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

Percentage Accurate: 97.1% → 99.6%

Time: 10.7s

Alternatives: 11

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: 97.1% 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: 99.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. sub-neg 98.0%

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

   2. +-commutative 98.0%

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

   3. associate-/r/ 99.6%

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

   4. *-commutative 99.6%

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

   5. distribute-rgt-neg-in 99.6%

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

   6. fma-def 99.6%

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

   7. div-sub 99.6%

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

   8. sub-neg 99.6%

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

   9. +-commutative 99.6%

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

   10. distribute-neg-in 99.6%

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

   11. remove-double-neg 99.6%

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

   12. sub-neg 99.6%

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

   13. div-sub 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 87.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.3 \cdot 10^{+43} \lor \neg \left(z \leq 2.05 \cdot 10^{+72}\right):\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.3e+43) (not (<= z 2.05e+72)))
   (+ x (* a (/ z (+ (- t z) 1.0))))
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.3e+43) || !(z <= 2.05e+72)) {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	} 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 <= (-8.3d+43)) .or. (.not. (z <= 2.05d+72))) then
        tmp = x + (a * (z / ((t - z) + 1.0d0)))
    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 <= -8.3e+43) || !(z <= 2.05e+72)) {
		tmp = x + (a * (z / ((t - z) + 1.0)));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.3e+43) or not (z <= 2.05e+72):
		tmp = x + (a * (z / ((t - z) + 1.0)))
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.3e+43) || !(z <= 2.05e+72))
		tmp = Float64(x + Float64(a * Float64(z / Float64(Float64(t - z) + 1.0))));
	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 <= -8.3e+43) || ~((z <= 2.05e+72)))
		tmp = x + (a * (z / ((t - z) + 1.0)));
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.3e+43], N[Not[LessEqual[z, 2.05e+72]], $MachinePrecision]], N[(x + N[(a * N[(z / N[(N[(t - z), $MachinePrecision] + 1.0), $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 < -8.29999999999999958e43 or 2.04999999999999982e72 < z

   1. Initial program 95.0%

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

      1. sub-neg 95.0%

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

      2. +-commutative 95.0%

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

      3. associate-/r/ 99.9%

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

      4. *-commutative 99.9%

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

      5. distribute-rgt-neg-in 99.9%

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

      6. fma-def 99.9%

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

      7. div-sub 99.9%

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

      8. sub-neg 99.9%

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

      9. +-commutative 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. remove-double-neg 99.9%

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

      12. sub-neg 99.9%

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

      13. div-sub 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 68.7%

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

      1. expm1-log1p-u 64.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a \cdot z}{\left(1 + t\right) - z}\right)\right)} + x \]

      2. expm1-udef 52.8%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{a \cdot z}{\left(1 + t\right) - z}\right)} - 1\right)} + x \]

      3. associate-/l* 63.4%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{a}{\frac{\left(1 + t\right) - z}{z}}}\right)} - 1\right) + x \]

      4. associate--l+ 63.4%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\frac{a}{\frac{\color{blue}{1 + \left(t - z\right)}}{z}}\right)} - 1\right) + x \]

   6. Applied egg-rr 63.4%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{a}{\frac{1 + \left(t - z\right)}{z}}\right)} - 1\right)} + x \]
   7. Step-by-step derivation

      1. expm1-def 75.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a}{\frac{1 + \left(t - z\right)}{z}}\right)\right)} + x \]

      2. expm1-log1p 90.1%

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

      3. associate-/r/ 86.3%

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

      4. *-commutative 86.3%

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

      5. associate-*r/ 68.7%

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

      6. *-commutative 68.7%

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

      7. associate-*r/ 90.0%

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

   8. Simplified 90.0%

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

   if -8.29999999999999958e43 < z < 2.04999999999999982e72

   1. Initial program 99.9%

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

      1. associate-/r/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around 0 91.7%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.3 \cdot 10^{+43} \lor \neg \left(z \leq 2.05 \cdot 10^{+72}\right):\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]

