmp = t_1;
	elseif (z <= 6.2e-147)
		tmp = Float64(-2.0 + Float64(2.0 / Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (-2.0 + (2.0 / t));
	tmp = 0.0;
	if (z <= -3.1e-131)
		tmp = t_1;
	elseif (z <= 6.2e-147)
		tmp = -2.0 + (2.0 / (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e-131], t$95$1, If[LessEqual[z, 6.2e-147], N[(-2.0 + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.10000000000000021e-131 or 6.2000000000000005e-147 < z

   1. Initial program 83.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \frac{x}{y} + \color{blue}{2 \cdot \frac{1 - t}{t}} \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \frac{x}{y} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      2. sub-neg N/A

         \[\leadsto \frac{x}{y} + 2 \cdot \color{blue}{\left(\frac{1}{t} + \left(\mathsf{neg}\left(\frac{t}{t}\right)\right)\right)} \]

      3. *-inverses N/A

         \[\leadsto \frac{x}{y} + 2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(\color{blue}{1}\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \frac{x}{y} + 2 \cdot \left(\frac{1}{t} + \color{blue}{-1}\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot -1\right)} \]

      6. metadata-eval N/A

         \[\leadsto \frac{x}{y} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t} + -2\right)} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{2 \cdot 1}{t}} + -2\right) \]

      9. metadata-eval N/A

         \[\leadsto \frac{x}{y} + \left(\frac{\color{blue}{2}}{t} + -2\right) \]

      10. /-lowering-/.f64 91.1

          \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{2}{t}} + -2\right) \]

   5. Simplified 91.1%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{2}{t} + -2\right)} \]

   if -3.10000000000000021e-131 < z < 6.2000000000000005e-147

   1. Initial program 98.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]

   5. Simplified 91.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2}{t \cdot z}, z + 1, -2\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{2}{t \cdot z}, \color{blue}{1}, -2\right) \]
   7. Step-by-step derivation

   8. Simplified 91.5%

      \[\leadsto \mathsf{fma}\left(\frac{2}{t \cdot z}, \color{blue}{1}, -2\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{\frac{2}{t \cdot z} \cdot 1 + -2} \]

      2. *-rgt-identity N/A

         \[\leadsto \color{blue}{\frac{2}{t \cdot z}} + -2 \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2}{t \cdot z}} + -2 \]

      4. *-lowering-*.f64 91.5

         \[\leadsto \frac{2}{\color{blue}{t \cdot z}} + -2 \]

   10. Applied egg-rr 91.5%

       \[\leadsto \color{blue}{\frac{2}{t \cdot z} + -2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-131}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-147}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;z \leq -3 \cdot 10^{+204}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{-52}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)))
   (if (<= z -3e+204)
     (+ -2.0 (/ 2.0 t))
     (if (<= z -3.1e-131)
       t_1
       (if (<= z 1e-52) (+ -2.0 (/ 2.0 (* z t))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (z <= -3e+204) {
		tmp = -2.0 + (2.0 / t);
	} else if (z <= -3.1e-131) {
		tmp = t_1;
	} else if (z <= 1e-52) {
		tmp = -2.0 + (2.0 / (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (-2.0d0)
    if (z <= (-3d+204)) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else if (z <= (-3.1d-131)) then
        tmp = t_1
    else if (z <= 1d-52) then
        tmp = (-2.0d0) + (2.0d0 / (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (z <= -3e+204) {
		tmp = -2.0 + (2.0 / t);
	} else if (z <= -3.1e-131) {
		tmp = t_1;
	} else if (z <= 1e-52) {
		tmp = -2.0 + (2.0 / (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	tmp = 0
	if z <= -3e+204:
		tmp = -2.0 + (2.0 / t)
	elif z <= -3.1e-131:
		tmp = t_1
	elif z <= 1e-52:
		tmp = -2.0 + (2.0 / (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (z <= -3e+204)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	elseif (z <= -3.1e-131)
		tmp = t_1;
	elseif (z <= 1e-52)
		tmp = Float64(-2.0 + Float64(2.0 / Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	tmp = 0.0;
	if (z <= -3e+204)
		tmp = -2.0 + (2.0 / t);
	elseif (z <= -3.1e-131)
		tmp = t_1;
	elseif (z <= 1e-52)
		tmp = -2.0 + (2.0 / (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[z, -3e+204], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1e-131], t$95$1, If[LessEqual[z, 1e-52], N[(-2.0 + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.99999999999999983e204

