Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.3% → 94.8%

Time: 20.7s

Alternatives: 30

Speedup: 0.3×

Specification

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 80.3% accurate, 1.0× speedup

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 94.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}}\\ t_2 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-295}:\\ \;\;\;\;t_1 + x \cdot \left(\frac{z - y}{a - z} - -1\right)\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1 + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ (- a z) (- y z))))
        (t_2 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (<= t_2 -5e-295)
     (+ t_1 (* x (- (/ (- z y) (- a z)) -1.0)))
     (if (<= t_2 0.0)
       (+ t_1 (* x (/ (- y a) z)))
       (fma (- t x) (/ (- y z) (- a z)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / ((a - z) / (y - z));
	double t_2 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if (t_2 <= -5e-295) {
		tmp = t_1 + (x * (((z - y) / (a - z)) - -1.0));
	} else if (t_2 <= 0.0) {
		tmp = t_1 + (x * ((y - a) / z));
	} else {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(Float64(a - z) / Float64(y - z)))
	t_2 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -5e-295)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(Float64(z - y) / Float64(a - z)) - -1.0)));
	elseif (t_2 <= 0.0)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(y - a) / z)));
	else
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-295], N[(t$95$1 + N[(x * N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t$95$1 + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.00000000000000008e-295

   1. Initial program 90.9%

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

   2. Taylor expanded in x around -inf 85.4%

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

      1. mul-1-neg 85.4%

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

      2. unsub-neg 85.4%

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

      3. associate-/l* 98.7%

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

      4. *-commutative 98.7%

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

      5. associate--r+ 98.7%

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

      6. div-sub 98.7%

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

      7. sub-neg 98.7%

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

      8. metadata-eval 98.7%

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

   4. Simplified 98.7%

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

   if -5.00000000000000008e-295 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.3%

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

   2. Taylor expanded in x around -inf 58.1%

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

      1. mul-1-neg 58.1%

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

      2. unsub-neg 58.1%

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

      3. associate-/l* 68.4%

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

      4. *-commutative 68.4%

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

      5. associate--r+ 40.8%

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

      6. div-sub 40.8%

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

      7. sub-neg 40.8%

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

      8. metadata-eval 40.8%

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

   4. Simplified 40.8%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. sub-neg 99.8%

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

   7. Simplified 99.8%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.8%

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

      1. +-commutative 92.8%

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

      2. associate-*r/ 78.8%

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

      3. *-commutative 78.8%

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

      4. associate-*r/ 94.6%

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

      5. fma-def 94.6%

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

   3. Simplified 94.6%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -5 \cdot 10^{-295}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}} + x \cdot \left(\frac{z - y}{a - z} - -1\right)\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}} + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \]

Alternative 2: 95.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ t_2 := \frac{z}{t - x}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-295} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(t - \frac{y}{t_2}\right) + \frac{a}{t_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))) (t_2 (/ z (- t x))))
   (if (or (<= t_1 -5e-295) (not (<= t_1 0.0)))
     (- x (/ (- x t) (/ (- a z) (- y z))))
     (+ (- t (/ y t_2)) (/ a t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double t_2 = z / (t - x);
	double tmp;
	if ((t_1 <= -5e-295) || !(t_1 <= 0.0)) {
		tmp = x - ((x - t) / ((a - z) / (y - z)));
	} else {
		tmp = (t - (y / t_2)) + (a / 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 = x + ((z - y) * ((x - t) / (a - z)))
    t_2 = z / (t - x)
    if ((t_1 <= (-5d-295)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x - ((x - t) / ((a - z) / (y - z)))
    else
        tmp = (t - (y / t_2)) + (a / 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 = x + ((z - y) * ((x - t) / (a - z)));
	double t_2 = z / (t - x);
	double tmp;
	if ((t_1 <= -5e-295) || !(t_1 <= 0.0)) {
		tmp = x - ((x - t) / ((a - z) / (y - z)));
	} else {
		tmp = (t - (y / t_2)) + (a / t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((x - t) / (a - z)))
	t_2 = z / (t - x)
	tmp = 0
	if (t_1 <= -5e-295) or not (t_1 <= 0.0):
		tmp = x - ((x - t) / ((a - z) / (y - z)))
	else:
		tmp = (t - (y / t_2)) + (a / t_2)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	t_2 = Float64(z / Float64(t - x))
	tmp = 0.0
	if ((t_1 <= -5e-295) || !(t_1 <= 0.0))
		tmp = Float64(x - Float64(Float64(x - t) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(Float64(t - Float64(y / t_2)) + Float64(a / t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((x - t) / (a - z)));
	t_2 = z / (t - x);
	tmp = 0.0;
	if ((t_1 <= -5e-295) || ~((t_1 <= 0.0)))
		tmp = x - ((x - t) / ((a - z) / (y - z)));
	else
		tmp = (t - (y / t_2)) + (a / t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-295], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x - N[(N[(x - t), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - N[(y / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(a / t$95$2), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.00000000000000008e-295 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-*l/ 78.5%

