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

Percentage Accurate: 86.4% → 99.2%

Time: 11.0s

Alternatives: 13

Speedup: 1.3×

• 22.8% 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: 86.4% 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: 99.2% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.6%

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

2. Taylor expanded in t around 0 99.5%

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

   1. associate--l+ 99.5%

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

   2. associate-*r/ 99.5%

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

   3. metadata-eval 99.5%

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

   4. associate-/r* 99.5%

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

   5. metadata-eval 99.5%

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

   6. associate-*r/ 99.5%

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

   7. sub-neg 99.5%

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

   8. associate-*r/ 99.5%

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

   9. metadata-eval 99.5%

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

   10. metadata-eval 99.5%

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

4. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 2: 63.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-158}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-212}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 6500000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z))) (t_2 (- (/ x y) 2.0)))
   (if (<= t -1.7e-6)
     t_2
     (if (<= t -1.3e-130)
       t_1
       (if (<= t -1.75e-158)
         (/ 2.0 t)
         (if (<= t -7.4e-283)
           t_1
           (if (<= t 6.8e-212)
             (/ 2.0 t)
             (if (<= t 6500000000.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.7e-6) {
		tmp = t_2;
	} else if (t <= -1.3e-130) {
		tmp = t_1;
	} else if (t <= -1.75e-158) {
		tmp = 2.0 / t;
	} else if (t <= -7.4e-283) {
		tmp = t_1;
	} else if (t <= 6.8e-212) {
		tmp = 2.0 / t;
	} else if (t <= 6500000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 / (t * z)
    t_2 = (x / y) - 2.0d0
    if (t <= (-1.7d-6)) then
        tmp = t_2
    else if (t <= (-1.3d-130)) then
        tmp = t_1
    else if (t <= (-1.75d-158)) then
        tmp = 2.0d0 / t
    else if (t <= (-7.4d-283)) then
        tmp = t_1
    else if (t <= 6.8d-212) then
        tmp = 2.0d0 / t
    else if (t <= 6500000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.7e-6) {
		tmp = t_2;
	} else if (t <= -1.3e-130) {
		tmp = t_1;
	} else if (t <= -1.75e-158) {
		tmp = 2.0 / t;
	} else if (t <= -7.4e-283) {
		tmp = t_1;
	} else if (t <= 6.8e-212) {
		tmp = 2.0 / t;
	} else if (t <= 6500000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (x / y) - 2.0
	tmp = 0
	if t <= -1.7e-6:
		tmp = t_2
	elif t <= -1.3e-130:
		tmp = t_1
	elif t <= -1.75e-158:
		tmp = 2.0 / t
	elif t <= -7.4e-283:
		tmp = t_1
	elif t <= 6.8e-212:
		tmp = 2.0 / t
	elif t <= 6500000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -1.7e-6)
		tmp = t_2;
	elseif (t <= -1.3e-130)
		tmp = t_1;
	elseif (t <= -1.75e-158)
		tmp = Float64(2.0 / t);
	elseif (t <= -7.4e-283)
		tmp = t_1;
	elseif (t <= 6.8e-212)
		tmp = Float64(2.0 / t);
	elseif (t <= 6500000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -1.7e-6)
		tmp = t_2;
	elseif (t <= -1.3e-130)
		tmp = t_1;
	elseif (t <= -1.75e-158)
		tmp = 2.0 / t;
	elseif (t <= -7.4e-283)
		tmp = t_1;
	elseif (t <= 6.8e-212)
		tmp = 2.0 / t;
	elseif (t <= 6500000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	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[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -1.7e-6], t$95$2, If[LessEqual[t, -1.3e-130], t$95$1, If[LessEqual[t, -1.75e-158], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, -7.4e-283], t$95$1, If[LessEqual[t, 6.8e-212], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, 6500000000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.70000000000000003e-6 or 6.5e9 < t

   1. Initial program 70.0%

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

   2. Taylor expanded in t around inf 86.5%

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

   if -1.70000000000000003e-6 < t < -1.3e-130 or -1.75000000000000006e-158 < t < -7.4000000000000001e-283 or 6.79999999999999995e-212 < t < 6.5e9