   1. Initial program 78.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]

   5. Simplified 83.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2}{t \cdot z}, z + 1, -2\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \frac{1}{t} - 2} \]
   7. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right)} \]

      2. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t} + \color{blue}{-2} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + -2} \]

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{2 \cdot 1}{t}} + -2 \]

      5. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{2}}{t} + -2 \]

      6. /-lowering-/.f64 83.3

         \[\leadsto \color{blue}{\frac{2}{t}} + -2 \]

   8. Simplified 83.3%

      \[\leadsto \color{blue}{\frac{2}{t} + -2} \]

   if -2.99999999999999983e204 < z < -3.10000000000000021e-131 or 1e-52 < z

   1. Initial program 81.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Simplified 74.0%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]

   if -3.10000000000000021e-131 < z < 1e-52

   1. Initial program 98.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]

   5. Simplified 84.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2}{t \cdot z}, z + 1, -2\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\frac{2}{t \cdot z}, \color{blue}{1}, -2\right) \]
   7. Step-by-step derivation

   8. Simplified 84.5%

      \[\leadsto \mathsf{fma}\left(\frac{2}{t \cdot z}, \color{blue}{1}, -2\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{\frac{2}{t \cdot z} \cdot 1 + -2} \]

      2. *-rgt-identity N/A

         \[\leadsto \color{blue}{\frac{2}{t \cdot z}} + -2 \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2}{t \cdot z}} + -2 \]

      4. *-lowering-*.f64 84.5

         \[\leadsto \frac{2}{\color{blue}{t \cdot z}} + -2 \]

   10. Applied egg-rr 84.5%

       \[\leadsto \color{blue}{\frac{2}{t \cdot z} + -2} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+204}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-131}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;z \leq 10^{-52}:\\ \;\;\;\;-2 + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+204}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-143}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)))
   (if (<= z -4.6e+204)
     (+ -2.0 (/ 2.0 t))
     (if (<= z -3.1e-131) t_1 (if (<= z 4e-143) (/ 2.0 (* z t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (z <= -4.6e+204) {
		tmp = -2.0 + (2.0 / t);
	} else if (z <= -3.1e-131) {
		tmp = t_1;
	} else if (z <= 4e-143) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (-2.0d0)
    if (z <= (-4.6d+204)) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else if (z <= (-3.1d-131)) then
        tmp = t_1
    else if (z <= 4d-143) then
        tmp = 2.0d0 / (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (z <= -4.6e+204) {
		tmp = -2.0 + (2.0 / t);
	} else if (z <= -3.1e-131) {
		tmp = t_1;
	} else if (z <= 4e-143) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	tmp = 0
	if z <= -4.6e+204:
		tmp = -2.0 + (2.0 / t)
	elif z <= -3.1e-131:
		tmp = t_1
	elif z <= 4e-143:
		tmp = 2.0 / (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (z <= -4.6e+204)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	elseif (z <= -3.1e-131)
		tmp = t_1;
	elseif (z <= 4e-143)
		tmp = Float64(2.0 / Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	tmp = 0.0;
	if (z <= -4.6e+204)
		tmp = -2.0 + (2.0 / t);
	elseif (z <= -3.1e-131)
		tmp = t_1;
	elseif (z <= 4e-143)
		tmp = 2.0 / (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[z, -4.6e+204], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1e-131], t$95$1, If[LessEqual[z, 4e-143], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.59999999999999981e204

   1. Initial program 78.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]

   5. Simplified 83.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2}{t \cdot z}, z + 1, -2\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \frac{1}{t} - 2} \]
   7. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right)} \]

      2. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t} + \color{blue}{-2} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + -2} \]

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{2 \cdot 1}{t}} + -2 \]

      5. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{2}}{t} + -2 \]

      6. /-lowering-/.f64 83.3

         \[\leadsto \color{blue}{\frac{2}{t}} + -2 \]