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

      3. associate-*r/ 95.3%

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

      4. clear-num 95.0%

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

      5. un-div-inv 95.2%

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

   3. Applied egg-rr 95.2%

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

   if -5.00000000000000008e-295 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.3%

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

      1. *-commutative 3.3%

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

      2. associate-*l/ 2.6%

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

      3. associate-*r/ 3.3%

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

      4. clear-num 3.3%

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

      5. un-div-inv 3.3%

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

   3. Applied egg-rr 3.3%

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

   4. Taylor expanded in z around inf 94.3%

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

      1. sub-neg 94.3%

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

      2. +-commutative 94.3%

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

      3. mul-1-neg 94.3%

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

      4. unsub-neg 94.3%

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

      5. associate-/l* 94.6%

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

      6. mul-1-neg 94.6%

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

      7. remove-double-neg 94.6%

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

      8. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -5 \cdot 10^{-295} \lor \neg \left(x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0\right):\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(t - \frac{y}{\frac{z}{t - x}}\right) + \frac{a}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 3: 95.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ t_2 := \frac{a - z}{y - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-295} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x - \frac{x - t}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{t_2} + x \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))) (t_2 (/ (- a z) (- y z))))
   (if (or (<= t_1 -5e-295) (not (<= t_1 0.0)))
     (- x (/ (- x t) t_2))
     (+ (/ t t_2) (* x (/ (- y a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double t_2 = (a - z) / (y - z);
	double tmp;
	if ((t_1 <= -5e-295) || !(t_1 <= 0.0)) {
		tmp = x - ((x - t) / t_2);
	} else {
		tmp = (t / t_2) + (x * ((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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((z - y) * ((x - t) / (a - z)))
    t_2 = (a - z) / (y - z)
    if ((t_1 <= (-5d-295)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x - ((x - t) / t_2)
    else
        tmp = (t / t_2) + (x * ((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 t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double t_2 = (a - z) / (y - z);
	double tmp;
	if ((t_1 <= -5e-295) || !(t_1 <= 0.0)) {
		tmp = x - ((x - t) / t_2);
	} else {
		tmp = (t / t_2) + (x * ((y - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((x - t) / (a - z)))
	t_2 = (a - z) / (y - z)
	tmp = 0
	if (t_1 <= -5e-295) or not (t_1 <= 0.0):
		tmp = x - ((x - t) / t_2)
	else:
		tmp = (t / t_2) + (x * ((y - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	t_2 = Float64(Float64(a - z) / Float64(y - z))
	tmp = 0.0
	if ((t_1 <= -5e-295) || !(t_1 <= 0.0))
		tmp = Float64(x - Float64(Float64(x - t) / t_2));
	else
		tmp = Float64(Float64(t / t_2) + Float64(x * Float64(Float64(y - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((x - t) / (a - z)));
	t_2 = (a - z) / (y - z);
	tmp = 0.0;
	if ((t_1 <= -5e-295) || ~((t_1 <= 0.0)))
		tmp = x - ((x - t) / t_2);
	else
		tmp = (t / t_2) + (x * ((y - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-295], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x - N[(N[(x - t), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(t / t$95$2), $MachinePrecision] + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.00000000000000008e-295 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-*l/ 78.5%

