Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 68.0% → 89.3%

Time: 24.1s

Alternatives: 23

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{y - a}\\ t_2 := t + \frac{a}{\frac{z}{t - x}} \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+114}:\\ \;\;\;\;t_2 - {\left(\frac{t_1}{t - x}\right)}^{-1}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+140}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 + \frac{x - t}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (- y a))) (t_2 (+ t (* (/ a (/ z (- t x))) (/ (- a y) z)))))
   (if (<= z -4.5e+114)
     (- t_2 (pow (/ t_1 (- t x)) -1.0))
     (if (<= z 2.9e+140)
       (fma (/ (- y z) (- a z)) (- t x) x)
       (+ t_2 (/ (- x t) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (y - a);
	double t_2 = t + ((a / (z / (t - x))) * ((a - y) / z));
	double tmp;
	if (z <= -4.5e+114) {
		tmp = t_2 - pow((t_1 / (t - x)), -1.0);
	} else if (z <= 2.9e+140) {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	} else {
		tmp = t_2 + ((x - t) / t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(y - a))
	t_2 = Float64(t + Float64(Float64(a / Float64(z / Float64(t - x))) * Float64(Float64(a - y) / z)))
	tmp = 0.0
	if (z <= -4.5e+114)
		tmp = Float64(t_2 - (Float64(t_1 / Float64(t - x)) ^ -1.0));
	elseif (z <= 2.9e+140)
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	else
		tmp = Float64(t_2 + Float64(Float64(x - t) / t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+114], N[(t$95$2 - N[Power[N[(t$95$1 / N[(t - x), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+140], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], N[(t$95$2 + N[(N[(x - t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5000000000000001e114

   1. Initial program 33.5%

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

      1. associate-*l/ 65.8%

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

   3. Simplified 65.8%

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

   4. Taylor expanded in z around -inf 44.6%

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

      1. associate-+r+ 44.6%

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

      2. mul-1-neg 44.6%

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

      3. distribute-rgt-out-- 44.6%

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

      4. unsub-neg 44.6%

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

   6. Simplified 81.8%

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

      1. clear-num 81.8%

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

      2. inv-pow 81.8%

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

   8. Applied egg-rr 81.8%

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

   if -4.5000000000000001e114 < z < 2.8999999999999999e140

   1. Initial program 84.6%

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

      1. +-commutative 84.6%

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

      2. associate-*l/ 90.0%

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

      3. fma-def 90.0%

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

   3. Simplified 90.0%

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

   if 2.8999999999999999e140 < z

   1. Initial program 31.2%

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

      1. associate-*l/ 68.1%

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

   3. Simplified 68.1%

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

   4. Taylor expanded in z around -inf 53.6%

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

      1. associate-+r+ 53.6%

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

      2. mul-1-neg 53.6%

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

      3. distribute-rgt-out-- 53.6%

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

      4. unsub-neg 53.6%

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

   6. Simplified 96.3%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+114}:\\ \;\;\;\;\left(t + \frac{a}{\frac{z}{t - x}} \cdot \frac{a - y}{z}\right) - {\left(\frac{\frac{z}{y - a}}{t - x}\right)}^{-1}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+140}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + \frac{a}{\frac{z}{t - x}} \cdot \frac{a - y}{z}\right) + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]

Alternative 2: 89.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+117} \lor \neg \left(z \leq 1.5 \cdot 10^{+140}\right):\\ \;\;\;\;\left(t + \frac{a}{\frac{z}{t - x}} \cdot \frac{a - y}{z}\right) + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.4e+117) (not (<= z 1.5e+140)))
   (+ (+ t (* (/ a (/ z (- t x))) (/ (- a y) z))) (/ (- x t) (/ z (- y a))))
   (fma (/ (- y z) (- a z)) (- t x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.4e+117) || !(z <= 1.5e+140)) {
		tmp = (t + ((a / (z / (t - x))) * ((a - y) / z))) + ((x - t) / (z / (y - a)));
	} else {
		tmp = fma(((y - z) / (a - z)), (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.4e+117) || !(z <= 1.5e+140))
		tmp = Float64(Float64(t + Float64(Float64(a / Float64(z / Float64(t - x))) * Float64(Float64(a - y) / z))) + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.4e+117], N[Not[LessEqual[z, 1.5e+140]], $MachinePrecision]], N[(N[(t + N[(N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.39999999999999999e117 or 1.49999999999999998e140 < z

   1. Initial program 32.5%

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

      1. associate-*l/ 66.8%

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

   3. Simplified 66.8%

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

   4. Taylor expanded in z around -inf 48.6%

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

      1. associate-+r+ 48.6%

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

      2. mul-1-neg 48.6%

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

      3. distribute-rgt-out-- 48.6%

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

      4. unsub-neg 48.6%

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

   6. Simplified 88.1%

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

   if -1.39999999999999999e117 < z < 1.49999999999999998e140

   1. Initial program 84.6%

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

      1. +-commutative 84.6%

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

      2. associate-*l/ 90.0%

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

      3. fma-def 90.0%

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

   3. Simplified 90.0%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+117} \lor \neg \left(z \leq 1.5 \cdot 10^{+140}\right):\\ \;\;\;\;\left(t + \frac{a}{\frac{z}{t - x}} \cdot \frac{a - y}{z}\right) + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t - x, x\right)\\ \end{array} \]

Alternative 3: 89.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+117} \lor \neg \left(z \leq 1.55 \cdot 10^{+140}\right):\\ \;\;\;\;\left(t + \frac{a}{\frac{z}{t - x}} \cdot \frac{a - y}{z}\right) + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \left(\left(y - z\right) \cdot \frac{1}{a - z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.05e+117) (not (<= z 1.55e+140)))
   (+ (+ t (* (/ a (/ z (- t x))) (/ (- a y) z))) (/ (- x t) (/ z (- y a))))
   (+ x (* (- t x) (* (- y z) (/ 1.0 (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.05e+117) || !(z <= 1.55e+140)) {
		tmp = (t + ((a / (z / (t - x))) * ((a - y) / z))) + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) * ((y - z) * (1.0 / (a - 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) :: tmp
    if ((z <= (-2.05d+117)) .or. (.not. (z <= 1.55d+140))) then
        tmp = (t + ((a / (z / (t - x))) * ((a - y) / z))) + ((x - t) / (z / (y - a)))
    else
        tmp = x + ((t - x) * ((y - z) * (1.0d0 / (a - z))))
    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 <= -2.05e+117) || !(z <= 1.55e+140)) {
		tmp = (t + ((a / (z / (t - x))) * ((a - y) / z))) + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) * ((y - z) * (1.0 / (a - z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.05e+117) or not (z <= 1.55e+140):
		tmp = (t + ((a / (z / (t - x))) * ((a - y) / z))) + ((x - t) / (z / (y - a)))
	else:
		tmp = x + ((t - x) * ((y - z) * (1.0 / (a - z))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.05e+117) || !(z <= 1.55e+140))
		tmp = Float64(Float64(t + Float64(Float64(a / Float64(z / Float64(t - x))) * Float64(Float64(a - y) / z))) + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) * Float64(1.0 / Float64(a - z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.05e+117) || ~((z <= 1.55e+140)))
		tmp = (t + ((a / (z / (t - x))) * ((a - y) / z))) + ((x - t) / (z / (y - a)));
	else
		tmp = x + ((t - x) * ((y - z) * (1.0 / (a - z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.05e+117], N[Not[LessEqual[z, 1.55e+140]], $MachinePrecision]], N[(N[(t + N[(N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] * N[(1.0 / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.05e117 or 1.55e140 < z

   1. Initial program 32.5%

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

      1. associate-*l/ 66.8%

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

   3. Simplified 66.8%

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

   4. Taylor expanded in z around -inf 48.6%

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

      1. associate-+r+ 48.6%

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

      2. mul-1-neg 48.6%

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

      3. distribute-rgt-out-- 48.6%

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

      4. unsub-neg 48.6%

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

   6. Simplified 88.1%

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

   if -2.05e117 < z < 1.55e140

   1. Initial program 84.6%

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

      1. associate-*l/ 90.0%

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

   3. Simplified 90.0%

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

      1. clear-num 89.9%

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

      2. associate-/r/ 90.0%

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

   5. Applied egg-rr 90.0%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+117} \lor \neg \left(z \leq 1.55 \cdot 10^{+140}\right):\\ \;\;\;\;\left(t + \frac{a}{\frac{z}{t - x}} \cdot \frac{a - y}{z}\right) + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \left(\left(y - z\right) \cdot \frac{1}{a - z}\right)\\ \end{array} \]

