Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3

Percentage Accurate: 97.3% → 99.7%

Time: 12.8s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.0%

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

   1. associate-/r/ 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
4. Add Preprocessing

5. Final simplification 99.9%

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

Alternative 2: 73.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + a \cdot \frac{z}{1 - z}\\ t_2 := x + a \cdot \frac{y}{z + -1}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+210}:\\ \;\;\;\;x + z \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq -1.04 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-238}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+82}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* a (/ z (- 1.0 z))))) (t_2 (+ x (* a (/ y (+ z -1.0))))))
   (if (<= t -1.05e+210)
     (+ x (* z (/ a t)))
     (if (<= t -1.04e-103)
       t_1
       (if (<= t 1.1e-238)
         t_2
         (if (<= t 1.25e-119)
           t_1
           (if (<= t 1.9e+82) t_2 (- x (* y (/ a t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * (z / (1.0 - z)));
	double t_2 = x + (a * (y / (z + -1.0)));
	double tmp;
	if (t <= -1.05e+210) {
		tmp = x + (z * (a / t));
	} else if (t <= -1.04e-103) {
		tmp = t_1;
	} else if (t <= 1.1e-238) {
		tmp = t_2;
	} else if (t <= 1.25e-119) {
		tmp = t_1;
	} else if (t <= 1.9e+82) {
		tmp = t_2;
	} else {
		tmp = x - (y * (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a * (z / (1.0d0 - z)))
    t_2 = x + (a * (y / (z + (-1.0d0))))
    if (t <= (-1.05d+210)) then
        tmp = x + (z * (a / t))
    else if (t <= (-1.04d-103)) then
        tmp = t_1
    else if (t <= 1.1d-238) then
        tmp = t_2
    else if (t <= 1.25d-119) then
        tmp = t_1
    else if (t <= 1.9d+82) then
        tmp = t_2
    else
        tmp = x - (y * (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (a * (z / (1.0 - z)));
	double t_2 = x + (a * (y / (z + -1.0)));
	double tmp;
	if (t <= -1.05e+210) {
		tmp = x + (z * (a / t));
	} else if (t <= -1.04e-103) {
		tmp = t_1;
	} else if (t <= 1.1e-238) {
		tmp = t_2;
	} else if (t <= 1.25e-119) {
		tmp = t_1;
	} else if (t <= 1.9e+82) {
		tmp = t_2;
	} else {
		tmp = x - (y * (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (a * (z / (1.0 - z)))
	t_2 = x + (a * (y / (z + -1.0)))
	tmp = 0
	if t <= -1.05e+210:
		tmp = x + (z * (a / t))
	elif t <= -1.04e-103:
		tmp = t_1
	elif t <= 1.1e-238:
		tmp = t_2
	elif t <= 1.25e-119:
		tmp = t_1
	elif t <= 1.9e+82:
		tmp = t_2
	else:
		tmp = x - (y * (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(a * Float64(z / Float64(1.0 - z))))
	t_2 = Float64(x + Float64(a * Float64(y / Float64(z + -1.0))))
	tmp = 0.0
	if (t <= -1.05e+210)
		tmp = Float64(x + Float64(z * Float64(a / t)));
	elseif (t <= -1.04e-103)
		tmp = t_1;
	elseif (t <= 1.1e-238)
		tmp = t_2;
	elseif (t <= 1.25e-119)
		tmp = t_1;
	elseif (t <= 1.9e+82)
		tmp = t_2;
	else
		tmp = Float64(x - Float64(y * Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (a * (z / (1.0 - z)));
	t_2 = x + (a * (y / (z + -1.0)));
	tmp = 0.0;
	if (t <= -1.05e+210)
		tmp = x + (z * (a / t));
	elseif (t <= -1.04e-103)
		tmp = t_1;
	elseif (t <= 1.1e-238)
		tmp = t_2;
	elseif (t <= 1.25e-119)
		tmp = t_1;
	elseif (t <= 1.9e+82)
		tmp = t_2;
	else
		tmp = x - (y * (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(a * N[(z / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a * N[(y / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e+210], N[(x + N[(z * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.04e-103], t$95$1, If[LessEqual[t, 1.1e-238], t$95$2, If[LessEqual[t, 1.25e-119], t$95$1, If[LessEqual[t, 1.9e+82], t$95$2, N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.0499999999999999e210