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-*r/ 99.9%

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

      7. sub-neg 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

      10. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around 0 61.7%

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

   if -1.3e-130 < t < -1.75000000000000006e-158 or -7.4000000000000001e-283 < t < 6.79999999999999995e-212

   1. Initial program 96.8%

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

   2. Taylor expanded in t around 0 89.1%

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

      1. associate-*r/ 89.1%

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

      2. metadata-eval 89.1%

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

   4. Simplified 89.1%

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

   5. Taylor expanded in z around inf 67.0%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-130}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-158}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-283}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-212}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 6500000000:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 3: 63.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-159}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-211}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 7200000000:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z))) (t_2 (- (/ x y) 2.0)))
   (if (<= t -1.8e-5)
     t_2
     (if (<= t -2.1e-134)
       t_1
       (if (<= t -7e-159)
         (/ 2.0 t)
         (if (<= t -8.5e-286)
           t_1
           (if (<= t 3.5e-211)
             (/ 2.0 t)
             (if (<= t 7200000000.0) (/ (/ 2.0 t) z) t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.8e-5) {
		tmp = t_2;
	} else if (t <= -2.1e-134) {
		tmp = t_1;
	} else if (t <= -7e-159) {
		tmp = 2.0 / t;
	} else if (t <= -8.5e-286) {
		tmp = t_1;
	} else if (t <= 3.5e-211) {
		tmp = 2.0 / t;
	} else if (t <= 7200000000.0) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 / (t * z)
    t_2 = (x / y) - 2.0d0
    if (t <= (-1.8d-5)) then
        tmp = t_2
    else if (t <= (-2.1d-134)) then
        tmp = t_1
    else if (t <= (-7d-159)) then
        tmp = 2.0d0 / t
    else if (t <= (-8.5d-286)) then
        tmp = t_1
    else if (t <= 3.5d-211) then
        tmp = 2.0d0 / t
    else if (t <= 7200000000.0d0) then
        tmp = (2.0d0 / t) / z
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.8e-5) {
		tmp = t_2;
	} else if (t <= -2.1e-134) {
		tmp = t_1;
	} else if (t <= -7e-159) {
		tmp = 2.0 / t;
	} else if (t <= -8.5e-286) {
		tmp = t_1;
	} else if (t <= 3.5e-211) {
		tmp = 2.0 / t;
	} else if (t <= 7200000000.0) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (x / y) - 2.0
	tmp = 0
	if t <= -1.8e-5:
		tmp = t_2
	elif t <= -2.1e-134:
		tmp = t_1
	elif t <= -7e-159:
		tmp = 2.0 / t
	elif t <= -8.5e-286:
		tmp = t_1
	elif t <= 3.5e-211:
		tmp = 2.0 / t
	elif t <= 7200000000.0:
		tmp = (2.0 / t) / z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -1.8e-5)
		tmp = t_2;
	elseif (t <= -2.1e-134)
		tmp = t_1;
	elseif (t <= -7e-159)
		tmp = Float64(2.0 / t);
	elseif (t <= -8.5e-286)
		tmp = t_1;
	elseif (t <= 3.5e-211)
		tmp = Float64(2.0 / t);
	elseif (t <= 7200000000.0)
		tmp = Float64(Float64(2.0 / t) / z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -1.8e-5)
		tmp = t_2;
	elseif (t <= -2.1e-134)
		tmp = t_1;
	elseif (t <= -7e-159)
		tmp = 2.0 / t;
	elseif (t <= -8.5e-286)
		tmp = t_1;
	elseif (t <= 3.5e-211)
		tmp = 2.0 / t;
	elseif (t <= 7200000000.0)
		tmp = (2.0 / t) / z;
	else
		tmp = t_2;
	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[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -1.8e-5], t$95$2, If[LessEqual[t, -2.1e-134], t$95$1, If[LessEqual[t, -7e-159], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, -8.5e-286], t$95$1, If[LessEqual[t, 3.5e-211], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, 7200000000.0], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.80000000000000005e-5 or 7.2e9 < t