Alternative 4: 45.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+88}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.05 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-239}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-297}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-7} \lor \neg \left(z \leq 3 \cdot 10^{+51}\right) \land z \leq 5.5 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= z -1.35e+88)
     t
     (if (<= z -3.05e-170)
       t_1
       (if (<= z -4.6e-239)
         (/ (* t y) a)
         (if (<= z -1.3e-297)
           t_1
           (if (<= z 4.9e-297)
             (/ t (/ a y))
             (if (or (<= z 1.7e-7) (and (not (<= z 3e+51)) (<= z 5.5e+141)))
               t_1
               t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (z <= -1.35e+88) {
		tmp = t;
	} else if (z <= -3.05e-170) {
		tmp = t_1;
	} else if (z <= -4.6e-239) {
		tmp = (t * y) / a;
	} else if (z <= -1.3e-297) {
		tmp = t_1;
	} else if (z <= 4.9e-297) {
		tmp = t / (a / y);
	} else if ((z <= 1.7e-7) || (!(z <= 3e+51) && (z <= 5.5e+141))) {
		tmp = t_1;
	} else {
		tmp = 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) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (z <= (-1.35d+88)) then
        tmp = t
    else if (z <= (-3.05d-170)) then
        tmp = t_1
    else if (z <= (-4.6d-239)) then
        tmp = (t * y) / a
    else if (z <= (-1.3d-297)) then
        tmp = t_1
    else if (z <= 4.9d-297) then
        tmp = t / (a / y)
    else if ((z <= 1.7d-7) .or. (.not. (z <= 3d+51)) .and. (z <= 5.5d+141)) then
        tmp = t_1
    else
        tmp = 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 * (1.0 - (y / a));
	double tmp;
	if (z <= -1.35e+88) {
		tmp = t;
	} else if (z <= -3.05e-170) {
		tmp = t_1;
	} else if (z <= -4.6e-239) {
		tmp = (t * y) / a;
	} else if (z <= -1.3e-297) {
		tmp = t_1;
	} else if (z <= 4.9e-297) {
		tmp = t / (a / y);
	} else if ((z <= 1.7e-7) || (!(z <= 3e+51) && (z <= 5.5e+141))) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if z <= -1.35e+88:
		tmp = t
	elif z <= -3.05e-170:
		tmp = t_1
	elif z <= -4.6e-239:
		tmp = (t * y) / a
	elif z <= -1.3e-297:
		tmp = t_1
	elif z <= 4.9e-297:
		tmp = t / (a / y)
	elif (z <= 1.7e-7) or (not (z <= 3e+51) and (z <= 5.5e+141)):
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (z <= -1.35e+88)
		tmp = t;
	elseif (z <= -3.05e-170)
		tmp = t_1;
	elseif (z <= -4.6e-239)
		tmp = Float64(Float64(t * y) / a);
	elseif (z <= -1.3e-297)
		tmp = t_1;
	elseif (z <= 4.9e-297)
		tmp = Float64(t / Float64(a / y));
	elseif ((z <= 1.7e-7) || (!(z <= 3e+51) && (z <= 5.5e+141)))
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (z <= -1.35e+88)
		tmp = t;
	elseif (z <= -3.05e-170)
		tmp = t_1;
	elseif (z <= -4.6e-239)
		tmp = (t * y) / a;
	elseif (z <= -1.3e-297)
		tmp = t_1;
	elseif (z <= 4.9e-297)
		tmp = t / (a / y);
	elseif ((z <= 1.7e-7) || (~((z <= 3e+51)) && (z <= 5.5e+141)))
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+88], t, If[LessEqual[z, -3.05e-170], t$95$1, If[LessEqual[z, -4.6e-239], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, -1.3e-297], t$95$1, If[LessEqual[z, 4.9e-297], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.7e-7], And[N[Not[LessEqual[z, 3e+51]], $MachinePrecision], LessEqual[z, 5.5e+141]]], t$95$1, t]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.35000000000000008e88 or 1.69999999999999987e-7 < z < 3e51 or 5.49999999999999967e141 < z

   1. Initial program 39.2%

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

      1. associate-*l/ 69.0%

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

   3. Simplified 69.0%

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

   4. Taylor expanded in z around inf 53.2%

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

   if -1.35000000000000008e88 < z < -3.05e-170 or -4.5999999999999998e-239 < z < -1.3e-297 or 4.89999999999999997e-297 < z < 1.69999999999999987e-7 or 3e51 < z < 5.49999999999999967e141

   1. Initial program 88.5%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in z around 0 71.3%

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

   5. Taylor expanded in x around inf 54.7%

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

      1. mul-1-neg 54.7%

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

      2. unsub-neg 54.7%

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

   7. Simplified 54.7%

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

   if -3.05e-170 < z < -4.5999999999999998e-239

   1. Initial program 84.0%

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

      1. associate-*l/ 77.2%

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

   3. Simplified 77.2%

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

   4. Taylor expanded in x around 0 55.9%

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

   5. Taylor expanded in z around 0 48.4%

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

   if -1.3e-297 < z < 4.89999999999999997e-297

   1. Initial program 80.9%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 80.9%

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

   5. Taylor expanded in z around 0 80.9%

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

      1. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+88}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.05 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-239}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-297}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-297}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-7} \lor \neg \left(z \leq 3 \cdot 10^{+51}\right) \land z \leq 5.5 \cdot 10^{+141}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 71.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{\frac{z}{t - x}}\\ t_2 := x - \frac{x - t}{\frac{a}{y - z}}\\ t_3 := x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -7.6 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -92000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 110:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ y (/ z (- t x)))))
        (t_2 (- x (/ (- x t) (/ a (- y z)))))
        (t_3 (+ x (* (- t x) (/ y a)))))
   (if (<= a -7.6e+14)
     t_2
     (if (<= a -92000.0)
       t_1
       (if (<= a -1.2e-56)
         t_3
         (if (<= a 5.1e-18)
           t_1
           (if (<= a 110.0)
             t_3
             (if (<= a 3.1e+125) (* t (/ (- y z) (- a z))) t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (y / (z / (t - x)));
	double t_2 = x - ((x - t) / (a / (y - z)));
	double t_3 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -7.6e+14) {
		tmp = t_2;
	} else if (a <= -92000.0) {
		tmp = t_1;
	} else if (a <= -1.2e-56) {
		tmp = t_3;
	} else if (a <= 5.1e-18) {
		tmp = t_1;
	} else if (a <= 110.0) {
		tmp = t_3;
	} else if (a <= 3.1e+125) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_2;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = t - (y / (z / (t - x)))
    t_2 = x - ((x - t) / (a / (y - z)))
    t_3 = x + ((t - x) * (y / a))
    if (a <= (-7.6d+14)) then
        tmp = t_2
    else if (a <= (-92000.0d0)) then
        tmp = t_1
    else if (a <= (-1.2d-56)) then
        tmp = t_3
    else if (a <= 5.1d-18) then
        tmp = t_1
    else if (a <= 110.0d0) then
        tmp = t_3
    else if (a <= 3.1d+125) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (y / (z / (t - x)));
	double t_2 = x - ((x - t) / (a / (y - z)));
	double t_3 = x + ((t - x) * (y / a));
	double tmp;
	if (a <= -7.6e+14) {
		tmp = t_2;
	} else if (a <= -92000.0) {
		tmp = t_1;
	} else if (a <= -1.2e-56) {
		tmp = t_3;
	} else if (a <= 5.1e-18) {
		tmp = t_1;
	} else if (a <= 110.0) {
		tmp = t_3;
	} else if (a <= 3.1e+125) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (y / (z / (t - x)))
	t_2 = x - ((x - t) / (a / (y - z)))
	t_3 = x + ((t - x) * (y / a))
	tmp = 0
	if a <= -7.6e+14:
		tmp = t_2
	elif a <= -92000.0:
		tmp = t_1
	elif a <= -1.2e-56:
		tmp = t_3
	elif a <= 5.1e-18:
		tmp = t_1
	elif a <= 110.0:
		tmp = t_3
	elif a <= 3.1e+125:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(y / Float64(z / Float64(t - x))))
	t_2 = Float64(x - Float64(Float64(x - t) / Float64(a / Float64(y - z))))
	t_3 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	tmp = 0.0
	if (a <= -7.6e+14)
		tmp = t_2;
	elseif (a <= -92000.0)
		tmp = t_1;
	elseif (a <= -1.2e-56)
		tmp = t_3;
	elseif (a <= 5.1e-18)
		tmp = t_1;
	elseif (a <= 110.0)
		tmp = t_3;
	elseif (a <= 3.1e+125)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (y / (z / (t - x)));
	t_2 = x - ((x - t) / (a / (y - z)));
	t_3 = x + ((t - x) * (y / a));
	tmp = 0.0;
	if (a <= -7.6e+14)
		tmp = t_2;
	elseif (a <= -92000.0)
		tmp = t_1;
	elseif (a <= -1.2e-56)
		tmp = t_3;
	elseif (a <= 5.1e-18)
		tmp = t_1;
	elseif (a <= 110.0)
		tmp = t_3;
	elseif (a <= 3.1e+125)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.6e+14], t$95$2, If[LessEqual[a, -92000.0], t$95$1, If[LessEqual[a, -1.2e-56], t$95$3, If[LessEqual[a, 5.1e-18], t$95$1, If[LessEqual[a, 110.0], t$95$3, If[LessEqual[a, 3.1e+125], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.6e14 or 3.1e125 < a