   1. Initial program 99.9%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 76.5%

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

      1. mul-1-neg 76.5%

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

      2. *-commutative 76.5%

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

      3. associate--l+ 76.5%

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

      4. +-commutative 76.5%

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

      5. associate-*r/ 98.0%

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

      6. distribute-rgt-neg-in 98.0%

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

      7. distribute-neg-frac 98.0%

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

      8. +-commutative 98.0%

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

      9. associate--l+ 98.0%

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

   7. Simplified 98.0%

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

   8. Taylor expanded in t around inf 91.9%

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

      1. associate-*r/ 91.9%

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

      2. mul-1-neg 91.9%

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

   10. Simplified 91.9%

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

   if -1.0499999999999999e210 < t < -1.04000000000000001e-103 or 1.09999999999999996e-238 < t < 1.24999999999999998e-119

   1. Initial program 94.8%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.3%

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

      1. mul-1-neg 71.3%

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

      2. *-commutative 71.3%

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

      3. associate--l+ 71.3%

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

      4. +-commutative 71.3%

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

      5. associate-*r/ 80.4%

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

      6. distribute-rgt-neg-in 80.4%

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

      7. distribute-neg-frac 80.4%

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

      8. +-commutative 80.4%

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

      9. associate--l+ 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in t around 0 69.4%

      \[\leadsto \color{blue}{x - -1 \cdot \frac{a \cdot z}{1 - z}} \]
   9. Step-by-step derivation

      1. sub-neg 69.4%

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

      2. mul-1-neg 69.4%

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

      3. remove-double-neg 69.4%

         \[\leadsto x + \color{blue}{\frac{a \cdot z}{1 - z}} \]

      4. associate-/l* 81.0%

         \[\leadsto x + \color{blue}{a \cdot \frac{z}{1 - z}} \]

   10. Simplified 81.0%

       \[\leadsto \color{blue}{x + a \cdot \frac{z}{1 - z}} \]

   if -1.04000000000000001e-103 < t < 1.09999999999999996e-238 or 1.24999999999999998e-119 < t < 1.90000000000000017e82

   1. Initial program 97.0%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 95.4%

      \[\leadsto x - \frac{a}{\color{blue}{\frac{1 - z}{y - z}}} \]

   8. Taylor expanded in y around inf 69.3%

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 - z}} \]
   9. Step-by-step derivation

      1. associate-/l* 73.2%

         \[\leadsto x - \color{blue}{a \cdot \frac{y}{1 - z}} \]

   10. Simplified 73.2%

       \[\leadsto x - \color{blue}{a \cdot \frac{y}{1 - z}} \]

   if 1.90000000000000017e82 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 87.8%

      \[\leadsto x - \frac{y - z}{\color{blue}{\frac{t}{a}}} \]

   4. Taylor expanded in y around inf 75.9%

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{t}} \]
   5. Step-by-step derivation

      1. *-commutative 75.9%

         \[\leadsto x - \frac{\color{blue}{y \cdot a}}{t} \]

      2. associate-*r/ 91.7%

         \[\leadsto x - \color{blue}{y \cdot \frac{a}{t}} \]