   1. Initial program 70.0%

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

   2. Taylor expanded in t around inf 86.5%

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

   if -1.80000000000000005e-5 < t < -2.0999999999999999e-134 or -7.00000000000000005e-159 < t < -8.4999999999999998e-286

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 99.8%

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

      5. metadata-eval 99.8%

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

      6. associate-*r/ 99.8%

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

      7. sub-neg 99.8%

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

      8. associate-*r/ 99.8%

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

      9. metadata-eval 99.8%

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

      10. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in z around 0 61.4%

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

   if -2.0999999999999999e-134 < t < -7.00000000000000005e-159 or -8.4999999999999998e-286 < t < 3.5e-211

   1. Initial program 96.8%

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

   2. Taylor expanded in t around 0 89.1%

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

      1. associate-*r/ 89.1%

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

      2. metadata-eval 89.1%

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

   4. Simplified 89.1%

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

   5. Taylor expanded in z around inf 67.0%

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

   if 3.5e-211 < t < 7.2e9

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-*r/ 100.0%

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

      7. sub-neg 100.0%

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

      8. associate-*r/ 100.0%

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

      9. metadata-eval 100.0%

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

      10. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 81.1%

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

      1. sub-neg 81.1%

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

      2. associate-*r/ 81.1%

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

      3. metadata-eval 81.1%

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

      4. associate-*r/ 81.1%

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

      5. metadata-eval 81.1%

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

      6. +-commutative 81.1%

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

      7. metadata-eval 81.1%

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

      8. associate-+r+ 81.1%

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

      9. +-commutative 81.1%

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

   7. Simplified 81.1%

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

   8. Taylor expanded in z around 0 62.1%

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

      1. associate-/l/ 62.0%

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

   10. Simplified 62.0%

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

   11. Taylor expanded in z around 0 62.1%

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

       1. associate-/r* 62.2%

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

   13. Simplified 62.2%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-134}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-159}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-286}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-211}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 7200000000:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 4: 63.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-134}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-158}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-281}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 7200000000:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -4.4e-7)
     t_1
     (if (<= t -3.8e-134)
       (/ (/ 2.0 z) t)
       (if (<= t -2e-158)
         (/ 2.0 t)
         (if (<= t -2.05e-281)
           (/ 2.0 (* t z))
           (if (<= t 2.5e-203)
             (/ 2.0 t)
             (if (<= t 7200000000.0) (/ (/ 2.0 t) z) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -4.4e-7) {
		tmp = t_1;
	} else if (t <= -3.8e-134) {
		tmp = (2.0 / z) / t;
	} else if (t <= -2e-158) {
		tmp = 2.0 / t;
	} else if (t <= -2.05e-281) {
		tmp = 2.0 / (t * z);
	} else if (t <= 2.5e-203) {
		tmp = 2.0 / t;
	} else if (t <= 7200000000.0) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-4.4d-7)) then
        tmp = t_1
    else if (t <= (-3.8d-134)) then
        tmp = (2.0d0 / z) / t
    else if (t <= (-2d-158)) then
        tmp = 2.0d0 / t
    else if (t <= (-2.05d-281)) then
        tmp = 2.0d0 / (t * z)
    else if (t <= 2.5d-203) then
        tmp = 2.0d0 / t
    else if (t <= 7200000000.0d0) then
        tmp = (2.0d0 / t) / z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -4.4e-7) {
		tmp = t_1;
	} else if (t <= -3.8e-134) {
		tmp = (2.0 / z) / t;
	} else if (t <= -2e-158) {
		tmp = 2.0 / t;
	} else if (t <= -2.05e-281) {
		tmp = 2.0 / (t * z);
	} else if (t <= 2.5e-203) {
		tmp = 2.0 / t;
	} else if (t <= 7200000000.0) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -4.4e-7:
		tmp = t_1
	elif t <= -3.8e-134:
		tmp = (2.0 / z) / t
	elif t <= -2e-158:
		tmp = 2.0 / t
	elif t <= -2.05e-281:
		tmp = 2.0 / (t * z)
	elif t <= 2.5e-203:
		tmp = 2.0 / t
	elif t <= 7200000000.0:
		tmp = (2.0 / t) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -4.4e-7)
		tmp = t_1;
	elseif (t <= -3.8e-134)
		tmp = Float64(Float64(2.0 / z) / t);
	elseif (t <= -2e-158)
		tmp = Float64(2.0 / t);
	elseif (t <= -2.05e-281)
		tmp = Float64(2.0 / Float64(t * z));
	elseif (t <= 2.5e-203)
		tmp = Float64(2.0 / t);
	elseif (t <= 7200000000.0)
		tmp = Float64(Float64(2.0 / t) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -4.4e-7)
		tmp = t_1;
	elseif (t <= -3.8e-134)
		tmp = (2.0 / z) / t;
	elseif (t <= -2e-158)
		tmp = 2.0 / t;
	elseif (t <= -2.05e-281)
		tmp = 2.0 / (t * z);
	elseif (t <= 2.5e-203)
		tmp = 2.0 / t;
	elseif (t <= 7200000000.0)
		tmp = (2.0 / t) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -4.4e-7], t$95$1, If[LessEqual[t, -3.8e-134], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, -2e-158], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, -2.05e-281], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e-203], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, 7200000000.0], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.4000000000000002e-7 or 7.2e9 < t

