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

Percentage Accurate: 86.8% → 99.4%

Time: 11.5s

Alternatives: 14

Speedup: 1.1×

• 22.9% 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: 86.8% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 86.2%

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

3. Taylor expanded in x around 0

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

   1. associate-+r+ N/A

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

   2. +-commutative N/A

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

   3. associate-*r/ N/A

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

   4. *-commutative N/A

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

   5. associate-/l* N/A

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

   6. metadata-eval N/A

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

   7. associate-*r/ N/A

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

   8. associate-/r* N/A

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

   9. associate-*r/ N/A

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

   10. metadata-eval N/A

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

   11. associate-*r* N/A

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

   12. associate-*l/ N/A

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

   13. distribute-rgt-out N/A

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

   14. lower-fma.f64 N/A

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

5. Applied rewrites 99.5%

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

Alternative 2: 68.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{2}{t} - 2\\ t_3 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_4 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{+157}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 10^{+119}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+287}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z)))
        (t_2 (- (/ 2.0 t) 2.0))
        (t_3 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))
        (t_4 (+ (/ x y) -2.0)))
   (if (<= t_3 -2e+307)
     t_1
     (if (<= t_3 -2e+157)
       t_2
       (if (<= t_3 1e+119)
         t_4
         (if (<= t_3 2e+287) t_2 (if (<= t_3 INFINITY) t_1 t_4)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (2.0 / t) - 2.0;
	double t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_4 = (x / y) + -2.0;
	double tmp;
	if (t_3 <= -2e+307) {
		tmp = t_1;
	} else if (t_3 <= -2e+157) {
		tmp = t_2;
	} else if (t_3 <= 1e+119) {
		tmp = t_4;
	} else if (t_3 <= 2e+287) {
		tmp = t_2;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (2.0 / t) - 2.0;
	double t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_4 = (x / y) + -2.0;
	double tmp;
	if (t_3 <= -2e+307) {
		tmp = t_1;
	} else if (t_3 <= -2e+157) {
		tmp = t_2;
	} else if (t_3 <= 1e+119) {
		tmp = t_4;
	} else if (t_3 <= 2e+287) {
		tmp = t_2;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (2.0 / t) - 2.0
	t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	t_4 = (x / y) + -2.0
	tmp = 0
	if t_3 <= -2e+307:
		tmp = t_1
	elif t_3 <= -2e+157:
		tmp = t_2
	elif t_3 <= 1e+119:
		tmp = t_4
	elif t_3 <= 2e+287:
		tmp = t_2
	elif t_3 <= math.inf:
		tmp = t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(2.0 / t) - 2.0)
	t_3 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	t_4 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t_3 <= -2e+307)
		tmp = t_1;
	elseif (t_3 <= -2e+157)
		tmp = t_2;
	elseif (t_3 <= 1e+119)
		tmp = t_4;
	elseif (t_3 <= 2e+287)
		tmp = t_2;
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = (2.0 / t) - 2.0;
	t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	t_4 = (x / y) + -2.0;
	tmp = 0.0;
	if (t_3 <= -2e+307)
		tmp = t_1;
	elseif (t_3 <= -2e+157)
		tmp = t_2;
	elseif (t_3 <= 1e+119)
		tmp = t_4;
	elseif (t_3 <= 2e+287)
		tmp = t_2;
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+307], t$95$1, If[LessEqual[t$95$3, -2e+157], t$95$2, If[LessEqual[t$95$3, 1e+119], t$95$4, If[LessEqual[t$95$3, 2e+287], t$95$2, If[LessEqual[t$95$3, Infinity], t$95$1, t$95$4]]]]]]]]]

Derivation

1. Split input into 3 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)) < -1.99999999999999997e307 or 2.0000000000000002e287 < (/.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 90.3%

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

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 97.5%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 92.7