   1. Initial program 73.4%

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

      1. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in a around inf 67.7%

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

      1. associate-/l* 82.4%

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

   6. Simplified 82.4%

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

   if -7.6e14 < a < -92000 or -1.2e-56 < a < 5.09999999999999983e-18

   1. Initial program 69.8%

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

      1. associate-*l/ 75.9%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in z around -inf 62.1%

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

      1. associate-+r+ 62.1%

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

      2. mul-1-neg 62.1%

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

      3. distribute-rgt-out-- 62.1%

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

      4. unsub-neg 62.1%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in a around 0 76.9%

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

      1. associate-/l* 77.4%

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

   9. Simplified 77.4%

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

   if -92000 < a < -1.2e-56 or 5.09999999999999983e-18 < a < 110

   1. Initial program 87.5%

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

      1. associate-*l/ 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in z around 0 76.1%

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

   if 110 < a < 3.1e125

   1. Initial program 62.6%

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

      1. associate-*l/ 82.7%

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

   3. Simplified 82.7%

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

   4. Taylor expanded in x around 0 39.1%

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

      1. associate-*r/ 62.5%

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

   6. Simplified 62.5%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{+14}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq -92000:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-56}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-18}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 110:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y - z}}\\ \end{array} \]

Alternative 6: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ t_2 := x - \frac{x - t}{\frac{a}{y - z}}\\ \mathbf{if}\;a \leq -9 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 95:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z (- y a)))))
        (t_2 (- x (/ (- x t) (/ a (- y z))))))
   (if (<= a -9e+14)
     t_2
     (if (<= a 3.6e-16)
       t_1
       (if (<= a 95.0)
         (+ x (* (- t x) (/ y a)))
         (if (<= a 3.1e+125) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double t_2 = x - ((x - t) / (a / (y - z)));
	double tmp;
	if (a <= -9e+14) {
		tmp = t_2;
	} else if (a <= 3.6e-16) {
		tmp = t_1;
	} else if (a <= 95.0) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 3.1e+125) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = t + ((x - t) / (z / (y - a)))
    t_2 = x - ((x - t) / (a / (y - z)))
    if (a <= (-9d+14)) then
        tmp = t_2
    else if (a <= 3.6d-16) then
        tmp = t_1
    else if (a <= 95.0d0) then
        tmp = x + ((t - x) * (y / a))
    else if (a <= 3.1d+125) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double t_2 = x - ((x - t) / (a / (y - z)));
	double tmp;
	if (a <= -9e+14) {
		tmp = t_2;
	} else if (a <= 3.6e-16) {
		tmp = t_1;
	} else if (a <= 95.0) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 3.1e+125) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / (y - a)))
	t_2 = x - ((x - t) / (a / (y - z)))
	tmp = 0
	if a <= -9e+14:
		tmp = t_2
	elif a <= 3.6e-16:
		tmp = t_1
	elif a <= 95.0:
		tmp = x + ((t - x) * (y / a))
	elif a <= 3.1e+125:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))))
	t_2 = Float64(x - Float64(Float64(x - t) / Float64(a / Float64(y - z))))
	tmp = 0.0
	if (a <= -9e+14)
		tmp = t_2;
	elseif (a <= 3.6e-16)
		tmp = t_1;
	elseif (a <= 95.0)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (a <= 3.1e+125)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) / (z / (y - a)));
	t_2 = x - ((x - t) / (a / (y - z)));
	tmp = 0.0;
	if (a <= -9e+14)
		tmp = t_2;
	elseif (a <= 3.6e-16)
		tmp = t_1;
	elseif (a <= 95.0)
		tmp = x + ((t - x) * (y / a));
	elseif (a <= 3.1e+125)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9e+14], t$95$2, If[LessEqual[a, 3.6e-16], t$95$1, If[LessEqual[a, 95.0], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e+125], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9e14 or 3.1e125 < a

   1. Initial program 73.4%

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

      1. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in a around inf 67.7%

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

      1. associate-/l* 82.4%

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

   6. Simplified 82.4%

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

   if -9e14 < a < 3.59999999999999983e-16 or 95 < a < 3.1e125

   1. Initial program 69.4%

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

      1. associate-*l/ 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in z around inf 70.7%

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

      1. associate--l+ 70.7%

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

      2. associate-*r/ 70.7%

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

      3. associate-*r/ 70.7%

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

      4. div-sub 72.1%

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

      5. distribute-lft-out-- 72.1%

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

      6. mul-1-neg 72.1%

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

      7. distribute-neg-frac 72.1%

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

      8. distribute-rgt-out-- 72.1%

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

      9. unsub-neg 72.1%

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

      10. associate-/l* 78.9%

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

   6. Simplified 78.9%

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

   if 3.59999999999999983e-16 < a < 95

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+14}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y - z}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-16}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 95:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+125}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y - z}}\\ \end{array} \]

Alternative 7: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{if}\;a \leq -8.2 \cdot 10^{+14}:\\ \;\;\;\;x - \left(t - x\right) \cdot \left(\left(y - z\right) \cdot \frac{-1}{a}\right)\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 16:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- x t) (/ z (- y a))))))
   (if (<= a -8.2e+14)
     (- x (* (- t x) (* (- y z) (/ -1.0 a))))
     (if (<= a 6.6e-18)
       t_1
       (if (<= a 16.0)
         (+ x (* (- t x) (/ y a)))
         (if (<= a 3.1e+125) t_1 (- x (/ (- x t) (/ a (- y z))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (a <= -8.2e+14) {
		tmp = x - ((t - x) * ((y - z) * (-1.0 / a)));
	} else if (a <= 6.6e-18) {
		tmp = t_1;
	} else if (a <= 16.0) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 3.1e+125) {
		tmp = t_1;
	} else {
		tmp = x - ((x - t) / (a / (y - 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 = t + ((x - t) / (z / (y - a)))
    if (a <= (-8.2d+14)) then
        tmp = x - ((t - x) * ((y - z) * ((-1.0d0) / a)))
    else if (a <= 6.6d-18) then
        tmp = t_1
    else if (a <= 16.0d0) then
        tmp = x + ((t - x) * (y / a))
    else if (a <= 3.1d+125) then
        tmp = t_1
    else
        tmp = x - ((x - t) / (a / (y - 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 = t + ((x - t) / (z / (y - a)));
	double tmp;
	if (a <= -8.2e+14) {
		tmp = x - ((t - x) * ((y - z) * (-1.0 / a)));
	} else if (a <= 6.6e-18) {
		tmp = t_1;
	} else if (a <= 16.0) {
		tmp = x + ((t - x) * (y / a));
	} else if (a <= 3.1e+125) {
		tmp = t_1;
	} else {
		tmp = x - ((x - t) / (a / (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((x - t) / (z / (y - a)))
	tmp = 0
	if a <= -8.2e+14:
		tmp = x - ((t - x) * ((y - z) * (-1.0 / a)))
	elif a <= 6.6e-18:
		tmp = t_1
	elif a <= 16.0:
		tmp = x + ((t - x) * (y / a))
	elif a <= 3.1e+125:
		tmp = t_1
	else:
		tmp = x - ((x - t) / (a / (y - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))))
	tmp = 0.0
	if (a <= -8.2e+14)
		tmp = Float64(x - Float64(Float64(t - x) * Float64(Float64(y - z) * Float64(-1.0 / a))));
	elseif (a <= 6.6e-18)
		tmp = t_1;
	elseif (a <= 16.0)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (a <= 3.1e+125)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(x - t) / Float64(a / Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((x - t) / (z / (y - a)));
	tmp = 0.0;
	if (a <= -8.2e+14)
		tmp = x - ((t - x) * ((y - z) * (-1.0 / a)));
	elseif (a <= 6.6e-18)
		tmp = t_1;
	elseif (a <= 16.0)
		tmp = x + ((t - x) * (y / a));
	elseif (a <= 3.1e+125)
		tmp = t_1;
	else
		tmp = x - ((x - t) / (a / (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.2e+14], N[(x - N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.6e-18], t$95$1, If[LessEqual[a, 16.0], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e+125], t$95$1, N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.2e14