   6. Simplified 91.7%

      \[\leadsto x - \color{blue}{y \cdot \frac{a}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+210}:\\ \;\;\;\;x + z \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq -1.04 \cdot 10^{-103}:\\ \;\;\;\;x + a \cdot \frac{z}{1 - z}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-238}:\\ \;\;\;\;x + a \cdot \frac{y}{z + -1}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-119}:\\ \;\;\;\;x + a \cdot \frac{z}{1 - z}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+82}:\\ \;\;\;\;x + a \cdot \frac{y}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \frac{y}{z + \left(-1 - t\right)}\\ \mathbf{if}\;y \leq -1.88 \cdot 10^{+230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+172}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+128} \lor \neg \left(y \leq 3.1 \cdot 10^{+139}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* a (/ y (+ z (- -1.0 t))))))
   (if (<= y -1.88e+230)
     t_1
     (if (<= y -7.2e+172)
       (- x (* a (/ y t)))
       (if (or (<= y -2.8e+128) (not (<= y 3.1e+139)))
         t_1
         (+ x (* a (/ z (- 1.0 z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a * (y / (z + (-1.0 - t)));
	double tmp;
	if (y <= -1.88e+230) {
		tmp = t_1;
	} else if (y <= -7.2e+172) {
		tmp = x - (a * (y / t));
	} else if ((y <= -2.8e+128) || !(y <= 3.1e+139)) {
		tmp = t_1;
	} else {
		tmp = x + (a * (z / (1.0 - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (y / (z + ((-1.0d0) - t)))
    if (y <= (-1.88d+230)) then
        tmp = t_1
    else if (y <= (-7.2d+172)) then
        tmp = x - (a * (y / t))
    else if ((y <= (-2.8d+128)) .or. (.not. (y <= 3.1d+139))) then
        tmp = t_1
    else
        tmp = x + (a * (z / (1.0d0 - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = a * (y / (z + (-1.0 - t)));
	double tmp;
	if (y <= -1.88e+230) {
		tmp = t_1;
	} else if (y <= -7.2e+172) {
		tmp = x - (a * (y / t));
	} else if ((y <= -2.8e+128) || !(y <= 3.1e+139)) {
		tmp = t_1;
	} else {
		tmp = x + (a * (z / (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a * (y / (z + (-1.0 - t)))
	tmp = 0
	if y <= -1.88e+230:
		tmp = t_1
	elif y <= -7.2e+172:
		tmp = x - (a * (y / t))
	elif (y <= -2.8e+128) or not (y <= 3.1e+139):
		tmp = t_1
	else:
		tmp = x + (a * (z / (1.0 - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a * Float64(y / Float64(z + Float64(-1.0 - t))))
	tmp = 0.0
	if (y <= -1.88e+230)
		tmp = t_1;
	elseif (y <= -7.2e+172)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	elseif ((y <= -2.8e+128) || !(y <= 3.1e+139))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(a * Float64(z / Float64(1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a * (y / (z + (-1.0 - t)));
	tmp = 0.0;
	if (y <= -1.88e+230)
		tmp = t_1;
	elseif (y <= -7.2e+172)
		tmp = x - (a * (y / t));
	elseif ((y <= -2.8e+128) || ~((y <= 3.1e+139)))
		tmp = t_1;
	else
		tmp = x + (a * (z / (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a * N[(y / N[(z + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.88e+230], t$95$1, If[LessEqual[y, -7.2e+172], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.8e+128], N[Not[LessEqual[y, 3.1e+139]], $MachinePrecision]], t$95$1, N[(x + N[(a * N[(z / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.88e230 or -7.1999999999999995e172 < y < -2.79999999999999983e128 or 3.1e139 < y

   1. Initial program 95.3%

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

      1. sub-neg 95.3%

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

      2. +-commutative 95.3%

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

      3. associate-/r/ 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

      5. associate-*l/ 74.4%

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

      6. associate-/l* 95.5%

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

      7. fma-define 95.5%

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

      8. distribute-frac-neg 95.5%

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

      9. distribute-neg-frac2 95.5%

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

      10. distribute-neg-in 95.5%

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

      11. sub-neg 95.5%

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

      12. distribute-neg-in 95.5%

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

      13. remove-double-neg 95.5%

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

      14. +-commutative 95.5%

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

      15. sub-neg 95.5%

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

      16. metadata-eval 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around inf 49.5%

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

      1. associate-/l* 63.8%

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

   7. Simplified 63.8%

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

   if -1.88e230 < y < -7.1999999999999995e172

   1. Initial program 100.0%

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

      1. associate-/r/ 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 83.9%

      \[\leadsto x - \color{blue}{\frac{y - z}{t}} \cdot a \]

   6. Taylor expanded in y around inf 76.3%

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

      1. associate-/l* 84.2%

         \[\leadsto x - \color{blue}{a \cdot \frac{y}{t}} \]