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

   8. Applied rewrites 92.7%

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

   if -1.99999999999999997e307 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.99999999999999997e157 or 9.99999999999999944e118 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2.0000000000000002e287

   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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 75.4

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

   5. Applied rewrites 75.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 55.2%

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

   if -1.99999999999999997e157 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 9.99999999999999944e118 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 78.1%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 78.3%

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

Alternative 3: 89.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+62} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z} - 2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+62) (not (<= (/ x y) 5e-9)))
   (+ (/ x y) (- (/ 2.0 t) 2.0))
   (- -2.0 (/ (- (/ -2.0 z) 2.0) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+62) || !((x / y) <= 5e-9)) {
		tmp = (x / y) + ((2.0 / t) - 2.0);
	} else {
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	}
	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) <= (-1d+62)) .or. (.not. ((x / y) <= 5d-9))) then
        tmp = (x / y) + ((2.0d0 / t) - 2.0d0)
    else
        tmp = (-2.0d0) - ((((-2.0d0) / z) - 2.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+62) || !((x / y) <= 5e-9)) {
		tmp = (x / y) + ((2.0 / t) - 2.0);
	} else {
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+62) or not ((x / y) <= 5e-9):
		tmp = (x / y) + ((2.0 / t) - 2.0)
	else:
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e+62) || !(Float64(x / y) <= 5e-9))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) - 2.0));
	else
		tmp = Float64(-2.0 - Float64(Float64(Float64(-2.0 / z) - 2.0) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e+62) || ~(((x / y) <= 5e-9)))
		tmp = (x / y) + ((2.0 / t) - 2.0);
	else
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e+62], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-9]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(-2.0 - N[(N[(N[(-2.0 / z), $MachinePrecision] - 2.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.00000000000000004e62 or 5.0000000000000001e-9 < (/.f64 x y)

   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 t around 0

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

   5. Applied rewrites 96.9%

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

   6. Taylor expanded in z around inf

      \[\leadsto \frac{x}{y} + \left(\frac{2}{t} - 2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 84.3%

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

   if -1.00000000000000004e62 < (/.f64 x y) < 5.0000000000000001e-9

   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 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-/l* N/A

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

      5. div-add-rev N/A

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

      6. distribute-lft-out N/A

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

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. +-commutative N/A

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

      10. count-2-rev N/A

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

      11. count-2-rev N/A

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

   8. Applied rewrites 98.8%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+62} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z} - 2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+171}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+84}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z} - 2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+171)
   (/ x y)
   (if (<= (/ x y) 5e+84) (- -2.0 (/ (- (/ -2.0 z) 2.0) t)) (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+171) {
		tmp = x / y;
	} else if ((x / y) <= 5e+84) {
		tmp = -2.0 - (((-2.0 / z) - 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) <= (-5d+171)) then
        tmp = x / y
    else if ((x / y) <= 5d+84) then
        tmp = (-2.0d0) - ((((-2.0d0) / z) - 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) <= -5e+171) {
		tmp = x / y;
	} else if ((x / y) <= 5e+84) {
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+171:
		tmp = x / y
	elif (x / y) <= 5e+84:
		tmp = -2.0 - (((-2.0 / z) - 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) <= -5e+171)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 5e+84)
		tmp = Float64(-2.0 - Float64(Float64(Float64(-2.0 / z) - 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) <= -5e+171)
		tmp = x / y;
	elseif ((x / y) <= 5e+84)
		tmp = -2.0 - (((-2.0 / z) - 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], -5e+171], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e+84], N[(-2.0 - N[(N[(N[(-2.0 / z), $MachinePrecision] - 2.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.0000000000000004e171

   1. Initial program 76.8%

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

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 97.4%

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

   7. Applied rewrites 80.9%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 87.3%

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

   if -5.0000000000000004e171 < (/.f64 x y) < 5.0000000000000001e84

   1. Initial program 88.1%

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

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-/l* N/A

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

      5. div-add-rev N/A

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

      6. distribute-lft-out N/A

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

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. +-commutative N/A

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

      10. count-2-rev N/A

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

      11. count-2-rev N/A

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

   8. Applied rewrites 90.8%

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

   if 5.0000000000000001e84 < (/.f64 x y)