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

      3. associate-*r/ 95.3%

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

      4. clear-num 95.0%

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

      5. un-div-inv 95.2%

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

   3. Applied egg-rr 95.2%

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

   if -5.00000000000000008e-295 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.3%

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

   2. Taylor expanded in x around -inf 58.1%

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

      1. mul-1-neg 58.1%

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

      2. unsub-neg 58.1%

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

      3. associate-/l* 68.4%

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

      4. *-commutative 68.4%

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

      5. associate--r+ 40.8%

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

      6. div-sub 40.8%

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

      7. sub-neg 40.8%

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

      8. metadata-eval 40.8%

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

   4. Simplified 40.8%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. sub-neg 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -5 \cdot 10^{-295} \lor \neg \left(x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0\right):\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}} + x \cdot \frac{y - a}{z}\\ \end{array} \]

Alternative 4: 94.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - z}{y - z}\\ t_2 := \frac{t}{t_1}\\ t_3 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_3 \leq -5 \cdot 10^{-295}:\\ \;\;\;\;t_2 + x \cdot \left(\frac{z - y}{a - z} - -1\right)\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;t_2 + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- a z) (- y z)))
        (t_2 (/ t t_1))
        (t_3 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (<= t_3 -5e-295)
     (+ t_2 (* x (- (/ (- z y) (- a z)) -1.0)))
     (if (<= t_3 0.0) (+ t_2 (* x (/ (- y a) z))) (- x (/ (- x t) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a - z) / (y - z);
	double t_2 = t / t_1;
	double t_3 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if (t_3 <= -5e-295) {
		tmp = t_2 + (x * (((z - y) / (a - z)) - -1.0));
	} else if (t_3 <= 0.0) {
		tmp = t_2 + (x * ((y - a) / z));
	} else {
		tmp = x - ((x - t) / 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a - z) / (y - z)
    t_2 = t / t_1
    t_3 = x + ((z - y) * ((x - t) / (a - z)))
    if (t_3 <= (-5d-295)) then
        tmp = t_2 + (x * (((z - y) / (a - z)) - (-1.0d0)))
    else if (t_3 <= 0.0d0) then
        tmp = t_2 + (x * ((y - a) / z))
    else
        tmp = x - ((x - t) / 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 = (a - z) / (y - z);
	double t_2 = t / t_1;
	double t_3 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if (t_3 <= -5e-295) {
		tmp = t_2 + (x * (((z - y) / (a - z)) - -1.0));
	} else if (t_3 <= 0.0) {
		tmp = t_2 + (x * ((y - a) / z));
	} else {
		tmp = x - ((x - t) / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a - z) / (y - z)
	t_2 = t / t_1
	t_3 = x + ((z - y) * ((x - t) / (a - z)))
	tmp = 0
	if t_3 <= -5e-295:
		tmp = t_2 + (x * (((z - y) / (a - z)) - -1.0))
	elif t_3 <= 0.0:
		tmp = t_2 + (x * ((y - a) / z))
	else:
		tmp = x - ((x - t) / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a - z) / Float64(y - z))
	t_2 = Float64(t / t_1)
	t_3 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if (t_3 <= -5e-295)
		tmp = Float64(t_2 + Float64(x * Float64(Float64(Float64(z - y) / Float64(a - z)) - -1.0)));
	elseif (t_3 <= 0.0)
		tmp = Float64(t_2 + Float64(x * Float64(Float64(y - a) / z)));
	else
		tmp = Float64(x - Float64(Float64(x - t) / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a - z) / (y - z);
	t_2 = t / t_1;
	t_3 = x + ((z - y) * ((x - t) / (a - z)));
	tmp = 0.0;
	if (t_3 <= -5e-295)
		tmp = t_2 + (x * (((z - y) / (a - z)) - -1.0));
	elseif (t_3 <= 0.0)
		tmp = t_2 + (x * ((y - a) / z));
	else
		tmp = x - ((x - t) / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e-295], N[(t$95$2 + N[(x * N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 0.0], N[(t$95$2 + N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(x - t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.00000000000000008e-295