Alternative 3: 89.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - z\right) + 1\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+61} \lor \neg \left(z \leq 1.6 \cdot 10^{+94}\right):\\ \;\;\;\;x + a \cdot \frac{z}{t_1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t_1}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (- t z) 1.0)))
   (if (or (<= z -3.2e+61) (not (<= z 1.6e+94)))
     (+ x (* a (/ z t_1)))
     (- x (/ y (/ t_1 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) + 1.0;
	double tmp;
	if ((z <= -3.2e+61) || !(z <= 1.6e+94)) {
		tmp = x + (a * (z / t_1));
	} else {
		tmp = x - (y / (t_1 / 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) :: t_1
    real(8) :: tmp
    t_1 = (t - z) + 1.0d0
    if ((z <= (-3.2d+61)) .or. (.not. (z <= 1.6d+94))) then
        tmp = x + (a * (z / t_1))
    else
        tmp = x - (y / (t_1 / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) + 1.0;
	double tmp;
	if ((z <= -3.2e+61) || !(z <= 1.6e+94)) {
		tmp = x + (a * (z / t_1));
	} else {
		tmp = x - (y / (t_1 / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - z) + 1.0
	tmp = 0
	if (z <= -3.2e+61) or not (z <= 1.6e+94):
		tmp = x + (a * (z / t_1))
	else:
		tmp = x - (y / (t_1 / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) + 1.0)
	tmp = 0.0
	if ((z <= -3.2e+61) || !(z <= 1.6e+94))
		tmp = Float64(x + Float64(a * Float64(z / t_1)));
	else
		tmp = Float64(x - Float64(y / Float64(t_1 / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - z) + 1.0;
	tmp = 0.0;
	if ((z <= -3.2e+61) || ~((z <= 1.6e+94)))
		tmp = x + (a * (z / t_1));
	else
		tmp = x - (y / (t_1 / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision]}, If[Or[LessEqual[z, -3.2e+61], N[Not[LessEqual[z, 1.6e+94]], $MachinePrecision]], N[(x + N[(a * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1999999999999998e61 or 1.60000000000000007e94 < z

   1. Initial program 94.6%

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

      1. sub-neg 94.6%

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

      2. +-commutative 94.6%

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

      3. associate-/r/ 99.9%

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

      4. *-commutative 99.9%

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

      5. distribute-rgt-neg-in 99.9%

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

      6. fma-def 99.9%

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

      7. div-sub 99.9%

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

      8. sub-neg 99.9%

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

      9. +-commutative 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. remove-double-neg 99.9%

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

      12. sub-neg 99.9%

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

      13. div-sub 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 69.2%

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

      1. expm1-log1p-u 64.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a \cdot z}{\left(1 + t\right) - z}\right)\right)} + x \]

      2. expm1-udef 54.1%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{a \cdot z}{\left(1 + t\right) - z}\right)} - 1\right)} + x \]

      3. associate-/l* 65.6%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\frac{a}{\frac{\left(1 + t\right) - z}{z}}}\right)} - 1\right) + x \]

      4. associate--l+ 65.6%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\frac{a}{\frac{\color{blue}{1 + \left(t - z\right)}}{z}}\right)} - 1\right) + x \]

   6. Applied egg-rr 65.6%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{a}{\frac{1 + \left(t - z\right)}{z}}\right)} - 1\right)} + x \]
   7. Step-by-step derivation

      1. expm1-def 76.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a}{\frac{1 + \left(t - z\right)}{z}}\right)\right)} + x \]

      2. expm1-log1p 92.5%

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

      3. associate-/r/ 88.4%

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

      4. *-commutative 88.4%

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

      5. associate-*r/ 69.2%

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

      6. *-commutative 69.2%

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

      7. associate-*r/ 92.5%

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

   8. Simplified 92.5%

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

   if -3.1999999999999998e61 < z < 1.60000000000000007e94

   1. Initial program 99.8%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+r- 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in y around inf 89.9%

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

      1. associate-+r- 89.9%

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

      2. associate-/l* 94.3%

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

   6. Simplified 94.3%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+61} \lor \neg \left(z \leq 1.6 \cdot 10^{+94}\right):\\ \;\;\;\;x + a \cdot \frac{z}{\left(t - z\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{\left(t - z\right) + 1}{a}}\\ \end{array} \]