   1. Initial program 70.0%

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

   2. Taylor expanded in t around inf 86.5%

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

   if -4.4000000000000002e-7 < t < -3.80000000000000003e-134

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 99.8%

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

      5. metadata-eval 99.8%

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

      6. associate-*r/ 99.8%

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

      7. sub-neg 99.8%

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

      8. associate-*r/ 99.8%

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

      9. metadata-eval 99.8%

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

      10. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in x around 0 84.8%

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

      1. sub-neg 84.8%

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

      2. associate-*r/ 84.8%

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

      3. metadata-eval 84.8%

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

      4. associate-*r/ 84.8%

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

      5. metadata-eval 84.8%

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

      6. +-commutative 84.8%

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

      7. metadata-eval 84.8%

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

      8. associate-+r+ 84.8%

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

      9. +-commutative 84.8%

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

   7. Simplified 84.8%

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

   8. Taylor expanded in z around 0 59.4%

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

      1. associate-/l/ 59.5%

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

   10. Simplified 59.5%

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

   if -3.80000000000000003e-134 < t < -2.00000000000000013e-158 or -2.05e-281 < t < 2.5000000000000001e-203

   1. Initial program 96.8%

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

   2. Taylor expanded in t around 0 89.1%

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

      1. associate-*r/ 89.1%

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

      2. metadata-eval 89.1%

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

   4. Simplified 89.1%

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

   5. Taylor expanded in z around inf 67.0%

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

   if -2.00000000000000013e-158 < t < -2.05e-281

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

      4. associate-/r* 99.8%

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

      5. metadata-eval 99.8%

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

      6. associate-*r/ 99.8%

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

      7. sub-neg 99.8%

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

      8. associate-*r/ 99.8%

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

      9. metadata-eval 99.8%

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

      10. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in z around 0 63.0%

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

   if 2.5000000000000001e-203 < t < 7.2e9

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-*r/ 100.0%

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

      7. sub-neg 100.0%

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

      8. associate-*r/ 100.0%

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

      9. metadata-eval 100.0%

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

      10. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 81.1%

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

      1. sub-neg 81.1%

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

      2. associate-*r/ 81.1%

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

      3. metadata-eval 81.1%

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

      4. associate-*r/ 81.1%

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

      5. metadata-eval 81.1%

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

      6. +-commutative 81.1%

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

      7. metadata-eval 81.1%

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

      8. associate-+r+ 81.1%

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

      9. +-commutative 81.1%

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

   7. Simplified 81.1%

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

   8. Taylor expanded in z around 0 62.1%

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

      1. associate-/l/ 62.0%

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

   10. Simplified 62.0%

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

   11. Taylor expanded in z around 0 62.1%

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

       1. associate-/r* 62.2%

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

   13. Simplified 62.2%

       \[\leadsto \color{blue}{\frac{\frac{2}{t}}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-134}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-158}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-281}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 7200000000:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 5: 65.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.05 \cdot 10^{+26} \lor \neg \left(\frac{x}{y} \leq 3500\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -3.05e+26) (not (<= (/ x y) 3500.0)))