   1. Initial program 90.9%

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

   2. Taylor expanded in x around -inf 85.4%

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

      1. mul-1-neg 85.4%

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

      2. unsub-neg 85.4%

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

      3. associate-/l* 98.7%

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

      4. *-commutative 98.7%

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

      5. associate--r+ 98.7%

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

      6. div-sub 98.7%

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

      7. sub-neg 98.7%

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

      8. metadata-eval 98.7%

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

   4. Simplified 98.7%

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

   if -5.00000000000000008e-295 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.3%

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

   2. Taylor expanded in x around -inf 58.1%

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

      1. mul-1-neg 58.1%

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

      2. unsub-neg 58.1%

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

      3. associate-/l* 68.4%

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

      4. *-commutative 68.4%

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

      5. associate--r+ 40.8%

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

      6. div-sub 40.8%

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

      7. sub-neg 40.8%

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

      8. metadata-eval 40.8%

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

   4. Simplified 40.8%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. sub-neg 99.8%

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

   7. Simplified 99.8%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.8%

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

      1. *-commutative 92.8%

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

      2. associate-*l/ 78.8%

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

      3. associate-*r/ 94.6%

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

      4. clear-num 93.9%

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

      5. un-div-inv 94.4%

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

   3. Applied egg-rr 94.4%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -5 \cdot 10^{-295}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}} + x \cdot \left(\frac{z - y}{a - z} - -1\right)\\ \mathbf{elif}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}} + x \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 5: 89.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-295} \lor \neg \left(t_1 \leq 10^{-242}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (or (<= t_1 -5e-295) (not (<= t_1 1e-242)))
     t_1
     (+ t (/ (* (- y a) (- x t)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-295) || !(t_1 <= 1e-242)) {
		tmp = t_1;
	} else {
		tmp = t + (((y - a) * (x - t)) / 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 = x + ((z - y) * ((x - t) / (a - z)))
    if ((t_1 <= (-5d-295)) .or. (.not. (t_1 <= 1d-242))) then
        tmp = t_1
    else
        tmp = t + (((y - a) * (x - t)) / 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 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-295) || !(t_1 <= 1e-242)) {
		tmp = t_1;
	} else {
		tmp = t + (((y - a) * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((x - t) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-295) or not (t_1 <= 1e-242):
		tmp = t_1
	else:
		tmp = t + (((y - a) * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-295) || !(t_1 <= 1e-242))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((x - t) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-295) || ~((t_1 <= 1e-242)))
		tmp = t_1;
	else
		tmp = t + (((y - a) * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-295], N[Not[LessEqual[t$95$1, 1e-242]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.00000000000000008e-295 or 1e-242 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.9%

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

   if -5.00000000000000008e-295 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1e-242

   1. Initial program 7.0%

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

   2. Taylor expanded in z around inf 90.2%

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

      1. +-commutative 90.2%

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

      2. associate--l+ 90.2%

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

      3. associate-*r/ 90.2%

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

      4. associate-*r/ 90.2%

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

      5. div-sub 90.2%

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

      6. distribute-lft-out-- 90.2%

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

      7. mul-1-neg 90.2%

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

      8. distribute-neg-frac 90.2%

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

      9. unsub-neg 90.2%

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

      10. distribute-rgt-out-- 90.4%

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

   4. Simplified 90.4%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -5 \cdot 10^{-295} \lor \neg \left(x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 10^{-242}\right):\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \]