   8. Simplified 84.2%

      \[\leadsto x - \color{blue}{a \cdot \frac{y}{t}} \]

   if -2.79999999999999983e128 < y < 3.1e139

   1. Initial program 97.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 77.1%

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

      1. mul-1-neg 77.1%

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

      2. *-commutative 77.1%

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

      3. associate--l+ 77.1%

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

      4. +-commutative 77.1%

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

      5. associate-*r/ 87.5%

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

      6. distribute-rgt-neg-in 87.5%

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

      7. distribute-neg-frac 87.5%

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

      8. +-commutative 87.5%

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

      9. associate--l+ 87.5%

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

   7. Simplified 87.5%

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

   8. Taylor expanded in t around 0 72.4%

      \[\leadsto \color{blue}{x - -1 \cdot \frac{a \cdot z}{1 - z}} \]
   9. Step-by-step derivation

      1. sub-neg 72.4%

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

      2. mul-1-neg 72.4%

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

      3. remove-double-neg 72.4%

         \[\leadsto x + \color{blue}{\frac{a \cdot z}{1 - z}} \]

      4. associate-/l* 81.5%

         \[\leadsto x + \color{blue}{a \cdot \frac{z}{1 - z}} \]

   10. Simplified 81.5%

       \[\leadsto \color{blue}{x + a \cdot \frac{z}{1 - z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.88 \cdot 10^{+230}:\\ \;\;\;\;a \cdot \frac{y}{z + \left(-1 - t\right)}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+172}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+128} \lor \neg \left(y \leq 3.1 \cdot 10^{+139}\right):\\ \;\;\;\;a \cdot \frac{y}{z + \left(-1 - t\right)}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{z}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+100}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -720000000000:\\ \;\;\;\;x + a \cdot \frac{y}{z + -1}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-16} \lor \neg \left(z \leq 4.4 \cdot 10^{-22}\right):\\ \;\;\;\;x + a \cdot \frac{z}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.6e+100)
   (- x a)
   (if (<= z -720000000000.0)
     (+ x (* a (/ y (+ z -1.0))))
     (if (or (<= z -1.8e-16) (not (<= z 4.4e-22)))
       (+ x (* a (/ z (- 1.0 z))))
       (- x (* a (/ y (+ t 1.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.6e+100) {
		tmp = x - a;
	} else if (z <= -720000000000.0) {
		tmp = x + (a * (y / (z + -1.0)));
	} else if ((z <= -1.8e-16) || !(z <= 4.4e-22)) {
		tmp = x + (a * (z / (1.0 - z)));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.6d+100)) then
        tmp = x - a
    else if (z <= (-720000000000.0d0)) then
        tmp = x + (a * (y / (z + (-1.0d0))))
    else if ((z <= (-1.8d-16)) .or. (.not. (z <= 4.4d-22))) then
        tmp = x + (a * (z / (1.0d0 - z)))
    else
        tmp = x - (a * (y / (t + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.6e+100) {
		tmp = x - a;
	} else if (z <= -720000000000.0) {
		tmp = x + (a * (y / (z + -1.0)));
	} else if ((z <= -1.8e-16) || !(z <= 4.4e-22)) {
		tmp = x + (a * (z / (1.0 - z)));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.6e+100:
		tmp = x - a
	elif z <= -720000000000.0:
		tmp = x + (a * (y / (z + -1.0)))
	elif (z <= -1.8e-16) or not (z <= 4.4e-22):
		tmp = x + (a * (z / (1.0 - z)))
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.6e+100)
		tmp = Float64(x - a);
	elseif (z <= -720000000000.0)
		tmp = Float64(x + Float64(a * Float64(y / Float64(z + -1.0))));
	elseif ((z <= -1.8e-16) || !(z <= 4.4e-22))
		tmp = Float64(x + Float64(a * Float64(z / Float64(1.0 - z))));
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.6e+100)
		tmp = x - a;
	elseif (z <= -720000000000.0)
		tmp = x + (a * (y / (z + -1.0)));
	elseif ((z <= -1.8e-16) || ~((z <= 4.4e-22)))
		tmp = x + (a * (z / (1.0 - z)));
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.6e+100], N[(x - a), $MachinePrecision], If[LessEqual[z, -720000000000.0], N[(x + N[(a * N[(y / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.8e-16], N[Not[LessEqual[z, 4.4e-22]], $MachinePrecision]], N[(x + N[(a * N[(z / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.6e100