Alternative 4: 87.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+20} \lor \neg \left(z \leq 3.1 \cdot 10^{+21}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.65e+20) (not (<= z 3.1e+21)))
   (+ x (/ (- z y) (/ (- z) a)))
   (- x (* a (/ y (+ t 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.65e+20) || !(z <= 3.1e+21)) {
		tmp = x + ((z - y) / (-z / a));
	} 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 <= (-2.65d+20)) .or. (.not. (z <= 3.1d+21))) then
        tmp = x + ((z - y) / (-z / a))
    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 <= -2.65e+20) || !(z <= 3.1e+21)) {
		tmp = x + ((z - y) / (-z / a));
	} else {
		tmp = x - (a * (y / (t + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.65e+20) or not (z <= 3.1e+21):
		tmp = x + ((z - y) / (-z / a))
	else:
		tmp = x - (a * (y / (t + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.65e+20) || !(z <= 3.1e+21))
		tmp = Float64(x + Float64(Float64(z - y) / Float64(Float64(-z) / a)));
	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 <= -2.65e+20) || ~((z <= 3.1e+21)))
		tmp = x + ((z - y) / (-z / a));
	else
		tmp = x - (a * (y / (t + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.65e+20], N[Not[LessEqual[z, 3.1e+21]], $MachinePrecision]], N[(x + N[(N[(z - y), $MachinePrecision] / N[((-z) / a), $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 < -2.65e20 or 3.1e21 < z

   1. Initial program 95.9%

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

   2. Taylor expanded in z around inf 80.9%

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

      1. mul-1-neg 80.9%

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

      2. distribute-neg-frac 80.9%

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

   4. Simplified 80.9%

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

   if -2.65e20 < z < 3.1e21

   1. Initial program 99.9%

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

      1. associate-/r/ 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 94.5%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+20} \lor \neg \left(z \leq 3.1 \cdot 10^{+21}\right):\\ \;\;\;\;x + \frac{z - y}{\frac{-z}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \end{array} \]

Alternative 5: 70.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+172}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.2e+172)
   (+ x (/ a (/ t z)))
   (if (<= t 1.6e+21) (+ x (/ a (/ (- 1.0 z) z))) (- x (/ a (/ t y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.2e+172) {
		tmp = x + (a / (t / z));
	} else if (t <= 1.6e+21) {
		tmp = x + (a / ((1.0 - z) / z));
	} else {
		tmp = x - (a / (t / y));
	}
	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 <= (-7.2d+172)) then
        tmp = x + (a / (t / z))
    else if (t <= 1.6d+21) then
        tmp = x + (a / ((1.0d0 - z) / z))
    else
        tmp = x - (a / (t / y))
    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 <= -7.2e+172) {
		tmp = x + (a / (t / z));
	} else if (t <= 1.6e+21) {
		tmp = x + (a / ((1.0 - z) / z));
	} else {
		tmp = x - (a / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.2e+172:
		tmp = x + (a / (t / z))
	elif t <= 1.6e+21:
		tmp = x + (a / ((1.0 - z) / z))
	else:
		tmp = x - (a / (t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.2e+172)
		tmp = Float64(x + Float64(a / Float64(t / z)));
	elseif (t <= 1.6e+21)
		tmp = Float64(x + Float64(a / Float64(Float64(1.0 - z) / z)));
	else
		tmp = Float64(x - Float64(a / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -7.2e+172)
		tmp = x + (a / (t / z));
	elseif (t <= 1.6e+21)
		tmp = x + (a / ((1.0 - z) / z));
	else
		tmp = x - (a / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.2e+172], N[(x + N[(a / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+21], N[(x + N[(a / N[(N[(1.0 - z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.1999999999999995e172