   1. Initial program 87.3%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 76.3%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+171}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+84}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z} - 2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-9}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1e+62)
   (/ x y)
   (if (<= (/ x y) 5e-9) (- -2.0 (/ (/ -2.0 z) t)) (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e+62) {
		tmp = x / y;
	} else if ((x / y) <= 5e-9) {
		tmp = -2.0 - ((-2.0 / z) / 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) <= (-1d+62)) then
        tmp = x / y
    else if ((x / y) <= 5d-9) then
        tmp = (-2.0d0) - (((-2.0d0) / z) / 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) <= -1e+62) {
		tmp = x / y;
	} else if ((x / y) <= 5e-9) {
		tmp = -2.0 - ((-2.0 / z) / t);
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1e+62:
		tmp = x / y
	elif (x / y) <= 5e-9:
		tmp = -2.0 - ((-2.0 / z) / t)
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1e+62)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 5e-9)
		tmp = Float64(-2.0 - Float64(Float64(-2.0 / z) / 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) <= -1e+62)
		tmp = x / y;
	elseif ((x / y) <= 5e-9)
		tmp = -2.0 - ((-2.0 / z) / t);
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1e+62], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-9], N[(-2.0 - N[(N[(-2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.00000000000000004e62

   1. Initial program 82.4%

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

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 98.2%

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

   7. Applied rewrites 78.9%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 74.6%

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

   if -1.00000000000000004e62 < (/.f64 x y) < 5.0000000000000001e-9

   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 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-/l* N/A

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

      5. div-add-rev N/A

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

      6. distribute-lft-out N/A

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

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. +-commutative N/A

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

      10. count-2-rev N/A

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

      11. count-2-rev N/A

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

   8. Applied rewrites 98.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 70.6%

       \[\leadsto -2 - \frac{\frac{-2}{z}}{t} \]

   if 5.0000000000000001e-9 < (/.f64 x y)

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 69.9%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-9}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-9}:\\ \;\;\;\;-2 - \frac{-2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1e+62)
   (/ x y)
   (if (<= (/ x y) 5e-9) (- -2.0 (/ -2.0 (* t z))) (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e+62) {
		tmp = x / y;
	} else if ((x / y) <= 5e-9) {
		tmp = -2.0 - (-2.0 / (t * z));
	} 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) <= (-1d+62)) then
        tmp = x / y
    else if ((x / y) <= 5d-9) then
        tmp = (-2.0d0) - ((-2.0d0) / (t * z))
    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) <= -1e+62) {
		tmp = x / y;
	} else if ((x / y) <= 5e-9) {
		tmp = -2.0 - (-2.0 / (t * z));
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1e+62:
		tmp = x / y
	elif (x / y) <= 5e-9:
		tmp = -2.0 - (-2.0 / (t * z))
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1e+62)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 5e-9)
		tmp = Float64(-2.0 - Float64(-2.0 / Float64(t * z)));
	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) <= -1e+62)
		tmp = x / y;
	elseif ((x / y) <= 5e-9)
		tmp = -2.0 - (-2.0 / (t * z));
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1e+62], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-9], N[(-2.0 - N[(-2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.00000000000000004e62

   1. Initial program 82.4%

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

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 98.2%

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

   7. Applied rewrites 78.9%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 74.6%

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

   if -1.00000000000000004e62 < (/.f64 x y) < 5.0000000000000001e-9

   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 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-/l* N/A

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

      5. div-add-rev N/A

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

      6. distribute-lft-out N/A

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

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. +-commutative N/A

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

      10. count-2-rev N/A

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

      11. count-2-rev N/A

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

   8. Applied rewrites 98.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 70.5%

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

   if 5.0000000000000001e-9 < (/.f64 x y)