   (/ x y)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -3.05e+26) || !((x / y) <= 3500.0)) {
		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) <= (-3.05d+26)) .or. (.not. ((x / y) <= 3500.0d0))) 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) <= -3.05e+26) || !((x / y) <= 3500.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -3.05e+26) or not ((x / y) <= 3500.0):
		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) <= -3.05e+26) || !(Float64(x / y) <= 3500.0))
		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) <= -3.05e+26) || ~(((x / y) <= 3500.0)))
		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], -3.05e+26], N[Not[LessEqual[N[(x / y), $MachinePrecision], 3500.0]], $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) < -3.0500000000000001e26 or 3500 < (/.f64 x y)

   1. Initial program 82.8%

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

   2. Taylor expanded in x around inf 64.4%

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

   if -3.0500000000000001e26 < (/.f64 x y) < 3500

   1. Initial program 86.1%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-*r/ 99.9%

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

      7. sub-neg 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

      10. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in x around 0 98.7%

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

      1. sub-neg 98.7%

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

      2. associate-*r/ 98.7%

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

      3. metadata-eval 98.7%

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

      4. associate-*r/ 98.7%

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

      5. metadata-eval 98.7%

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

      6. +-commutative 98.7%

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

      7. metadata-eval 98.7%

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

      8. associate-+r+ 98.7%

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

      9. +-commutative 98.7%

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

   7. Simplified 98.7%

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

   8. Taylor expanded in z around inf 59.1%

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

      1. sub-neg 59.1%

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

      2. associate-*r/ 59.1%

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

      3. metadata-eval 59.1%

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

      4. metadata-eval 59.1%

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

      5. +-commutative 59.1%

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

   10. Simplified 59.1%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.05 \cdot 10^{+26} \lor \neg \left(\frac{x}{y} \leq 3500\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]

Alternative 6: 92.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-15} \lor \neg \left(z \leq 7.5 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.8e-15) (not (<= z 7.5e-30)))
   (+ (/ 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 <= -6.8e-15) || !(z <= 7.5e-30)) {
		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 <= (-6.8d-15)) .or. (.not. (z <= 7.5d-30))) 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 <= -6.8e-15) || !(z <= 7.5e-30)) {
		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 <= -6.8e-15) or not (z <= 7.5e-30):
		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 <= -6.8e-15) || !(z <= 7.5e-30))
		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 <= -6.8e-15) || ~((z <= 7.5e-30)))
		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, -6.8e-15], N[Not[LessEqual[z, 7.5e-30]], $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 < -6.8000000000000001e-15 or 7.5000000000000006e-30 < z

   1. Initial program 73.1%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/r* 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-*r/ 100.0%

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

      7. sub-neg 100.0%

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

      8. associate-*r/ 100.0%

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

      9. metadata-eval 100.0%

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

      10. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 98.8%

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

      1. sub-neg 98.8%

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

      2. associate-*r/ 98.8%

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

      3. metadata-eval 98.8%

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

      4. +-commutative 98.8%

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

      5. metadata-eval 98.8%

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

      6. associate-+r+ 98.8%

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

      7. +-commutative 98.8%

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

   7. Simplified 98.8%

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

   if -6.8000000000000001e-15 < z < 7.5000000000000006e-30

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 86.6%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-15} \lor \neg \left(z \leq 7.5 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \]

Alternative 7: 52.4% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2.0d0)) .or. (.not. ((x / y) <= 2.0d0))) then
        tmp = x / y
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 83.8%