   8. Simplified 83.3%

      \[\leadsto \color{blue}{\frac{2}{t} + -2} \]

   if -4.59999999999999981e204 < z < -3.10000000000000021e-131 or 3.9999999999999998e-143 < z

   1. Initial program 84.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Simplified 72.4%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]

   if -3.10000000000000021e-131 < z < 3.9999999999999998e-143

   1. Initial program 98.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{2}{t \cdot z}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2}{t \cdot z}} \]

      2. *-lowering-*.f64 84.3

         \[\leadsto \frac{2}{\color{blue}{t \cdot z}} \]

   5. Simplified 84.3%

      \[\leadsto \color{blue}{\frac{2}{t \cdot z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+204}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-131}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-143}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-9}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 45000:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4e-9) -2.0 (if (<= t 45000.0) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4e-9) {
		tmp = -2.0;
	} else if (t <= 45000.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-4d-9)) then
        tmp = -2.0d0
    else if (t <= 45000.0d0) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4e-9) {
		tmp = -2.0;
	} else if (t <= 45000.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4e-9:
		tmp = -2.0
	elif t <= 45000.0:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4e-9)
		tmp = -2.0;
	elseif (t <= 45000.0)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4e-9)
		tmp = -2.0;
	elseif (t <= 45000.0)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4e-9], -2.0, If[LessEqual[t, 45000.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -4.00000000000000025e-9 or 45000 < t

   1. Initial program 77.2%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]

   5. Simplified 54.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2}{t \cdot z}, z + 1, -2\right)} \]

   6. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-2} \]
   7. Step-by-step derivation

   8. Simplified 38.2%

      \[\leadsto \color{blue}{-2} \]

   if -4.00000000000000025e-9 < t < 45000

   1. Initial program 98.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]

   5. Simplified 81.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2}{t \cdot z}, z + 1, -2\right)} \]

   6. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \frac{1}{t} - 2} \]
   7. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right)} \]

      2. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t} + \color{blue}{-2} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + -2} \]

      4. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{2 \cdot 1}{t}} + -2 \]

      5. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{2}}{t} + -2 \]

      6. /-lowering-/.f64 36.1

         \[\leadsto \color{blue}{\frac{2}{t}} + -2 \]

   8. Simplified 36.1%

      \[\leadsto \color{blue}{\frac{2}{t} + -2} \]

   9. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2}{t}} \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 35.8

          \[\leadsto \color{blue}{\frac{2}{t}} \]

   11. Simplified 35.8%

       \[\leadsto \color{blue}{\frac{2}{t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 20.4% accurate, 47.0× speedup

Math

\[\begin{array}{l} \\ -2 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 -2.0)

C

double code(double x, double y, double z, double t) {
	return -2.0;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = -2.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return -2.0;
}

Python

def code(x, y, z, t):
	return -2.0

Julia

function code(x, y, z, t)
	return -2.0
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = -2.0;
end

Wolfram

code[x_, y_, z_, t_] := -2.0

Derivation

1. Initial program 87.7%

   \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]

5. Simplified 67.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2}{t \cdot z}, z + 1, -2\right)} \]

6. Taylor expanded in t around inf

   \[\leadsto \color{blue}{-2} \]
7. Step-by-step derivation

8. Simplified 20.8%

   \[\leadsto \color{blue}{-2} \]
9. Add Preprocessing

Developer Target 1: 99.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y))))

C

double code(double x, double y, double z, double t) {
	return (((2.0 / z) + 2.0) / t) - (2.0 - (x / y));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((2.0d0 / z) + 2.0d0) / t) - (2.0d0 - (x / y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((2.0 / z) + 2.0) / t) - (2.0 - (x / y));
}

Python

def code(x, y, z, t):
	return (((2.0 / z) + 2.0) / t) - (2.0 - (x / y))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(2.0 / z) + 2.0) / t) - Float64(2.0 - Float64(x / y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((2.0 / z) + 2.0) / t) - (2.0 - (x / y));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(2.0 / z), $MachinePrecision] + 2.0), $MachinePrecision] / t), $MachinePrecision] - N[(2.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024198 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y))))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))