   1. Initial program 95.8%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 80.4%

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

   if -3.6e100 < z < -7.2e11

   1. Initial program 94.6%

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

      1. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

      1. *-commutative 99.7%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around 0 77.1%

      \[\leadsto x - \frac{a}{\color{blue}{\frac{1 - z}{y - z}}} \]

   8. Taylor expanded in y around inf 76.8%

      \[\leadsto x - \color{blue}{\frac{a \cdot y}{1 - z}} \]
   9. Step-by-step derivation

      1. associate-/l* 81.8%

         \[\leadsto x - \color{blue}{a \cdot \frac{y}{1 - z}} \]

   10. Simplified 81.8%

       \[\leadsto x - \color{blue}{a \cdot \frac{y}{1 - z}} \]

   if -7.2e11 < z < -1.79999999999999991e-16 or 4.4000000000000001e-22 < z

   1. Initial program 93.4%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 68.7%

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

      1. mul-1-neg 68.7%

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

      2. *-commutative 68.7%

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

      3. associate--l+ 68.7%

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

      4. +-commutative 68.7%

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

      5. associate-*r/ 82.6%

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

      6. distribute-rgt-neg-in 82.6%

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

      7. distribute-neg-frac 82.6%

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

      8. +-commutative 82.6%

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

      9. associate--l+ 82.6%

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

   7. Simplified 82.6%

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

   8. Taylor expanded in t around 0 63.1%

      \[\leadsto \color{blue}{x - -1 \cdot \frac{a \cdot z}{1 - z}} \]
   9. Step-by-step derivation

      1. sub-neg 63.1%

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

      2. mul-1-neg 63.1%

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

      3. remove-double-neg 63.1%

         \[\leadsto x + \color{blue}{\frac{a \cdot z}{1 - z}} \]

      4. associate-/l* 77.4%

         \[\leadsto x + \color{blue}{a \cdot \frac{z}{1 - z}} \]

   10. Simplified 77.4%

       \[\leadsto \color{blue}{x + a \cdot \frac{z}{1 - z}} \]

   if -1.79999999999999991e-16 < z < 4.4000000000000001e-22

   1. Initial program 99.8%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 93.0%

      \[\leadsto x - \color{blue}{\frac{y}{1 + t}} \cdot a \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+100}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -720000000000:\\ \;\;\;\;x + a \cdot \frac{y}{z + -1}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-16} \lor \neg \left(z \leq 4.4 \cdot 10^{-22}\right):\\ \;\;\;\;x + a \cdot \frac{z}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -15.2:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-298}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-6}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -15.2)
   (- x a)
   (if (<= z -8.5e-298)
     (- x (* y a))
     (if (<= z 1.9e-6) (- x (* a (/ y t))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -15.2) {
		tmp = x - a;
	} else if (z <= -8.5e-298) {
		tmp = x - (y * a);
	} else if (z <= 1.9e-6) {
		tmp = x - (a * (y / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-15.2d0)) then
        tmp = x - a
    else if (z <= (-8.5d-298)) then
        tmp = x - (y * a)
    else if (z <= 1.9d-6) then
        tmp = x - (a * (y / t))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -15.2) {
		tmp = x - a;
	} else if (z <= -8.5e-298) {
		tmp = x - (y * a);
	} else if (z <= 1.9e-6) {
		tmp = x - (a * (y / t));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -15.2:
		tmp = x - a
	elif z <= -8.5e-298:
		tmp = x - (y * a)
	elif z <= 1.9e-6:
		tmp = x - (a * (y / t))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -15.2)
		tmp = Float64(x - a);
	elseif (z <= -8.5e-298)
		tmp = Float64(x - Float64(y * a));
	elseif (z <= 1.9e-6)
		tmp = Float64(x - Float64(a * Float64(y / t)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -15.2)
		tmp = x - a;
	elseif (z <= -8.5e-298)
		tmp = x - (y * a);
	elseif (z <= 1.9e-6)
		tmp = x - (a * (y / t));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -15.2], N[(x - a), $MachinePrecision], If[LessEqual[z, -8.5e-298], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-6], N[(x - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -15.199999999999999 or 1.9e-6 < z

   1. Initial program 94.2%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 75.4%

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

   if -15.199999999999999 < z < -8.49999999999999957e-298

   1. Initial program 99.7%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around 0 83.5%

      \[\leadsto x - \frac{a}{\color{blue}{\frac{1 - z}{y - z}}} \]