   1. Initial program 97.3%

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

      1. sub-neg 97.3%

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

      2. +-commutative 97.3%

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

      3. associate-/r/ 99.8%

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

      4. *-commutative 99.8%

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

      5. distribute-rgt-neg-in 99.8%

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

      6. fma-def 99.8%

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

      7. div-sub 99.8%

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

      8. sub-neg 99.8%

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

      9. +-commutative 99.8%

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

      10. distribute-neg-in 99.8%

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

      11. remove-double-neg 99.8%

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

      12. sub-neg 99.8%

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

      13. div-sub 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 89.0%

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

   5. Taylor expanded in t around inf 88.6%

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

      1. associate-/l* 88.8%

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

   7. Simplified 88.8%

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

   if -7.1999999999999995e172 < t < 1.6e21

   1. Initial program 98.1%

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

      1. sub-neg 98.1%

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

      2. +-commutative 98.1%

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

      3. associate-/r/ 99.9%

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

      4. *-commutative 99.9%

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

      5. distribute-rgt-neg-in 99.9%

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

      6. fma-def 99.9%

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

      7. div-sub 99.9%

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

      8. sub-neg 99.9%

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

      9. +-commutative 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. remove-double-neg 99.9%

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

      12. sub-neg 99.9%

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

      13. div-sub 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 59.8%

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

   5. Taylor expanded in t around 0 59.9%

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

      1. associate-/l* 69.5%

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

   7. Simplified 69.5%

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

   if 1.6e21 < t

   1. Initial program 98.4%

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

      1. associate-/r/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in t around inf 82.6%

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

   5. Taylor expanded in y around inf 81.0%

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

      1. *-commutative 81.0%

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

      2. associate-/l* 85.7%

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

   7. Simplified 85.7%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+172}:\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \end{array} \]

Alternative 6: 84.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+125}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+74}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e+125)
   (- x a)
   (if (<= z 2.8e+74) (- x (* a (/ y (+ t 1.0)))) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+125) {
		tmp = x - a;
	} else if (z <= 2.8e+74) {
		tmp = x - (a * (y / (t + 1.0)));
	} 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 <= (-4.5d+125)) then
        tmp = x - a
    else if (z <= 2.8d+74) then
        tmp = x - (a * (y / (t + 1.0d0)))
    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 <= -4.5e+125) {
		tmp = x - a;
	} else if (z <= 2.8e+74) {
		tmp = x - (a * (y / (t + 1.0)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e+125:
		tmp = x - a
	elif z <= 2.8e+74:
		tmp = x - (a * (y / (t + 1.0)))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+125)
		tmp = Float64(x - a);
	elseif (z <= 2.8e+74)
		tmp = Float64(x - Float64(a * Float64(y / Float64(t + 1.0))));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.5e+125)
		tmp = x - a;
	elseif (z <= 2.8e+74)
		tmp = x - (a * (y / (t + 1.0)));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e+125], N[(x - a), $MachinePrecision], If[LessEqual[z, 2.8e+74], N[(x - N[(a * N[(y / N[(t + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5e125 or 2.80000000000000002e74 < 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. Taylor expanded in z around inf 83.8%

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

   if -4.5e125 < z < 2.80000000000000002e74

   1. Initial program 99.8%

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

      1. associate-/r/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in z around 0 88.2%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+125}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+74}:\\ \;\;\;\;x - a \cdot \frac{y}{t + 1}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 7: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 * ((z - y) / ((t - z) + 1.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. associate-/r/ 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 8: 64.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+172} \lor \neg \left(t \leq 5.2 \cdot 10^{+103}\right):\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.3e+172) (not (<= t 5.2e+103))) (+ x (/ a (/ t z))) (- x a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.3e+172) || !(t <= 5.2e+103)) {
		tmp = x + (a / (t / z));
	} 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 ((t <= (-3.3d+172)) .or. (.not. (t <= 5.2d+103))) then
        tmp = x + (a / (t / z))
    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 ((t <= -3.3e+172) || !(t <= 5.2e+103)) {
		tmp = x + (a / (t / z));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.3e+172) or not (t <= 5.2e+103):
		tmp = x + (a / (t / z))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.3e+172) || !(t <= 5.2e+103))
		tmp = Float64(x + Float64(a / Float64(t / z)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.3e+172) || ~((t <= 5.2e+103)))
		tmp = x + (a / (t / z));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.3e+172], N[Not[LessEqual[t, 5.2e+103]], $MachinePrecision]], N[(x + N[(a / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.29999999999999983e172 or 5.2000000000000003e103 < t