Alternative 6: 93.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-295} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (or (<= t_1 -5e-295) (not (<= t_1 0.0)))
     (- x (/ (- x t) (/ (- a z) (- y z))))
     (+ t (/ (* (- y a) (- x t)) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-295) || !(t_1 <= 0.0)) {
		tmp = x - ((x - t) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((y - a) * (x - t)) / 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 = x + ((z - y) * ((x - t) / (a - z)))
    if ((t_1 <= (-5d-295)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x - ((x - t) / ((a - z) / (y - z)))
    else
        tmp = t + (((y - a) * (x - t)) / 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 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-295) || !(t_1 <= 0.0)) {
		tmp = x - ((x - t) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((y - a) * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((x - t) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-295) or not (t_1 <= 0.0):
		tmp = x - ((x - t) / ((a - z) / (y - z)))
	else:
		tmp = t + (((y - a) * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-295) || !(t_1 <= 0.0))
		tmp = Float64(x - Float64(Float64(x - t) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((x - t) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-295) || ~((t_1 <= 0.0)))
		tmp = x - ((x - t) / ((a - z) / (y - z)));
	else
		tmp = t + (((y - a) * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-295], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x - N[(N[(x - t), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.00000000000000008e-295 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-*l/ 78.5%

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

      3. associate-*r/ 95.3%

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

      4. clear-num 95.0%

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

      5. un-div-inv 95.2%

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

   3. Applied egg-rr 95.2%

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

   if -5.00000000000000008e-295 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.3%

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

   2. Taylor expanded in z around inf 94.3%

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

      1. +-commutative 94.3%

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

      2. associate--l+ 94.3%

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

      3. associate-*r/ 94.3%

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

      4. associate-*r/ 94.3%

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

      5. div-sub 94.3%

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

      6. distribute-lft-out-- 94.3%

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

      7. mul-1-neg 94.3%

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

      8. distribute-neg-frac 94.3%

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

      9. unsub-neg 94.3%

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

      10. distribute-rgt-out-- 94.7%

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

   4. Simplified 94.7%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -5 \cdot 10^{-295} \lor \neg \left(x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0\right):\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \]

Alternative 7: 95.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(z - y\right) \cdot \frac{x - t}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-295} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{-1}{\frac{\frac{z}{t - x}}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- z y) (/ (- x t) (- a z))))))
   (if (or (<= t_1 -5e-295) (not (<= t_1 0.0)))
     (- x (/ (- x t) (/ (- a z) (- y z))))
     (+ t (/ -1.0 (/ (/ z (- t x)) (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-295) || !(t_1 <= 0.0)) {
		tmp = x - ((x - t) / ((a - z) / (y - z)));
	} else {
		tmp = t + (-1.0 / ((z / (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) :: t_1
    real(8) :: tmp
    t_1 = x + ((z - y) * ((x - t) / (a - z)))
    if ((t_1 <= (-5d-295)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x - ((x - t) / ((a - z) / (y - z)))
    else
        tmp = t + ((-1.0d0) / ((z / (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 t_1 = x + ((z - y) * ((x - t) / (a - z)));
	double tmp;
	if ((t_1 <= -5e-295) || !(t_1 <= 0.0)) {
		tmp = x - ((x - t) / ((a - z) / (y - z)));
	} else {
		tmp = t + (-1.0 / ((z / (t - x)) / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z - y) * ((x - t) / (a - z)))
	tmp = 0
	if (t_1 <= -5e-295) or not (t_1 <= 0.0):
		tmp = x - ((x - t) / ((a - z) / (y - z)))
	else:
		tmp = t + (-1.0 / ((z / (t - x)) / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -5e-295) || !(t_1 <= 0.0))
		tmp = Float64(x - Float64(Float64(x - t) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(-1.0 / Float64(Float64(z / Float64(t - x)) / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z - y) * ((x - t) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -5e-295) || ~((t_1 <= 0.0)))
		tmp = x - ((x - t) / ((a - z) / (y - z)));
	else
		tmp = t + (-1.0 / ((z / (t - x)) / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-295], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x - N[(N[(x - t), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(-1.0 / N[(N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5.00000000000000008e-295 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-*l/ 78.5%