   8. Taylor expanded in z around 0 75.0%

      \[\leadsto x - \color{blue}{a \cdot y} \]

   if -8.49999999999999957e-298 < z < 1.9e-6

   1. Initial program 99.8%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 73.0%

      \[\leadsto x - \color{blue}{\frac{y - z}{t}} \cdot a \]

   6. Taylor expanded in y around inf 68.1%

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

      1. associate-/l* 74.1%

         \[\leadsto x - \color{blue}{a \cdot \frac{y}{t}} \]

   8. Simplified 74.1%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -15.2:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-298}:\\ \;\;\;\;x - y \cdot a\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-6}:\\ \;\;\;\;x - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+129} \lor \neg \left(z \leq 9 \cdot 10^{+73}\right):\\ \;\;\;\;x - \left(a - a \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{z + \left(-1 - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e+129) (not (<= z 9e+73)))
   (- x (- a (* a (/ y z))))
   (+ x (* a (/ y (+ z (- -1.0 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+129) || !(z <= 9e+73)) {
		tmp = x - (a - (a * (y / z)));
	} else {
		tmp = x + (a * (y / (z + (-1.0 - t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.35d+129)) .or. (.not. (z <= 9d+73))) then
        tmp = x - (a - (a * (y / z)))
    else
        tmp = x + (a * (y / (z + ((-1.0d0) - t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+129) || !(z <= 9e+73)) {
		tmp = x - (a - (a * (y / z)));
	} else {
		tmp = x + (a * (y / (z + (-1.0 - t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.35e+129) or not (z <= 9e+73):
		tmp = x - (a - (a * (y / z)))
	else:
		tmp = x + (a * (y / (z + (-1.0 - t))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.35e+129) || !(z <= 9e+73))
		tmp = Float64(x - Float64(a - Float64(a * Float64(y / z))));
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(z + Float64(-1.0 - t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.35e+129) || ~((z <= 9e+73)))
		tmp = x - (a - (a * (y / z)));
	else
		tmp = x + (a * (y / (z + (-1.0 - t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.35e+129], N[Not[LessEqual[z, 9e+73]], $MachinePrecision]], N[(x - N[(a - N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(y / N[(z + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e129 or 8.99999999999999969e73 < z

   1. Initial program 93.6%

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

   3. Taylor expanded in z around inf 84.5%

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

      1. associate-*r/ 84.5%

         \[\leadsto x - \frac{y - z}{\color{blue}{\frac{-1 \cdot z}{a}}} \]

      2. neg-mul-1 84.5%

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

   5. Simplified 84.5%

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

   6. Taylor expanded in y around 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. unsub-neg 76.7%

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

      3. associate-/l* 89.6%

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

   8. Simplified 89.6%

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

   if -1.35e129 < z < 8.99999999999999969e73

   1. Initial program 98.6%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 89.9%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+129} \lor \neg \left(z \leq 9 \cdot 10^{+73}\right):\\ \;\;\;\;x - \left(a - a \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{z + \left(-1 - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 90.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+48}:\\ \;\;\;\;x - \frac{y - z}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+97}:\\ \;\;\;\;x + \frac{a}{\frac{z + -1}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{z + \left(-1 - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.4e+48)
   (- x (/ (- y z) (/ t a)))
   (if (<= t 4.8e+97)
     (+ x (/ a (/ (+ z -1.0) (- y z))))
     (+ x (* a (/ y (+ z (- -1.0 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.4e+48) {
		tmp = x - ((y - z) / (t / a));
	} else if (t <= 4.8e+97) {
		tmp = x + (a / ((z + -1.0) / (y - z)));
	} else {
		tmp = x + (a * (y / (z + (-1.0 - t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-9.4d+48)) then
        tmp = x - ((y - z) / (t / a))
    else if (t <= 4.8d+97) then
        tmp = x + (a / ((z + (-1.0d0)) / (y - z)))
    else
        tmp = x + (a * (y / (z + ((-1.0d0) - t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.4e+48) {
		tmp = x - ((y - z) / (t / a));
	} else if (t <= 4.8e+97) {
		tmp = x + (a / ((z + -1.0) / (y - z)));
	} else {
		tmp = x + (a * (y / (z + (-1.0 - t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.4e+48:
		tmp = x - ((y - z) / (t / a))
	elif t <= 4.8e+97:
		tmp = x + (a / ((z + -1.0) / (y - z)))
	else:
		tmp = x + (a * (y / (z + (-1.0 - t))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.4e+48)
		tmp = Float64(x - Float64(Float64(y - z) / Float64(t / a)));
	elseif (t <= 4.8e+97)
		tmp = Float64(x + Float64(a / Float64(Float64(z + -1.0) / Float64(y - z))));
	else
		tmp = Float64(x + Float64(a * Float64(y / Float64(z + Float64(-1.0 - t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.4e+48)
		tmp = x - ((y - z) / (t / a));
	elseif (t <= 4.8e+97)
		tmp = x + (a / ((z + -1.0) / (y - z)));
	else
		tmp = x + (a * (y / (z + (-1.0 - t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.4e+48], N[(x - N[(N[(y - z), $MachinePrecision] / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e+97], N[(x + N[(a / N[(N[(z + -1.0), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a * N[(y / N[(z + N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.40000000000000025e48