   1. Initial program 97.7%

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

      1. sub-neg 97.7%

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

      2. +-commutative 97.7%

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

      3. associate-/r/ 99.0%

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

      4. *-commutative 99.0%

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

      5. distribute-rgt-neg-in 99.0%

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

      6. fma-def 99.0%

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

      7. div-sub 99.0%

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

      8. sub-neg 99.0%

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

      9. +-commutative 99.0%

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

      10. distribute-neg-in 99.0%

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

      11. remove-double-neg 99.0%

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

      12. sub-neg 99.0%

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

      13. div-sub 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in y around 0 79.0%

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

   5. Taylor expanded in t around inf 78.8%

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

      1. associate-/l* 80.1%

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

   7. Simplified 80.1%

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

   if -3.29999999999999983e172 < t < 5.2000000000000003e103

   1. Initial program 98.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 61.2%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+172} \lor \neg \left(t \leq 5.2 \cdot 10^{+103}\right):\\ \;\;\;\;x + \frac{a}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 9: 70.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+60}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+89}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.3e+60) (- x a) (if (<= z 4.6e+89) (- x (/ a (/ t y))) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.3e+60) {
		tmp = x - a;
	} else if (z <= 4.6e+89) {
		tmp = x - (a / (t / y));
	} 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 <= (-5.3d+60)) then
        tmp = x - a
    else if (z <= 4.6d+89) then
        tmp = x - (a / (t / y))
    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 <= -5.3e+60) {
		tmp = x - a;
	} else if (z <= 4.6e+89) {
		tmp = x - (a / (t / y));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.3e+60:
		tmp = x - a
	elif z <= 4.6e+89:
		tmp = x - (a / (t / y))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.3e+60)
		tmp = Float64(x - a);
	elseif (z <= 4.6e+89)
		tmp = Float64(x - Float64(a / Float64(t / y)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.3e+60)
		tmp = x - a;
	elseif (z <= 4.6e+89)
		tmp = x - (a / (t / y));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.3e+60], N[(x - a), $MachinePrecision], If[LessEqual[z, 4.6e+89], N[(x - N[(a / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2999999999999997e60 or 4.5999999999999998e89 < z

   1. Initial program 94.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 80.6%

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

   if -5.2999999999999997e60 < z < 4.5999999999999998e89

   1. Initial program 99.8%

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

      1. associate-/r/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in t around inf 65.6%

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

   5. Taylor expanded in y around inf 66.8%

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

      1. *-commutative 66.8%

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

      2. associate-/l* 68.6%

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

   7. Simplified 68.6%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+60}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+89}:\\ \;\;\;\;x - \frac{a}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 10: 65.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+57}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.2e+57) (- x a) (if (<= z 2.4e+27) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+57) {
		tmp = x - a;
	} else if (z <= 2.4e+27) {
		tmp = x;
	} 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 <= (-4.2d+57)) then
        tmp = x - a
    else if (z <= 2.4d+27) then
        tmp = x
    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 <= -4.2e+57) {
		tmp = x - a;
	} else if (z <= 2.4e+27) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.2e+57:
		tmp = x - a
	elif z <= 2.4e+27:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.2e+57)
		tmp = Float64(x - a);
	elseif (z <= 2.4e+27)
		tmp = x;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.2e+57)
		tmp = x - a;
	elseif (z <= 2.4e+27)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.2e+57], N[(x - a), $MachinePrecision], If[LessEqual[z, 2.4e+27], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999982e57 or 2.39999999999999998e27 < z

   1. Initial program 95.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. Taylor expanded in z around inf 78.6%

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

   if -4.19999999999999982e57 < z < 2.39999999999999998e27

   1. Initial program 99.8%

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

      1. associate-/r/ 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around inf 57.4%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+57}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]

Alternative 11: 53.4% 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 98.0%

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

   1. associate-/r/ 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in x around inf 56.4%

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

5. Final simplification 56.4%

   \[\leadsto x \]

Developer target: 99.6% 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 2023199 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

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

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