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 69.9%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-9}:\\ \;\;\;\;-2 - \frac{-2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2900000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{\frac{2}{z}}{t} - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2900000.0) (not (<= z 1.0)))
   (+ (/ x y) (- (/ 2.0 t) 2.0))
   (+ (/ x y) (- (/ (/ 2.0 z) t) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2900000.0) || !(z <= 1.0)) {
		tmp = (x / y) + ((2.0 / t) - 2.0);
	} else {
		tmp = (x / y) + (((2.0 / z) / t) - 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 ((z <= (-2900000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (x / y) + ((2.0d0 / t) - 2.0d0)
    else
        tmp = (x / y) + (((2.0d0 / z) / t) - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2900000.0) || !(z <= 1.0)) {
		tmp = (x / y) + ((2.0 / t) - 2.0);
	} else {
		tmp = (x / y) + (((2.0 / z) / t) - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2900000.0) or not (z <= 1.0):
		tmp = (x / y) + ((2.0 / t) - 2.0)
	else:
		tmp = (x / y) + (((2.0 / z) / t) - 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2900000.0) || !(z <= 1.0))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) - 2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(Float64(2.0 / z) / t) - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2900000.0) || ~((z <= 1.0)))
		tmp = (x / y) + ((2.0 / t) - 2.0);
	else
		tmp = (x / y) + (((2.0 / z) / t) - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2900000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9e6 or 1 < z

   1. Initial program 76.5%

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

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around inf

      \[\leadsto \frac{x}{y} + \left(\frac{2}{t} - 2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 99.5%

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

   if -2.9e6 < z < 1

   1. Initial program 96.6%

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

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 96.6%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{x}{y} + \left(\frac{\frac{2}{z}}{t} - 2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 96.4%

      \[\leadsto \frac{x}{y} + \left(\frac{\frac{2}{z}}{t} - 2\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2900000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{\frac{2}{z}}{t} - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-29} \lor \neg \left(z \leq 0.000185\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2e-29) (not (<= z 0.000185)))
   (+ (/ x y) (- (/ 2.0 t) 2.0))
   (+ (/ x y) (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e-29) || !(z <= 0.000185)) {
		tmp = (x / y) + ((2.0 / t) - 2.0);
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	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 ((z <= (-2d-29)) .or. (.not. (z <= 0.000185d0))) then
        tmp = (x / y) + ((2.0d0 / t) - 2.0d0)
    else
        tmp = (x / y) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e-29) || !(z <= 0.000185)) {
		tmp = (x / y) + ((2.0 / t) - 2.0);
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2e-29) or not (z <= 0.000185):
		tmp = (x / y) + ((2.0 / t) - 2.0)
	else:
		tmp = (x / y) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2e-29) || !(z <= 0.000185))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) - 2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2e-29) || ~((z <= 0.000185)))
		tmp = (x / y) + ((2.0 / t) - 2.0);
	else
		tmp = (x / y) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2e-29], N[Not[LessEqual[z, 0.000185]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.99999999999999989e-29 or 1.85e-4 < z

   1. Initial program 77.5%

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

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around inf

      \[\leadsto \frac{x}{y} + \left(\frac{2}{t} - 2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 98.8%

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

   if -1.99999999999999989e-29 < z < 1.85e-4

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 86.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 86.3