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

      3. associate-*r/ 95.3%

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

      4. clear-num 95.0%

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

      5. un-div-inv 95.2%

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

   3. Applied egg-rr 95.2%

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

   if -5.00000000000000008e-295 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.3%

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

   2. Taylor expanded in z around inf 94.3%

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

      1. +-commutative 94.3%

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

      2. associate--l+ 94.3%

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

      3. associate-*r/ 94.3%

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

      4. associate-*r/ 94.3%

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

      5. div-sub 94.3%

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

      6. distribute-lft-out-- 94.3%

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

      7. mul-1-neg 94.3%

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

      8. distribute-neg-frac 94.3%

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

      9. unsub-neg 94.3%

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

      10. distribute-rgt-out-- 94.7%

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

   4. Simplified 94.7%

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

      1. clear-num 94.5%

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

      2. inv-pow 94.5%

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

   6. Applied egg-rr 94.5%

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

      1. unpow-1 94.5%

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

      2. associate-/r* 99.5%

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

   8. Simplified 99.5%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq -5 \cdot 10^{-295} \lor \neg \left(x + \left(z - y\right) \cdot \frac{x - t}{a - z} \leq 0\right):\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{-1}{\frac{\frac{z}{t - x}}{y - a}}\\ \end{array} \]

Alternative 8: 39.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ t_2 := x - \frac{z \cdot t}{a}\\ \mathbf{if}\;a \leq -5.1 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -51000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-144}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-282}:\\ \;\;\;\;\frac{-y \cdot t}{z}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-299}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-137}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-53}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))) (t_2 (- x (/ (* z t) a))))
   (if (<= a -5.1e+104)
     t_2
     (if (<= a -5e+16)
       t_1
       (if (<= a -51000000000000.0)
         x
         (if (<= a -7.5e-144)
           t
           (if (<= a -1.95e-282)
             (/ (- (* y t)) z)
             (if (<= a 1.85e-299)
               t
               (if (<= a 1.9e-137)
                 (* (- y a) (/ x z))
                 (if (<= a 5e-53) t (if (<= a 4.6e+122) t_1 t_2)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double t_2 = x - ((z * t) / a);
	double tmp;
	if (a <= -5.1e+104) {
		tmp = t_2;
	} else if (a <= -5e+16) {
		tmp = t_1;
	} else if (a <= -51000000000000.0) {
		tmp = x;
	} else if (a <= -7.5e-144) {
		tmp = t;
	} else if (a <= -1.95e-282) {
		tmp = -(y * t) / z;
	} else if (a <= 1.85e-299) {
		tmp = t;
	} else if (a <= 1.9e-137) {
		tmp = (y - a) * (x / z);
	} else if (a <= 5e-53) {
		tmp = t;
	} else if (a <= 4.6e+122) {
		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 = y * ((t - x) / a)
    t_2 = x - ((z * t) / a)
    if (a <= (-5.1d+104)) then
        tmp = t_2
    else if (a <= (-5d+16)) then
        tmp = t_1
    else if (a <= (-51000000000000.0d0)) then
        tmp = x
    else if (a <= (-7.5d-144)) then
        tmp = t
    else if (a <= (-1.95d-282)) then
        tmp = -(y * t) / z
    else if (a <= 1.85d-299) then
        tmp = t
    else if (a <= 1.9d-137) then
        tmp = (y - a) * (x / z)
    else if (a <= 5d-53) then
        tmp = t
    else if (a <= 4.6d+122) 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 = y * ((t - x) / a);
	double t_2 = x - ((z * t) / a);
	double tmp;
	if (a <= -5.1e+104) {
		tmp = t_2;
	} else if (a <= -5e+16) {
		tmp = t_1;
	} else if (a <= -51000000000000.0) {
		tmp = x;
	} else if (a <= -7.5e-144) {
		tmp = t;
	} else if (a <= -1.95e-282) {
		tmp = -(y * t) / z;
	} else if (a <= 1.85e-299) {
		tmp = t;
	} else if (a <= 1.9e-137) {
		tmp = (y - a) * (x / z);
	} else if (a <= 5e-53) {
		tmp = t;
	} else if (a <= 4.6e+122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	t_2 = x - ((z * t) / a)
	tmp = 0
	if a <= -5.1e+104:
		tmp = t_2
	elif a <= -5e+16:
		tmp = t_1
	elif a <= -51000000000000.0:
		tmp = x
	elif a <= -7.5e-144:
		tmp = t
	elif a <= -1.95e-282:
		tmp = -(y * t) / z
	elif a <= 1.85e-299:
		tmp = t
	elif a <= 1.9e-137:
		tmp = (y - a) * (x / z)
	elif a <= 5e-53:
		tmp = t
	elif a <= 4.6e+122:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	t_2 = Float64(x - Float64(Float64(z * t) / a))
	tmp = 0.0
	if (a <= -5.1e+104)
		tmp = t_2;
	elseif (a <= -5e+16)
		tmp = t_1;
	elseif (a <= -51000000000000.0)
		tmp = x;
	elseif (a <= -7.5e-144)
		tmp = t;
	elseif (a <= -1.95e-282)
		tmp = Float64(Float64(-Float64(y * t)) / z);
	elseif (a <= 1.85e-299)
		tmp = t;
	elseif (a <= 1.9e-137)
		tmp = Float64(Float64(y - a) * Float64(x / z));
	elseif (a <= 5e-53)
		tmp = t;
	elseif (a <= 4.6e+122)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	t_2 = x - ((z * t) / a);
	tmp = 0.0;
	if (a <= -5.1e+104)
		tmp = t_2;
	elseif (a <= -5e+16)
		tmp = t_1;
	elseif (a <= -51000000000000.0)
		tmp = x;
	elseif (a <= -7.5e-144)
		tmp = t;
	elseif (a <= -1.95e-282)
		tmp = -(y * t) / z;
	elseif (a <= 1.85e-299)
		tmp = t;
	elseif (a <= 1.9e-137)
		tmp = (y - a) * (x / z);
	elseif (a <= 5e-53)
		tmp = t;
	elseif (a <= 4.6e+122)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.1e+104], t$95$2, If[LessEqual[a, -5e+16], t$95$1, If[LessEqual[a, -51000000000000.0], x, If[LessEqual[a, -7.5e-144], t, If[LessEqual[a, -1.95e-282], N[((-N[(y * t), $MachinePrecision]) / z), $MachinePrecision], If[LessEqual[a, 1.85e-299], t, If[LessEqual[a, 1.9e-137], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-53], t, If[LessEqual[a, 4.6e+122], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -5.1000000000000002e104 or 4.6000000000000001e122 < a