   1. Initial program 72.3%

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

      1. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

      1. clear-num 90.5%

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

      2. associate-/r/ 90.6%

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

   5. Applied egg-rr 90.6%

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

   6. Taylor expanded in a around inf 79.5%

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

   if -8.2e14 < a < 6.6000000000000003e-18 or 16 < a < 3.1e125

   1. Initial program 69.4%

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

      1. associate-*l/ 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in z around inf 70.7%

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

      1. associate--l+ 70.7%

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

      2. associate-*r/ 70.7%

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

      3. associate-*r/ 70.7%

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

      4. div-sub 72.1%

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

      5. distribute-lft-out-- 72.1%

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

      6. mul-1-neg 72.1%

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

      7. distribute-neg-frac 72.1%

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

      8. distribute-rgt-out-- 72.1%

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

      9. unsub-neg 72.1%

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

      10. associate-/l* 78.9%

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

   6. Simplified 78.9%

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

   if 6.6000000000000003e-18 < a < 16

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

   if 3.1e125 < a

   1. Initial program 74.7%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in a around inf 67.9%

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

      1. associate-/l* 86.2%

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

   6. Simplified 86.2%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+14}:\\ \;\;\;\;x - \left(t - x\right) \cdot \left(\left(y - z\right) \cdot \frac{-1}{a}\right)\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-18}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;a \leq 16:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+125}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y - z}}\\ \end{array} \]

Alternative 8: 89.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+115} \lor \neg \left(z \leq 6.2 \cdot 10^{+140}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \left(\left(y - z\right) \cdot \frac{1}{a - z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.4e+115) (not (<= z 6.2e+140)))
   (+ t (/ (- x t) (/ z (- y a))))
   (+ x (* (- t x) (* (- y z) (/ 1.0 (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.4e+115) || !(z <= 6.2e+140)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) * ((y - z) * (1.0 / (a - 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) :: tmp
    if ((z <= (-1.4d+115)) .or. (.not. (z <= 6.2d+140))) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = x + ((t - x) * ((y - z) * (1.0d0 / (a - z))))
    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 <= -1.4e+115) || !(z <= 6.2e+140)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((t - x) * ((y - z) * (1.0 / (a - z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.4e+115) or not (z <= 6.2e+140):
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = x + ((t - x) * ((y - z) * (1.0 / (a - z))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.4e+115) || !(z <= 6.2e+140))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(Float64(y - z) * Float64(1.0 / Float64(a - z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.4e+115) || ~((z <= 6.2e+140)))
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = x + ((t - x) * ((y - z) * (1.0 / (a - z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.4e+115], N[Not[LessEqual[z, 6.2e+140]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] * N[(1.0 / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e115 or 6.2000000000000001e140 < z

   1. Initial program 32.5%

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

      1. associate-*l/ 66.8%

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

   3. Simplified 66.8%

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

   4. Taylor expanded in z around inf 62.3%

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

      1. associate--l+ 62.3%

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

      2. associate-*r/ 62.3%

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

      3. associate-*r/ 62.3%

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

      4. div-sub 62.3%

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

      5. distribute-lft-out-- 62.3%

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

      6. mul-1-neg 62.3%

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

      7. distribute-neg-frac 62.3%

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

      8. distribute-rgt-out-- 62.3%

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

      9. unsub-neg 62.3%

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

      10. associate-/l* 87.5%

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

   6. Simplified 87.5%

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

   if -1.4e115 < z < 6.2000000000000001e140

   1. Initial program 84.6%

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

      1. associate-*l/ 90.0%

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

   3. Simplified 90.0%

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

      1. clear-num 89.9%

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

      2. associate-/r/ 90.0%

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

   5. Applied egg-rr 90.0%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+115} \lor \neg \left(z \leq 6.2 \cdot 10^{+140}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \left(\left(y - z\right) \cdot \frac{1}{a - z}\right)\\ \end{array} \]

Alternative 9: 58.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-235}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-181}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-69}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -8.2e-144)
     t_1
     (if (<= t 8.2e-235)
       (- x (/ x (/ a y)))
       (if (<= t 1.15e-181)
         (/ (- x) (/ (- a z) y))
         (if (<= t 5e-69) (- x (/ (* x y) a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -8.2e-144) {
		tmp = t_1;
	} else if (t <= 8.2e-235) {
		tmp = x - (x / (a / y));
	} else if (t <= 1.15e-181) {
		tmp = -x / ((a - z) / y);
	} else if (t <= 5e-69) {
		tmp = x - ((x * y) / a);
	} else {
		tmp = t_1;
	}
	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 * ((y - z) / (a - z))
    if (t <= (-8.2d-144)) then
        tmp = t_1
    else if (t <= 8.2d-235) then
        tmp = x - (x / (a / y))
    else if (t <= 1.15d-181) then
        tmp = -x / ((a - z) / y)
    else if (t <= 5d-69) then
        tmp = x - ((x * y) / a)
    else
        tmp = t_1
    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 * ((y - z) / (a - z));
	double tmp;
	if (t <= -8.2e-144) {
		tmp = t_1;
	} else if (t <= 8.2e-235) {
		tmp = x - (x / (a / y));
	} else if (t <= 1.15e-181) {
		tmp = -x / ((a - z) / y);
	} else if (t <= 5e-69) {
		tmp = x - ((x * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -8.2e-144:
		tmp = t_1
	elif t <= 8.2e-235:
		tmp = x - (x / (a / y))
	elif t <= 1.15e-181:
		tmp = -x / ((a - z) / y)
	elif t <= 5e-69:
		tmp = x - ((x * y) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -8.2e-144)
		tmp = t_1;
	elseif (t <= 8.2e-235)
		tmp = Float64(x - Float64(x / Float64(a / y)));
	elseif (t <= 1.15e-181)
		tmp = Float64(Float64(-x) / Float64(Float64(a - z) / y));
	elseif (t <= 5e-69)
		tmp = Float64(x - Float64(Float64(x * y) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -8.2e-144)
		tmp = t_1;
	elseif (t <= 8.2e-235)
		tmp = x - (x / (a / y));
	elseif (t <= 1.15e-181)
		tmp = -x / ((a - z) / y);
	elseif (t <= 5e-69)
		tmp = x - ((x * y) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.2e-144], t$95$1, If[LessEqual[t, 8.2e-235], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-181], N[((-x) / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e-69], N[(x - N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.2e-144 or 5.00000000000000033e-69 < t

   1. Initial program 72.3%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in x around 0 50.7%

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

      1. associate-*r/ 64.8%

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

   6. Simplified 64.8%

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

   if -8.2e-144 < t < 8.19999999999999993e-235

   1. Initial program 71.8%

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

      1. associate-*l/ 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in z around 0 59.2%