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

   2. Taylor expanded in x around inf 61.7%

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

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

   1. Initial program 85.4%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-*r/ 99.9%

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

      7. sub-neg 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

      10. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in x around 0 99.3%

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

      1. sub-neg 99.3%

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

      2. associate-*r/ 99.3%

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

      3. metadata-eval 99.3%

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

      4. associate-*r/ 99.3%

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

      5. metadata-eval 99.3%

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

      6. +-commutative 99.3%

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

      7. metadata-eval 99.3%

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

      8. associate-+r+ 99.3%

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

      9. +-commutative 99.3%

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

   7. Simplified 99.3%

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

   8. Taylor expanded in t around inf 40.2%

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

4. Final simplification 50.6%

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

Alternative 8: 81.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.0031 \lor \neg \left(t \leq 7200000000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -0.0031) (not (<= t 7200000000.0)))
   (- (/ x y) 2.0)
   (/ (+ 2.0 (/ 2.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -0.0031) || !(t <= 7200000000.0)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / 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 <= (-0.0031d0)) .or. (.not. (t <= 7200000000.0d0))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 + (2.0d0 / z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -0.0031) || !(t <= 7200000000.0)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -0.0031) or not (t <= 7200000000.0):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -0.0031) || !(t <= 7200000000.0))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -0.0031) || ~((t <= 7200000000.0)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -0.0031], N[Not[LessEqual[t, 7200000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.00309999999999999989 or 7.2e9 < t

   1. Initial program 69.8%

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

   2. Taylor expanded in t around inf 87.1%

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

   if -0.00309999999999999989 < t < 7.2e9

   1. Initial program 99.0%

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

   2. Taylor expanded in t around 0 85.7%

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

      1. associate-*r/ 85.7%

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

      2. metadata-eval 85.7%

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

   4. Simplified 85.7%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0031 \lor \neg \left(t \leq 7200000000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 9: 81.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.00064:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq 6200000000:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot -2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -0.00064)
   (- (/ x y) 2.0)
   (if (<= t 6200000000.0) (/ (+ 2.0 (/ 2.0 z)) t) (/ (+ x (* y -2.0)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -0.00064) {
		tmp = (x / y) - 2.0;
	} else if (t <= 6200000000.0) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = (x + (y * -2.0)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-0.00064d0)) then
        tmp = (x / y) - 2.0d0
    else if (t <= 6200000000.0d0) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    else
        tmp = (x + (y * (-2.0d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -0.00064) {
		tmp = (x / y) - 2.0;
	} else if (t <= 6200000000.0) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = (x + (y * -2.0)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -0.00064:
		tmp = (x / y) - 2.0
	elif t <= 6200000000.0:
		tmp = (2.0 + (2.0 / z)) / t
	else:
		tmp = (x + (y * -2.0)) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -0.00064)
		tmp = Float64(Float64(x / y) - 2.0);
	elseif (t <= 6200000000.0)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	else
		tmp = Float64(Float64(x + Float64(y * -2.0)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -0.00064)
		tmp = (x / y) - 2.0;
	elseif (t <= 6200000000.0)
		tmp = (2.0 + (2.0 / z)) / t;
	else
		tmp = (x + (y * -2.0)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -0.00064], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[t, 6200000000.0], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(N[(x + N[(y * -2.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.40000000000000052e-4

   1. Initial program 66.1%

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

   2. Taylor expanded in t around inf 85.1%

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

   if -6.40000000000000052e-4 < t < 6.2e9

   1. Initial program 99.0%

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

   2. Taylor expanded in t around 0 85.7%

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

      1. associate-*r/ 85.7%

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

      2. metadata-eval 85.7%

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

   4. Simplified 85.7%

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

   if 6.2e9 < t

   1. Initial program 73.7%

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

      1. div-inv 73.6%

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

      2. fma-def 73.6%

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

      3. *-commutative 73.6%

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

      4. +-commutative 73.6%

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

      5. associate-*l* 73.6%

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

      6. fma-def 73.6%

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

   3. Applied egg-rr 73.6%

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

      1. fma-udef 73.6%

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

      2. div-inv 73.7%

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

      3. associate-/r* 79.1%

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

      4. frac-add 51.3%

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

   5. Applied egg-rr 51.3%

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

   6. Taylor expanded in t around inf 89.2%

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

      1. *-commutative 89.2%

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

   8. Simplified 89.2%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.00064:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq 6200000000:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot -2}{y}\\ \end{array} \]