   1. Initial program 98.2%

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

   3. Taylor expanded in t around inf 85.9%

      \[\leadsto x - \frac{y - z}{\color{blue}{\frac{t}{a}}} \]

   if -9.40000000000000025e48 < t < 4.8e97

   1. Initial program 95.8%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 96.7%

      \[\leadsto x - \frac{a}{\color{blue}{\frac{1 - z}{y - z}}} \]

   if 4.8e97 < t

   1. Initial program 99.9%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 95.1%

      \[\leadsto x - \color{blue}{\frac{y}{\left(1 + t\right) - z}} \cdot a \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+48}:\\ \;\;\;\;x - \frac{y - z}{\frac{t}{a}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+97}:\\ \;\;\;\;x + \frac{a}{\frac{z + -1}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \frac{y}{z + \left(-1 - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -400000 \lor \neg \left(z \leq 1.9 \cdot 10^{-6}\right):\\ \;\;\;\;x - \left(a - a \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -400000.0) (not (<= z 1.9e-6)))
   (- x (- a (* a (/ y z))))
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -400000.0) || !(z <= 1.9e-6)) {
		tmp = x - (a - (a * (y / z)));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-400000.0d0)) .or. (.not. (z <= 1.9d-6))) then
        tmp = x - (a - (a * (y / z)))
    else
        tmp = x - (a * (y / (t + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -400000.0) || !(z <= 1.9e-6)) {
		tmp = x - (a - (a * (y / z)));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -400000.0) or not (z <= 1.9e-6):
		tmp = x - (a - (a * (y / z)))
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -400000.0) || !(z <= 1.9e-6))
		tmp = Float64(x - Float64(a - Float64(a * Float64(y / z))));
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -400000.0) || ~((z <= 1.9e-6)))
		tmp = x - (a - (a * (y / z)));
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -400000.0], N[Not[LessEqual[z, 1.9e-6]], $MachinePrecision]], N[(x - N[(a - N[(a * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4e5 or 1.9e-6 < z

   1. Initial program 94.2%

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

   3. Taylor expanded in z around inf 81.1%

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

      1. associate-*r/ 81.1%

         \[\leadsto x - \frac{y - z}{\color{blue}{\frac{-1 \cdot z}{a}}} \]

      2. neg-mul-1 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in y around 0 75.0%

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

      1. mul-1-neg 75.0%

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

      2. unsub-neg 75.0%

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

      3. associate-/l* 85.0%

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

   8. Simplified 85.0%

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

   if -4e5 < z < 1.9e-6

   1. Initial program 99.8%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 91.0%

      \[\leadsto x - \color{blue}{\frac{y}{1 + t}} \cdot a \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -400000 \lor \neg \left(z \leq 1.9 \cdot 10^{-6}\right):\\ \;\;\;\;x - \left(a - a \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -110000 \lor \neg \left(z \leq 1.14 \cdot 10^{-7}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -110000.0) (not (<= z 1.14e-7))) (- x a) (- x (* y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -110000.0) || !(z <= 1.14e-7)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-110000.0d0)) .or. (.not. (z <= 1.14d-7))) then
        tmp = x - a
    else
        tmp = x - (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -110000.0) || !(z <= 1.14e-7)) {
		tmp = x - a;
	} else {
		tmp = x - (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -110000.0) or not (z <= 1.14e-7):
		tmp = x - a
	else:
		tmp = x - (y * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -110000.0) || !(z <= 1.14e-7))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -110000.0) || ~((z <= 1.14e-7)))
		tmp = x - a;
	else
		tmp = x - (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -110000.0], N[Not[LessEqual[z, 1.14e-7]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e5 or 1.14000000000000002e-7 < z