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

   5. Taylor expanded in t around 0 57.6%

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

      1. mul-1-neg 57.6%

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

      2. unsub-neg 57.6%

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

      3. associate-/l* 59.1%

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

   7. Simplified 59.1%

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

   if 8.19999999999999993e-235 < t < 1.14999999999999995e-181

   1. Initial program 67.4%

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

      1. associate-*l/ 67.6%

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

   3. Simplified 67.6%

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

   4. Taylor expanded in y around -inf 70.2%

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

   5. Taylor expanded in t around 0 70.2%

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

      1. mul-1-neg 70.2%

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

      2. associate-/l* 70.7%

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

      3. distribute-neg-frac 70.7%

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

   7. Simplified 70.7%

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

   if 1.14999999999999995e-181 < t < 5.00000000000000033e-69

   1. Initial program 67.3%

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

      1. associate-*l/ 58.3%

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

   3. Simplified 58.3%

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

   4. Taylor expanded in z around 0 41.9%

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

   5. Taylor expanded in t around 0 40.3%

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

      1. associate-*r/ 40.3%

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

      2. *-commutative 40.3%

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

      3. associate-*r* 40.3%

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

      4. neg-mul-1 40.3%

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

   7. Simplified 40.3%

      \[\leadsto x + \color{blue}{\frac{\left(-y\right) \cdot x}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-144}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-235}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-181}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-69}:\\ \;\;\;\;x - \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 10: 89.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+117} \lor \neg \left(z \leq 7.4 \cdot 10^{+170}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.85e+117) (not (<= z 7.4e+170)))
   (+ t (/ (- x t) (/ z (- y a))))
   (- x (* (- t x) (/ (- z y) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.85e+117) || !(z <= 7.4e+170)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x - ((t - x) * ((z - y) / (a - 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) :: tmp
    if ((z <= (-2.85d+117)) .or. (.not. (z <= 7.4d+170))) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = x - ((t - x) * ((z - y) / (a - z)))
    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 <= -2.85e+117) || !(z <= 7.4e+170)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x - ((t - x) * ((z - y) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.85e+117) or not (z <= 7.4e+170):
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = x - ((t - x) * ((z - y) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.85e+117) || !(z <= 7.4e+170))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x - Float64(Float64(t - x) * Float64(Float64(z - y) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.85e+117) || ~((z <= 7.4e+170)))
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = x - ((t - x) * ((z - y) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.85e+117], N[Not[LessEqual[z, 7.4e+170]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.85000000000000012e117 or 7.39999999999999975e170 < z

   1. Initial program 32.3%

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

      1. associate-*l/ 66.3%

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

   3. Simplified 66.3%

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

   4. Taylor expanded in z around inf 61.5%

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

      1. associate--l+ 61.5%

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

      2. associate-*r/ 61.5%

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

      3. associate-*r/ 61.5%

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

      4. div-sub 61.5%

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

      5. distribute-lft-out-- 61.5%

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

      6. mul-1-neg 61.5%

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

      7. distribute-neg-frac 61.5%

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

      8. distribute-rgt-out-- 61.5%

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

      9. unsub-neg 61.5%

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

      10. associate-/l* 88.8%

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

   6. Simplified 88.8%

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

   if -2.85000000000000012e117 < z < 7.39999999999999975e170

   1. Initial program 83.3%

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

      1. associate-*l/ 89.6%

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

   3. Simplified 89.6%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+117} \lor \neg \left(z \leq 7.4 \cdot 10^{+170}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(t - x\right) \cdot \frac{z - y}{a - z}\\ \end{array} \]

Alternative 11: 54.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(\frac{z}{a - z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))))
   (if (<= y -2.4e-75)
     t_1
     (if (<= y 6.8e-82)
       (* t (/ (- y z) (- a z)))
       (if (<= y 8e+74) (* x (+ (/ z (- a z)) 1.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -2.4e-75) {
		tmp = t_1;
	} else if (y <= 6.8e-82) {
		tmp = t * ((y - z) / (a - z));
	} else if (y <= 8e+74) {
		tmp = x * ((z / (a - z)) + 1.0);
	} else {
		tmp = t_1;
	}
	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 = y * ((t - x) / (a - z))
    if (y <= (-2.4d-75)) then
        tmp = t_1
    else if (y <= 6.8d-82) then
        tmp = t * ((y - z) / (a - z))
    else if (y <= 8d+74) then
        tmp = x * ((z / (a - z)) + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double tmp;
	if (y <= -2.4e-75) {
		tmp = t_1;
	} else if (y <= 6.8e-82) {
		tmp = t * ((y - z) / (a - z));
	} else if (y <= 8e+74) {
		tmp = x * ((z / (a - z)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	tmp = 0
	if y <= -2.4e-75:
		tmp = t_1
	elif y <= 6.8e-82:
		tmp = t * ((y - z) / (a - z))
	elif y <= 8e+74:
		tmp = x * ((z / (a - z)) + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	tmp = 0.0
	if (y <= -2.4e-75)
		tmp = t_1;
	elseif (y <= 6.8e-82)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (y <= 8e+74)
		tmp = Float64(x * Float64(Float64(z / Float64(a - z)) + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	tmp = 0.0;
	if (y <= -2.4e-75)
		tmp = t_1;
	elseif (y <= 6.8e-82)
		tmp = t * ((y - z) / (a - z));
	elseif (y <= 8e+74)
		tmp = x * ((z / (a - z)) + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e-75], t$95$1, If[LessEqual[y, 6.8e-82], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+74], N[(x * N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000019e-75 or 7.99999999999999961e74 < y

   1. Initial program 77.9%

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

      1. associate-*l/ 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in y around inf 73.7%

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

      1. div-sub 76.1%

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

   6. Simplified 76.1%

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

   if -2.40000000000000019e-75 < y < 6.7999999999999995e-82

   1. Initial program 67.0%

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

      1. associate-*l/ 75.9%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in x around 0 37.6%

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

      1. associate-*r/ 48.4%

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

   6. Simplified 48.4%

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

   if 6.7999999999999995e-82 < y < 7.99999999999999961e74

   1. Initial program 59.0%

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

      1. associate-*l/ 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in y around 0 53.2%

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

      1. mul-1-neg 53.2%

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

      2. associate-*r/ 69.2%

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

      3. unsub-neg 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in x around -inf 55.8%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-82}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(\frac{z}{a - z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]

Alternative 12: 55.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-75}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-81}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(\frac{z}{a - z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.2e-75)
   (* (- t x) (/ y (- a z)))
   (if (<= y 1.85e-81)
     (* t (/ (- y z) (- a z)))
     (if (<= y 6e+74) (* x (+ (/ z (- a z)) 1.0)) (* y (/ (- t x) (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.2e-75) {
		tmp = (t - x) * (y / (a - z));
	} else if (y <= 1.85e-81) {
		tmp = t * ((y - z) / (a - z));
	} else if (y <= 6e+74) {
		tmp = x * ((z / (a - z)) + 1.0);
	} else {
		tmp = y * ((t - x) / (a - 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) :: tmp
    if (y <= (-1.2d-75)) then
        tmp = (t - x) * (y / (a - z))
    else if (y <= 1.85d-81) then
        tmp = t * ((y - z) / (a - z))
    else if (y <= 6d+74) then
        tmp = x * ((z / (a - z)) + 1.0d0)
    else
        tmp = y * ((t - x) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.2e-75) {
		tmp = (t - x) * (y / (a - z));
	} else if (y <= 1.85e-81) {
		tmp = t * ((y - z) / (a - z));
	} else if (y <= 6e+74) {
		tmp = x * ((z / (a - z)) + 1.0);
	} else {
		tmp = y * ((t - x) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.2e-75:
		tmp = (t - x) * (y / (a - z))
	elif y <= 1.85e-81:
		tmp = t * ((y - z) / (a - z))
	elif y <= 6e+74:
		tmp = x * ((z / (a - z)) + 1.0)
	else:
		tmp = y * ((t - x) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.2e-75)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (y <= 1.85e-81)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (y <= 6e+74)
		tmp = Float64(x * Float64(Float64(z / Float64(a - z)) + 1.0));
	else
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.2e-75)
		tmp = (t - x) * (y / (a - z));
	elseif (y <= 1.85e-81)
		tmp = t * ((y - z) / (a - z));
	elseif (y <= 6e+74)
		tmp = x * ((z / (a - z)) + 1.0);
	else
		tmp = y * ((t - x) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.2e-75], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e-81], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+74], N[(x * N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.2000000000000001e-75

   1. Initial program 80.7%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

      1. clear-num 91.5%

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

      2. associate-/r/ 91.5%

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

   5. Applied egg-rr 91.5%

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

      1. +-commutative 91.5%

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

      2. associate-*l* 80.6%

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

      3. fma-def 80.7%

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

   7. Applied egg-rr 80.7%

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

   8. Taylor expanded in y around inf 71.0%

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

      1. div-sub 72.4%

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

      2. associate-*r/ 67.7%

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

      3. associate-*l/ 72.4%

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

      4. *-commutative 72.4%

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

   10. Simplified 72.4%

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

   if -1.2000000000000001e-75 < y < 1.84999999999999993e-81

   1. Initial program 67.0%

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

      1. associate-*l/ 75.9%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in x around 0 37.6%