Alternative 10: 81.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{elif}\;t \leq 6200000000:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot -2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.65e-5)
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (if (<= t 6200000000.0) (/ (+ 2.0 (/ 2.0 z)) t) (/ (+ x (* y -2.0)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.65e-5) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else if (t <= 6200000000.0) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = (x + (y * -2.0)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.65d-5)) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else if (t <= 6200000000.0d0) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    else
        tmp = (x + (y * (-2.0d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.65e-5) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else if (t <= 6200000000.0) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = (x + (y * -2.0)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.65e-5:
		tmp = (x / y) + ((2.0 / t) + -2.0)
	elif t <= 6200000000.0:
		tmp = (2.0 + (2.0 / z)) / t
	else:
		tmp = (x + (y * -2.0)) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.65e-5)
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	elseif (t <= 6200000000.0)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	else
		tmp = Float64(Float64(x + Float64(y * -2.0)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.65e-5)
		tmp = (x / y) + ((2.0 / t) + -2.0);
	elseif (t <= 6200000000.0)
		tmp = (2.0 + (2.0 / z)) / t;
	else
		tmp = (x + (y * -2.0)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.65e-5], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6200000000.0], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(N[(x + N[(y * -2.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6500000000000001e-5

   1. Initial program 66.6%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/r* 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-*r/ 99.9%

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

      7. sub-neg 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

      10. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around inf 85.3%

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

      1. sub-neg 85.3%

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

      2. associate-*r/ 85.3%

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

      3. metadata-eval 85.3%

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

      4. +-commutative 85.3%

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

      5. metadata-eval 85.3%

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

      6. associate-+r+ 85.3%

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

      7. +-commutative 85.3%

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

   7. Simplified 85.3%

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

   if -1.6500000000000001e-5 < t < 6.2e9

   1. Initial program 99.0%

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

   2. Taylor expanded in t around 0 86.0%

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

      1. associate-*r/ 86.0%

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

      2. metadata-eval 86.0%

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

   4. Simplified 86.0%

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

   if 6.2e9 < t

   1. Initial program 73.7%

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

      1. div-inv 73.6%

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

      2. fma-def 73.6%

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

      3. *-commutative 73.6%

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

      4. +-commutative 73.6%

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

      5. associate-*l* 73.6%

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

      6. fma-def 73.6%

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

   3. Applied egg-rr 73.6%

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

      1. fma-udef 73.6%

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

      2. div-inv 73.7%

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

      3. associate-/r* 79.1%

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

      4. frac-add 51.3%

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

   5. Applied egg-rr 51.3%

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

   6. Taylor expanded in t around inf 89.2%

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

      1. *-commutative 89.2%

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

   8. Simplified 89.2%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{elif}\;t \leq 6200000000:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot -2}{y}\\ \end{array} \]

Alternative 11: 61.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-20} \lor \neg \left(t \leq 5.3 \cdot 10^{-84}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.2e-20) (not (<= t 5.3e-84)))
   (- (/ x y) 2.0)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.2e-20) || !(t <= 5.3e-84)) {
		tmp = (x / y) - 2.0;
	} 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 ((t <= (-5.2d-20)) .or. (.not. (t <= 5.3d-84))) then
        tmp = (x / y) - 2.0d0
    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 ((t <= -5.2e-20) || !(t <= 5.3e-84)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.2e-20) or not (t <= 5.3e-84):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.2e-20) || !(t <= 5.3e-84))
		tmp = Float64(Float64(x / y) - 2.0);
	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 ((t <= -5.2e-20) || ~((t <= 5.3e-84)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.2e-20], N[Not[LessEqual[t, 5.3e-84]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.1999999999999999e-20 or 5.3000000000000004e-84 < t