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

   7. Applied rewrites 86.3%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-29} \lor \neg \left(z \leq 0.000185\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.3 \cdot 10^{+44} \lor \neg \left(\frac{x}{y} \leq 2.7 \cdot 10^{+84}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1.3e+44) (not (<= (/ x y) 2.7e+84)))
   (/ x y)
   (- (/ 2.0 t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.3e+44) || !((x / y) <= 2.7e+84)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) - 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) <= (-1.3d+44)) .or. (.not. ((x / y) <= 2.7d+84))) then
        tmp = x / y
    else
        tmp = (2.0d0 / t) - 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) <= -1.3e+44) || !((x / y) <= 2.7e+84)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1.3e+44) or not ((x / y) <= 2.7e+84):
		tmp = x / y
	else:
		tmp = (2.0 / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1.3e+44) || !(Float64(x / y) <= 2.7e+84))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(2.0 / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1.3e+44) || ~(((x / y) <= 2.7e+84)))
		tmp = x / y;
	else
		tmp = (2.0 / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1.3e+44], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2.7e+84]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.3e44 or 2.7e84 < (/.f64 x y)

   1. Initial program 85.2%

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

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 99.1%

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

   7. Applied rewrites 77.6%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 74.3%

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

   if -1.3e44 < (/.f64 x y) < 2.7e84

   1. Initial program 87.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 63.9

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

   5. Applied rewrites 63.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 60.1%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.3 \cdot 10^{+44} \lor \neg \left(\frac{x}{y} \leq 2.7 \cdot 10^{+84}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.3 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.7 \cdot 10^{+84}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.3e+44)
   (/ x y)
   (if (<= (/ x y) 2.7e+84) (- (/ 2.0 t) 2.0) (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.3e+44) {
		tmp = x / y;
	} else if ((x / y) <= 2.7e+84) {
		tmp = (2.0 / t) - 2.0;
	} 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) <= (-1.3d+44)) then
        tmp = x / y
    else if ((x / y) <= 2.7d+84) then
        tmp = (2.0d0 / t) - 2.0d0
    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) <= -1.3e+44) {
		tmp = x / y;
	} else if ((x / y) <= 2.7e+84) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.3e+44:
		tmp = x / y
	elif (x / y) <= 2.7e+84:
		tmp = (2.0 / t) - 2.0
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.3e+44)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 2.7e+84)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	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) <= -1.3e+44)
		tmp = x / y;
	elseif ((x / y) <= 2.7e+84)
		tmp = (2.0 / t) - 2.0;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.3e+44], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.7e+84], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.3e44

   1. Initial program 82.9%

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

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 98.2%

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

   7. Applied rewrites 79.6%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 72.2%

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

   if -1.3e44 < (/.f64 x y) < 2.7e84

   1. Initial program 87.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 63.9

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

   5. Applied rewrites 63.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 60.1%

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

   if 2.7e84 < (/.f64 x y)

   1. Initial program 87.3%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 76.3%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.3 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.7 \cdot 10^{+84}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 92.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-29} \lor \neg \left(z \leq 0.000185\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2e-29) (not (<= z 0.000185)))
   (+ (/ x y) (- (/ 2.0 t) 2.0))
   (+ (/ x y) (/ 2.0 (* t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e-29) || !(z <= 0.000185)) {
		tmp = (x / y) + ((2.0 / t) - 2.0);
	} else {
		tmp = (x / y) + (2.0 / (t * z));
	}
	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 ((z <= (-2d-29)) .or. (.not. (z <= 0.000185d0))) then
        tmp = (x / y) + ((2.0d0 / t) - 2.0d0)
    else
        tmp = (x / y) + (2.0d0 / (t * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e-29) || !(z <= 0.000185)) {
		tmp = (x / y) + ((2.0 / t) - 2.0);
	} else {
		tmp = (x / y) + (2.0 / (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2e-29) or not (z <= 0.000185):
		tmp = (x / y) + ((2.0 / t) - 2.0)
	else:
		tmp = (x / y) + (2.0 / (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2e-29) || !(z <= 0.000185))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) - 2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2e-29) || ~((z <= 0.000185)))
		tmp = (x / y) + ((2.0 / t) - 2.0);
	else
		tmp = (x / y) + (2.0 / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2e-29], N[Not[LessEqual[z, 0.000185]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.99999999999999989e-29 or 1.85e-4 < z