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

      1. associate-*r/ 48.4%

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

   6. Simplified 48.4%

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

   if 1.84999999999999993e-81 < y < 6e74

   1. Initial program 59.0%

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

      1. associate-*l/ 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in y around 0 53.2%

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

      1. mul-1-neg 53.2%

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

      2. associate-*r/ 69.2%

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

      3. unsub-neg 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in x around -inf 55.8%

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

   if 6e74 < y

   1. Initial program 73.9%

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

      1. associate-*l/ 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in y around inf 77.6%

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

      1. div-sub 81.3%

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

   6. Simplified 81.3%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-75}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-81}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(\frac{z}{a - z} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \end{array} \]

Alternative 13: 36.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-113}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-56}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3e-65)
   x
   (if (<= a -6.8e-184)
     (* y (- (/ t z)))
     (if (<= a 1.2e-113)
       t
       (if (<= a 7e-56) (* y (/ t a)) (if (<= a 6e+125) t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3e-65) {
		tmp = x;
	} else if (a <= -6.8e-184) {
		tmp = y * -(t / z);
	} else if (a <= 1.2e-113) {
		tmp = t;
	} else if (a <= 7e-56) {
		tmp = y * (t / a);
	} else if (a <= 6e+125) {
		tmp = t;
	} 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 (a <= (-3d-65)) then
        tmp = x
    else if (a <= (-6.8d-184)) then
        tmp = y * -(t / z)
    else if (a <= 1.2d-113) then
        tmp = t
    else if (a <= 7d-56) then
        tmp = y * (t / a)
    else if (a <= 6d+125) then
        tmp = t
    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 (a <= -3e-65) {
		tmp = x;
	} else if (a <= -6.8e-184) {
		tmp = y * -(t / z);
	} else if (a <= 1.2e-113) {
		tmp = t;
	} else if (a <= 7e-56) {
		tmp = y * (t / a);
	} else if (a <= 6e+125) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3e-65:
		tmp = x
	elif a <= -6.8e-184:
		tmp = y * -(t / z)
	elif a <= 1.2e-113:
		tmp = t
	elif a <= 7e-56:
		tmp = y * (t / a)
	elif a <= 6e+125:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3e-65)
		tmp = x;
	elseif (a <= -6.8e-184)
		tmp = Float64(y * Float64(-Float64(t / z)));
	elseif (a <= 1.2e-113)
		tmp = t;
	elseif (a <= 7e-56)
		tmp = Float64(y * Float64(t / a));
	elseif (a <= 6e+125)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3e-65)
		tmp = x;
	elseif (a <= -6.8e-184)
		tmp = y * -(t / z);
	elseif (a <= 1.2e-113)
		tmp = t;
	elseif (a <= 7e-56)
		tmp = y * (t / a);
	elseif (a <= 6e+125)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3e-65], x, If[LessEqual[a, -6.8e-184], N[(y * (-N[(t / z), $MachinePrecision])), $MachinePrecision], If[LessEqual[a, 1.2e-113], t, If[LessEqual[a, 7e-56], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e+125], t, x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.99999999999999998e-65 or 6.0000000000000003e125 < a

   1. Initial program 70.9%

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

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in a around inf 42.9%

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

   if -2.99999999999999998e-65 < a < -6.80000000000000008e-184

   1. Initial program 90.7%

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

      1. associate-*l/ 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in x around 0 72.8%

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

   5. Taylor expanded in a around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. associate-/l* 52.5%

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

      3. distribute-neg-frac 52.5%

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

   7. Simplified 52.5%

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

   8. Taylor expanded in z around 0 62.6%

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

      1. mul-1-neg 62.6%

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

      2. unsub-neg 62.6%

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

      3. associate-/l* 52.5%

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

   10. Simplified 52.5%

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

   11. Taylor expanded in z around 0 57.3%

       \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{z}} \]
   12. Step-by-step derivation

       1. mul-1-neg 57.3%

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

       2. associate-*l/ 52.0%

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

       3. *-commutative 52.0%

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

       4. distribute-rgt-neg-in 52.0%

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

       5. distribute-neg-frac 52.0%

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

   13. Simplified 52.0%

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

   if -6.80000000000000008e-184 < a < 1.20000000000000006e-113 or 6.9999999999999996e-56 < a < 6.0000000000000003e125

   1. Initial program 67.3%

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

      1. associate-*l/ 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in z around inf 40.6%

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

   if 1.20000000000000006e-113 < a < 6.9999999999999996e-56

   1. Initial program 91.2%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in x around 0 81.5%

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

   5. Taylor expanded in z around 0 60.7%

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

      1. associate-/l* 51.4%

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

   7. Simplified 51.4%

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

      1. associate-/r/ 61.2%

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

   9. Applied egg-rr 61.2%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \left(-\frac{t}{z}\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-113}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-56}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 35.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-180}:\\ \;\;\;\;\frac{-t \cdot y}{z}\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-114}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.42e-65)
   x
   (if (<= a -2.3e-180)
     (/ (- (* t y)) z)
     (if (<= a 9.8e-114)
       t
       (if (<= a 5.9e-58) (* y (/ t a)) (if (<= a 6.2e+125) t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.42e-65) {
		tmp = x;
	} else if (a <= -2.3e-180) {
		tmp = -(t * y) / z;
	} else if (a <= 9.8e-114) {
		tmp = t;
	} else if (a <= 5.9e-58) {
		tmp = y * (t / a);
	} else if (a <= 6.2e+125) {
		tmp = t;
	} 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 (a <= (-1.42d-65)) then
        tmp = x
    else if (a <= (-2.3d-180)) then
        tmp = -(t * y) / z
    else if (a <= 9.8d-114) then
        tmp = t
    else if (a <= 5.9d-58) then
        tmp = y * (t / a)
    else if (a <= 6.2d+125) then
        tmp = t
    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 (a <= -1.42e-65) {
		tmp = x;
	} else if (a <= -2.3e-180) {
		tmp = -(t * y) / z;
	} else if (a <= 9.8e-114) {
		tmp = t;
	} else if (a <= 5.9e-58) {
		tmp = y * (t / a);
	} else if (a <= 6.2e+125) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.42e-65:
		tmp = x
	elif a <= -2.3e-180:
		tmp = -(t * y) / z
	elif a <= 9.8e-114:
		tmp = t
	elif a <= 5.9e-58:
		tmp = y * (t / a)
	elif a <= 6.2e+125:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.42e-65)
		tmp = x;
	elseif (a <= -2.3e-180)
		tmp = Float64(Float64(-Float64(t * y)) / z);
	elseif (a <= 9.8e-114)
		tmp = t;
	elseif (a <= 5.9e-58)
		tmp = Float64(y * Float64(t / a));
	elseif (a <= 6.2e+125)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.42e-65)
		tmp = x;
	elseif (a <= -2.3e-180)
		tmp = -(t * y) / z;
	elseif (a <= 9.8e-114)
		tmp = t;
	elseif (a <= 5.9e-58)
		tmp = y * (t / a);
	elseif (a <= 6.2e+125)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.42e-65], x, If[LessEqual[a, -2.3e-180], N[((-N[(t * y), $MachinePrecision]) / z), $MachinePrecision], If[LessEqual[a, 9.8e-114], t, If[LessEqual[a, 5.9e-58], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e+125], t, x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.41999999999999993e-65 or 6.2e125 < a

   1. Initial program 70.9%

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

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in a around inf 42.9%

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

   if -1.41999999999999993e-65 < a < -2.29999999999999996e-180

   1. Initial program 90.3%

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

      1. associate-*l/ 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in x around 0 76.8%

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

   5. Taylor expanded in a around 0 66.1%

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

      1. mul-1-neg 66.1%

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

      2. associate-/l* 55.3%

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

      3. distribute-neg-frac 55.3%

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

   7. Simplified 55.3%

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

   8. Taylor expanded in z around 0 60.3%

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

      1. associate-*r/ 60.3%

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

      2. mul-1-neg 60.3%

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

      3. distribute-rgt-neg-in 60.3%

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

   10. Simplified 60.3%

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

   if -2.29999999999999996e-180 < a < 9.7999999999999994e-114 or 5.9e-58 < a < 6.2e125