   1. Initial program 94.2%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 75.4%

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

   if -1.1e5 < z < 1.14000000000000002e-7

   1. Initial program 99.8%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 76.3%

      \[\leadsto x - \frac{a}{\color{blue}{\frac{1 - z}{y - z}}} \]

   8. Taylor expanded in z around 0 70.0%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -110000 \lor \neg \left(z \leq 1.14 \cdot 10^{-7}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -54 \lor \neg \left(z \leq 7 \cdot 10^{-36}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -54.0) (not (<= z 7e-36))) (- x a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -54.0) || !(z <= 7e-36)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-54.0d0)) .or. (.not. (z <= 7d-36))) then
        tmp = x - a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -54.0) || !(z <= 7e-36)) {
		tmp = x - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -54.0) or not (z <= 7e-36):
		tmp = x - a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -54.0) || !(z <= 7e-36))
		tmp = Float64(x - a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -54.0) || ~((z <= 7e-36)))
		tmp = x - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -54.0], N[Not[LessEqual[z, 7e-36]], $MachinePrecision]], N[(x - a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -54 or 6.9999999999999999e-36 < z

   1. Initial program 94.4%

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

      1. associate-/r/ 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 73.6%

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

   if -54 < z < 6.9999999999999999e-36

   1. Initial program 99.8%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 56.2%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -54 \lor \neg \left(z \leq 7 \cdot 10^{-36}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-205}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.75e-32) x (if (<= x 5.2e-205) (- a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.75e-32) {
		tmp = x;
	} else if (x <= 5.2e-205) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.75d-32)) then
        tmp = x
    else if (x <= 5.2d-205) then
        tmp = -a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.75e-32) {
		tmp = x;
	} else if (x <= 5.2e-205) {
		tmp = -a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.75e-32:
		tmp = x
	elif x <= 5.2e-205:
		tmp = -a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.75e-32)
		tmp = x;
	elseif (x <= 5.2e-205)
		tmp = Float64(-a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.75e-32)
		tmp = x;
	elseif (x <= 5.2e-205)
		tmp = -a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.75e-32], x, If[LessEqual[x, 5.2e-205], (-a), x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7499999999999999e-32 or 5.1999999999999997e-205 < x

   1. Initial program 99.3%

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

      1. associate-/r/ 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 67.5%

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

   if -1.7499999999999999e-32 < x < 5.1999999999999997e-205

   1. Initial program 91.7%

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

   3. Taylor expanded in z around inf 41.9%

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

      1. associate-*r/ 41.9%

         \[\leadsto x - \frac{y - z}{\color{blue}{\frac{-1 \cdot z}{a}}} \]

      2. neg-mul-1 41.9%

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

   5. Simplified 41.9%

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

   6. Taylor expanded in x around 0 27.3%

      \[\leadsto \color{blue}{\frac{a \cdot \left(y - z\right)}{z}} \]
   7. Step-by-step derivation

      1. associate-/l* 39.8%

         \[\leadsto \color{blue}{a \cdot \frac{y - z}{z}} \]

   8. Simplified 39.8%

      \[\leadsto \color{blue}{a \cdot \frac{y - z}{z}} \]

   9. Taylor expanded in y around 0 30.6%

      \[\leadsto \color{blue}{-1 \cdot a} \]
   10. Step-by-step derivation

       1. mul-1-neg 30.6%

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

   11. Simplified 30.6%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-205}:\\ \;\;\;\;-a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 97.0%

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

   1. associate-/r/ 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{x - \frac{y - z}{\left(t - z\right) + 1} \cdot a} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 52.4%

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

6. Final simplification 52.4%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024130 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :alt
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))