   1. Initial program 77.5%

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

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around inf

      \[\leadsto \frac{x}{y} + \left(\frac{2}{t} - 2\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 98.8%

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

   if -1.99999999999999989e-29 < z < 1.85e-4

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 86.2%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-29} \lor \neg \left(z \leq 0.000185\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (x / y) + ((((2.0 / z) - -2.0) / t) - 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 = (x / y) + ((((2.0d0 / z) - (-2.0d0)) / t) - 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.2%

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

3. Taylor expanded in t around 0

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

5. Applied rewrites 98.4%

   \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{\frac{2}{z} - -2}{t} - 2\right)} \]
6. Add Preprocessing

Alternative 13: 78.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+56} \lor \neg \left(t \leq 7.4 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.9e+56) (not (<= t 7.4e-6)))
   (+ (/ x y) -2.0)
   (/ (- (/ 2.0 z) -2.0) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.9e+56) || !(t <= 7.4e-6)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = ((2.0 / z) - -2.0) / t;
	}
	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 <= (-1.9d+56)) .or. (.not. (t <= 7.4d-6))) then
        tmp = (x / y) + (-2.0d0)
    else
        tmp = ((2.0d0 / z) - (-2.0d0)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.9e+56) || !(t <= 7.4e-6)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = ((2.0 / z) - -2.0) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.9e+56) or not (t <= 7.4e-6):
		tmp = (x / y) + -2.0
	else:
		tmp = ((2.0 / z) - -2.0) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.9e+56) || !(t <= 7.4e-6))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(Float64(Float64(2.0 / z) - -2.0) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.9e+56) || ~((t <= 7.4e-6)))
		tmp = (x / y) + -2.0;
	else
		tmp = ((2.0 / z) - -2.0) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.9e+56], N[Not[LessEqual[t, 7.4e-6]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.89999999999999998e56 or 7.4000000000000003e-6 < t

   1. Initial program 72.5%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 88.3%

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

   if -1.89999999999999998e56 < t < 7.4000000000000003e-6

   1. Initial program 97.0%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. metadata-eval N/A

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

      3. *-inverses N/A

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

      4. associate-/l* N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. div-add N/A

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

      8. +-commutative N/A

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

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

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

      10. metadata-eval N/A

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

      11. div-sub N/A

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

      12. metadata-eval N/A

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

      13. associate-*r/ N/A

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

      14. associate-*l/ N/A

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

      15. metadata-eval N/A

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

      16. associate-*r/ N/A

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

      17. associate-*l* N/A

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

      18. lft-mult-inverse N/A

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

      19. metadata-eval N/A

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

      20. lower--.f64 N/A

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

      21. associate-*r/ N/A

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

      22. metadata-eval N/A

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

      23. lower-/.f64 78.3

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

   5. Applied rewrites 78.3%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+56} \lor \neg \left(t \leq 7.4 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.2% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ x y))

C

double code(double x, double y, double z, double t) {
	return 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 = x / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 86.2%

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

3. Taylor expanded in x around 0

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

   1. associate-+r+ N/A

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

   2. +-commutative N/A

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

   3. associate-*r/ N/A

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

   4. *-commutative N/A

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

   5. associate-/l* N/A

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

   6. metadata-eval N/A

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

   7. associate-*r/ N/A

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

   8. associate-/r* N/A

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

   9. associate-*r/ N/A

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

   10. metadata-eval N/A

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

   11. associate-*r* N/A

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

   12. associate-*l/ N/A

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

   13. distribute-rgt-out N/A

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

   14. lower-fma.f64 N/A

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

5. Applied rewrites 99.5%

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

7. Applied rewrites 77.7%

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

8. Taylor expanded in x around inf

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

10. Applied rewrites 38.0%

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

11. Final simplification 38.0%

    \[\leadsto \frac{x}{y} \]
12. Add Preprocessing

Developer Target 1: 99.1% 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 2024337 
(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))))