   1. Initial program 75.3%

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

   2. Taylor expanded in t around inf 77.7%

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

   if -5.1999999999999999e-20 < t < 5.3000000000000004e-84

   1. Initial program 98.7%

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

   2. Taylor expanded in t around 0 98.9%

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

      1. associate--l+ 98.9%

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

      2. associate-*r/ 98.9%

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

      3. metadata-eval 98.9%

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

      4. associate-/r* 98.9%

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

      5. metadata-eval 98.9%

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

      6. associate-*r/ 98.9%

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

      7. sub-neg 98.9%

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

      8. associate-*r/ 98.9%

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

      9. metadata-eval 98.9%

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

      10. metadata-eval 98.9%

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

   4. Simplified 98.9%

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

   5. Taylor expanded in x around 0 91.8%

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

      1. sub-neg 91.8%

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

      2. associate-*r/ 91.8%

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

      3. metadata-eval 91.8%

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

      4. associate-*r/ 91.8%

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

      5. metadata-eval 91.8%

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

      6. +-commutative 91.8%

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

      7. metadata-eval 91.8%

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

      8. associate-+r+ 91.8%

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

      9. +-commutative 91.8%

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

   7. Simplified 91.8%

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

   8. Taylor expanded in z around inf 44.7%

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

      1. sub-neg 44.7%

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

      2. associate-*r/ 44.7%

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

      3. metadata-eval 44.7%

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

      4. metadata-eval 44.7%

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

      5. +-commutative 44.7%

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

   10. Simplified 44.7%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-20} \lor \neg \left(t \leq 5.3 \cdot 10^{-84}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]

Alternative 12: 36.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.004:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-38}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -0.004) -2.0 (if (<= t 9.5e-38) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -0.004) {
		tmp = -2.0;
	} else if (t <= 9.5e-38) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-0.004d0)) then
        tmp = -2.0d0
    else if (t <= 9.5d-38) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -0.004) {
		tmp = -2.0;
	} else if (t <= 9.5e-38) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -0.004:
		tmp = -2.0
	elif t <= 9.5e-38:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -0.004)
		tmp = -2.0;
	elseif (t <= 9.5e-38)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -0.004)
		tmp = -2.0;
	elseif (t <= 9.5e-38)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -0.004], -2.0, If[LessEqual[t, 9.5e-38], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -0.0040000000000000001 or 9.5000000000000009e-38 < t

   1. Initial program 72.0%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-*r/ 99.9%

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

      7. sub-neg 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

      10. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in x around 0 55.8%

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

      1. sub-neg 55.8%

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

      2. associate-*r/ 55.8%

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

      3. metadata-eval 55.8%

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

      4. associate-*r/ 55.8%

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

      5. metadata-eval 55.8%

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

      6. +-commutative 55.8%

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

      7. metadata-eval 55.8%

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

      8. associate-+r+ 55.8%

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

      9. +-commutative 55.8%

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

   7. Simplified 55.8%

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

   8. Taylor expanded in t around inf 39.1%

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

   if -0.0040000000000000001 < t < 9.5000000000000009e-38

   1. Initial program 98.9%

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

   2. Taylor expanded in t around 0 87.8%

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

      1. associate-*r/ 87.8%

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

      2. metadata-eval 87.8%

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

   4. Simplified 87.8%

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

   5. Taylor expanded in z around inf 39.6%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.004:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-38}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 13: 19.9% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.6%

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

2. Taylor expanded in t around 0 99.5%

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

   1. associate--l+ 99.5%

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

   2. associate-*r/ 99.5%

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

   3. metadata-eval 99.5%

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

   4. associate-/r* 99.5%

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

   5. metadata-eval 99.5%

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

   6. associate-*r/ 99.5%

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

   7. sub-neg 99.5%

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

   8. associate-*r/ 99.5%

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

   9. metadata-eval 99.5%

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

   10. metadata-eval 99.5%

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

4. Simplified 99.5%

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

5. Taylor expanded in x around 0 71.0%

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

   1. sub-neg 71.0%

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

   2. associate-*r/ 71.0%

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

   3. metadata-eval 71.0%

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

   4. associate-*r/ 71.0%

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

   5. metadata-eval 71.0%

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

   6. +-commutative 71.0%

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

   7. metadata-eval 71.0%

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

   8. associate-+r+ 71.0%

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

   9. +-commutative 71.0%

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

7. Simplified 71.0%

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

8. Taylor expanded in t around inf 22.0%

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

9. Final simplification 22.0%

   \[\leadsto -2 \]

Developer target: 99.2% accurate, 1.3× 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 2023336 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :herbie-target
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

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