   1. Initial program 67.5%

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

      1. associate-*l/ 76.4%

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

   3. Simplified 76.4%

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

   4. Taylor expanded in z around inf 40.3%

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

   if 9.7999999999999994e-114 < a < 5.9e-58

   1. Initial program 91.2%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in x around 0 81.5%

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

   5. Taylor expanded in z around 0 60.7%

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

      1. associate-/l* 51.4%

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

   7. Simplified 51.4%

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

      1. associate-/r/ 61.2%

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

   9. Applied egg-rr 61.2%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.42 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-180}:\\ \;\;\;\;\frac{-t \cdot y}{z}\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-114}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 35.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-82}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= y -1.6e-97) t_1 (if (<= y 2.55e-82) t (if (<= y 7e+74) x t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (y <= -1.6e-97) {
		tmp = t_1;
	} else if (y <= 2.55e-82) {
		tmp = t;
	} else if (y <= 7e+74) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	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 * (y / (a - z))
    if (y <= (-1.6d-97)) then
        tmp = t_1
    else if (y <= 2.55d-82) then
        tmp = t
    else if (y <= 7d+74) then
        tmp = x
    else
        tmp = t_1
    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 * (y / (a - z));
	double tmp;
	if (y <= -1.6e-97) {
		tmp = t_1;
	} else if (y <= 2.55e-82) {
		tmp = t;
	} else if (y <= 7e+74) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if y <= -1.6e-97:
		tmp = t_1
	elif y <= 2.55e-82:
		tmp = t
	elif y <= 7e+74:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -1.6e-97)
		tmp = t_1;
	elseif (y <= 2.55e-82)
		tmp = t;
	elseif (y <= 7e+74)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (y <= -1.6e-97)
		tmp = t_1;
	elseif (y <= 2.55e-82)
		tmp = t;
	elseif (y <= 7e+74)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e-97], t$95$1, If[LessEqual[y, 2.55e-82], t, If[LessEqual[y, 7e+74], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5999999999999999e-97 or 7.00000000000000029e74 < y

   1. Initial program 78.4%

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

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in x around 0 48.2%

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

      1. associate-*r/ 54.1%

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

   6. Simplified 54.1%

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

   7. Taylor expanded in y around inf 44.1%

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

   if -1.5999999999999999e-97 < y < 2.54999999999999996e-82

   1. Initial program 65.9%

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

      1. associate-*l/ 75.1%

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

   3. Simplified 75.1%

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

   4. Taylor expanded in z around inf 42.2%

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

   if 2.54999999999999996e-82 < y < 7.00000000000000029e74

   1. Initial program 59.0%

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

      1. associate-*l/ 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in a around inf 52.4%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-97}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-82}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \end{array} \]

Alternative 16: 48.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-269}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+126}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.6e-58)
   (* x (- 1.0 (/ y a)))
   (if (<= a 1.35e-269)
     (/ (- y) (/ z (- t x)))
     (if (<= a 1.6e+126) (- t (/ t (/ z y))) (- x (/ x (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e-58) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 1.35e-269) {
		tmp = -y / (z / (t - x));
	} else if (a <= 1.6e+126) {
		tmp = t - (t / (z / y));
	} else {
		tmp = x - (x / (a / 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 (a <= (-3.6d-58)) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= 1.35d-269) then
        tmp = -y / (z / (t - x))
    else if (a <= 1.6d+126) then
        tmp = t - (t / (z / y))
    else
        tmp = x - (x / (a / 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 (a <= -3.6e-58) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 1.35e-269) {
		tmp = -y / (z / (t - x));
	} else if (a <= 1.6e+126) {
		tmp = t - (t / (z / y));
	} else {
		tmp = x - (x / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.6e-58:
		tmp = x * (1.0 - (y / a))
	elif a <= 1.35e-269:
		tmp = -y / (z / (t - x))
	elif a <= 1.6e+126:
		tmp = t - (t / (z / y))
	else:
		tmp = x - (x / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.6e-58)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= 1.35e-269)
		tmp = Float64(Float64(-y) / Float64(z / Float64(t - x)));
	elseif (a <= 1.6e+126)
		tmp = Float64(t - Float64(t / Float64(z / y)));
	else
		tmp = Float64(x - Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.6e-58)
		tmp = x * (1.0 - (y / a));
	elseif (a <= 1.35e-269)
		tmp = -y / (z / (t - x));
	elseif (a <= 1.6e+126)
		tmp = t - (t / (z / y));
	else
		tmp = x - (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.6e-58], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e-269], N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+126], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.60000000000000009e-58

   1. Initial program 68.6%

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

      1. associate-*l/ 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in z around 0 65.4%

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

   5. Taylor expanded in x around inf 44.8%

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

      1. mul-1-neg 44.8%

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

      2. unsub-neg 44.8%

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

   7. Simplified 44.8%

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

   if -3.60000000000000009e-58 < a < 1.35000000000000008e-269

   1. Initial program 74.5%

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

      1. associate-*l/ 78.1%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in y around -inf 69.6%

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

   5. Taylor expanded in a around 0 59.2%

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

      1. mul-1-neg 59.2%

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

      2. associate-/l* 58.9%

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

   7. Simplified 58.9%

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

   if 1.35000000000000008e-269 < a < 1.5999999999999999e126

   1. Initial program 70.5%

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

      1. associate-*l/ 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in x around 0 54.2%

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

   5. Taylor expanded in a around 0 46.6%

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

      1. mul-1-neg 46.6%

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

      2. associate-/l* 57.2%

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

      3. distribute-neg-frac 57.2%

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

   7. Simplified 57.2%

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

   8. Taylor expanded in z around 0 54.7%

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

      1. mul-1-neg 54.7%

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

      2. unsub-neg 54.7%

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

      3. associate-/l* 57.2%

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

   10. Simplified 57.2%

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

   if 1.5999999999999999e126 < a

   1. Initial program 74.7%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in z around 0 79.2%

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

   5. Taylor expanded in t around 0 53.2%

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

      1. mul-1-neg 53.2%

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

      2. unsub-neg 53.2%

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

      3. associate-/l* 58.7%

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

   7. Simplified 58.7%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-269}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+126}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 17: 67.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-31} \lor \neg \left(z \leq 1.8 \cdot 10^{-16}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.8e-31) (not (<= z 1.8e-16)))
   (* t (/ (- y z) (- a z)))
   (+ x (* (- t x) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.8e-31) || !(z <= 1.8e-16)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - 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 <= (-1.8d-31)) .or. (.not. (z <= 1.8d-16))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + ((t - 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 <= -1.8e-31) || !(z <= 1.8e-16)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.8e-31) or not (z <= 1.8e-16):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.8e-31) || !(z <= 1.8e-16))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.8e-31) || ~((z <= 1.8e-16)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.8e-31], N[Not[LessEqual[z, 1.8e-16]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.80000000000000002e-31 or 1.79999999999999991e-16 < z

   1. Initial program 51.5%

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

      1. associate-*l/ 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in x around 0 39.7%

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

      1. associate-*r/ 59.6%

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

   6. Simplified 59.6%

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

   if -1.80000000000000002e-31 < z < 1.79999999999999991e-16

   1. Initial program 91.9%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around 0 76.7%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-31} \lor \neg \left(z \leq 1.8 \cdot 10^{-16}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 18: 70.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-31} \lor \neg \left(z \leq 1.05 \cdot 10^{-16}\right):\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.1e-31) (not (<= z 1.05e-16)))
   (- t (/ y (/ z (- t x))))
   (+ x (* (- t x) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.1e-31) || !(z <= 1.05e-16)) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x + ((t - 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 <= (-5.1d-31)) .or. (.not. (z <= 1.05d-16))) then
        tmp = t - (y / (z / (t - x)))
    else
        tmp = x + ((t - 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 <= -5.1e-31) || !(z <= 1.05e-16)) {
		tmp = t - (y / (z / (t - x)));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.1e-31) or not (z <= 1.05e-16):
		tmp = t - (y / (z / (t - x)))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.1e-31) || !(z <= 1.05e-16))
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.1e-31) || ~((z <= 1.05e-16)))
		tmp = t - (y / (z / (t - x)));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.1e-31], N[Not[LessEqual[z, 1.05e-16]], $MachinePrecision]], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.0999999999999997e-31 or 1.0500000000000001e-16 < z

   1. Initial program 51.5%

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

      1. associate-*l/ 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in z around -inf 49.9%

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

      1. associate-+r+ 49.9%

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

      2. mul-1-neg 49.9%

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

      3. distribute-rgt-out-- 49.9%

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

      4. unsub-neg 49.9%

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

   6. Simplified 73.3%

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

   7. Taylor expanded in a around 0 59.2%

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

      1. associate-/l* 66.1%

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

   9. Simplified 66.1%

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

   if -5.0999999999999997e-31 < z < 1.0500000000000001e-16

   1. Initial program 91.9%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in z around 0 76.7%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-31} \lor \neg \left(z \leq 1.05 \cdot 10^{-16}\right):\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 19: 37.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-113}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.5e+27)
   x
   (if (<= a 1.22e-113)
     t
     (if (<= a 4.3e-57) (* y (/ t a)) (if (<= a 3.3e+125) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.5e+27) {
		tmp = x;
	} else if (a <= 1.22e-113) {
		tmp = t;
	} else if (a <= 4.3e-57) {
		tmp = y * (t / a);
	} else if (a <= 3.3e+125) {
		tmp = t;
	} 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 (a <= (-7.5d+27)) then
        tmp = x
    else if (a <= 1.22d-113) then
        tmp = t
    else if (a <= 4.3d-57) then
        tmp = y * (t / a)
    else if (a <= 3.3d+125) then
        tmp = t
    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 (a <= -7.5e+27) {
		tmp = x;
	} else if (a <= 1.22e-113) {
		tmp = t;
	} else if (a <= 4.3e-57) {
		tmp = y * (t / a);
	} else if (a <= 3.3e+125) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.5e+27:
		tmp = x
	elif a <= 1.22e-113:
		tmp = t
	elif a <= 4.3e-57:
		tmp = y * (t / a)
	elif a <= 3.3e+125:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.5e+27)
		tmp = x;
	elseif (a <= 1.22e-113)
		tmp = t;
	elseif (a <= 4.3e-57)
		tmp = Float64(y * Float64(t / a));
	elseif (a <= 3.3e+125)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.5e+27)
		tmp = x;
	elseif (a <= 1.22e-113)
		tmp = t;
	elseif (a <= 4.3e-57)
		tmp = y * (t / a);
	elseif (a <= 3.3e+125)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.5e+27], x, If[LessEqual[a, 1.22e-113], t, If[LessEqual[a, 4.3e-57], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e+125], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.5000000000000002e27 or 3.30000000000000005e125 < a

   1. Initial program 73.7%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in a around inf 48.7%

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

   if -7.5000000000000002e27 < a < 1.21999999999999995e-113 or 4.30000000000000022e-57 < a < 3.30000000000000005e125

   1. Initial program 68.9%

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

      1. associate-*l/ 77.8%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in z around inf 34.7%

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

   if 1.21999999999999995e-113 < a < 4.30000000000000022e-57

   1. Initial program 91.2%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in x around 0 81.5%

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

   5. Taylor expanded in z around 0 60.7%

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

      1. associate-/l* 51.4%

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

   7. Simplified 51.4%

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

      1. associate-/r/ 61.2%

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

   9. Applied egg-rr 61.2%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-113}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 50.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-72} \lor \neg \left(a \leq 3.6 \cdot 10^{+125}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.75e-72) (not (<= a 3.6e+125)))
   (* x (- 1.0 (/ y a)))
   (- t (/ t (/ z y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.75e-72) || !(a <= 3.6e+125)) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t - (t / (z / 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 ((a <= (-1.75d-72)) .or. (.not. (a <= 3.6d+125))) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = t - (t / (z / 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 ((a <= -1.75e-72) || !(a <= 3.6e+125)) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t - (t / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.75e-72) or not (a <= 3.6e+125):
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t - (t / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.75e-72) || !(a <= 3.6e+125))
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(t - Float64(t / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.75e-72) || ~((a <= 3.6e+125)))
		tmp = x * (1.0 - (y / a));
	else
		tmp = t - (t / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.75e-72], N[Not[LessEqual[a, 3.6e+125]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.75e-72 or 3.6000000000000003e125 < a

   1. Initial program 71.1%

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

      1. associate-*l/ 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in z around 0 69.8%

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

   5. Taylor expanded in x around inf 49.7%

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

      1. mul-1-neg 49.7%

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

      2. unsub-neg 49.7%

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

   7. Simplified 49.7%

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

   if -1.75e-72 < a < 3.6000000000000003e125

   1. Initial program 72.0%

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

      1. associate-*l/ 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in x around 0 54.0%

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

   5. Taylor expanded in a around 0 46.5%

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

      1. mul-1-neg 46.5%

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

      2. associate-/l* 53.7%

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

      3. distribute-neg-frac 53.7%

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

   7. Simplified 53.7%

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

   8. Taylor expanded in z around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. unsub-neg 53.6%

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

      3. associate-/l* 53.7%

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

   10. Simplified 53.7%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{-72} \lor \neg \left(a \leq 3.6 \cdot 10^{+125}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \end{array} \]

Alternative 21: 50.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+125}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e-71)
   (* x (- 1.0 (/ y a)))
   (if (<= a 3.1e+125) (- t (/ t (/ z y))) (- x (/ x (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e-71) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 3.1e+125) {
		tmp = t - (t / (z / y));
	} else {
		tmp = x - (x / (a / 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 (a <= (-1.2d-71)) then
        tmp = x * (1.0d0 - (y / a))
    else if (a <= 3.1d+125) then
        tmp = t - (t / (z / y))
    else
        tmp = x - (x / (a / 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 (a <= -1.2e-71) {
		tmp = x * (1.0 - (y / a));
	} else if (a <= 3.1e+125) {
		tmp = t - (t / (z / y));
	} else {
		tmp = x - (x / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e-71:
		tmp = x * (1.0 - (y / a))
	elif a <= 3.1e+125:
		tmp = t - (t / (z / y))
	else:
		tmp = x - (x / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e-71)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (a <= 3.1e+125)
		tmp = Float64(t - Float64(t / Float64(z / y)));
	else
		tmp = Float64(x - Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.2e-71)
		tmp = x * (1.0 - (y / a));
	elseif (a <= 3.1e+125)
		tmp = t - (t / (z / y));
	else
		tmp = x - (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e-71], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e+125], N[(t - N[(t / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.2e-71

   1. Initial program 69.0%

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

      1. associate-*l/ 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in z around 0 64.4%

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

   5. Taylor expanded in x around inf 44.6%

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

      1. mul-1-neg 44.6%

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

      2. unsub-neg 44.6%

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

   7. Simplified 44.6%

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

   if -1.2e-71 < a < 3.1e125

   1. Initial program 72.0%

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

      1. associate-*l/ 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in x around 0 54.0%

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

   5. Taylor expanded in a around 0 46.5%

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

      1. mul-1-neg 46.5%

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

      2. associate-/l* 53.7%

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

      3. distribute-neg-frac 53.7%

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

   7. Simplified 53.7%

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

   8. Taylor expanded in z around 0 53.6%

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

      1. mul-1-neg 53.6%

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

      2. unsub-neg 53.6%

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

      3. associate-/l* 53.7%

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

   10. Simplified 53.7%

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

   if 3.1e125 < a

   1. Initial program 74.7%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in z around 0 79.2%

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

   5. Taylor expanded in t around 0 53.2%

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

      1. mul-1-neg 53.2%

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

      2. unsub-neg 53.2%

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

      3. associate-/l* 58.7%

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

   7. Simplified 58.7%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+125}:\\ \;\;\;\;t - \frac{t}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 22: 38.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.2e+28) x (if (<= a 3.1e+125) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.2e+28) {
		tmp = x;
	} else if (a <= 3.1e+125) {
		tmp = t;
	} 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 (a <= (-9.2d+28)) then
        tmp = x
    else if (a <= 3.1d+125) then
        tmp = t
    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 (a <= -9.2e+28) {
		tmp = x;
	} else if (a <= 3.1e+125) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.2e+28:
		tmp = x
	elif a <= 3.1e+125:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.2e+28)
		tmp = x;
	elseif (a <= 3.1e+125)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.2e+28)
		tmp = x;
	elseif (a <= 3.1e+125)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.2e+28], x, If[LessEqual[a, 3.1e+125], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -9.19999999999999935e28 or 3.1e125 < a

   1. Initial program 73.7%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in a around inf 48.7%

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

   if -9.19999999999999935e28 < a < 3.1e125

   1. Initial program 70.3%

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

      1. associate-*l/ 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in z around inf 33.3%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+125}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23: 25.3% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

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 = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.6%

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

   1. associate-*l/ 84.2%

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

3. Simplified 84.2%

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

4. Taylor expanded in z around inf 24.5%

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

5. Final simplification 24.5%

   \[\leadsto t \]

Developer target: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	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 - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    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 - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023277 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

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