   1. Initial program 91.9%

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

   2. Taylor expanded in a around inf 81.9%

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

   3. Taylor expanded in y around 0 61.6%

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

      1. +-commutative 61.6%

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

      2. *-commutative 61.6%

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

      3. mul-1-neg 61.6%

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

      4. unsub-neg 61.6%

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

      5. associate-/l* 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in t around inf 65.8%

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

   if -5.1000000000000002e104 < a < -5e16 or 5e-53 < a < 4.6000000000000001e122

   1. Initial program 87.3%

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

   2. Taylor expanded in a around inf 69.7%

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

   3. Taylor expanded in y around inf 52.1%

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

      1. div-sub 52.1%

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

      2. *-commutative 52.1%

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

   5. Simplified 52.1%

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

   if -5e16 < a < -5.1e13

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 100.0%

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

   if -5.1e13 < a < -7.49999999999999963e-144 or -1.95000000000000019e-282 < a < 1.85000000000000007e-299 or 1.89999999999999999e-137 < a < 5e-53

   1. Initial program 60.4%

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

   2. Taylor expanded in z around inf 53.0%

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

   if -7.49999999999999963e-144 < a < -1.95000000000000019e-282

   1. Initial program 75.9%

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

   2. Taylor expanded in y around inf 72.3%

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

      1. div-sub 72.3%

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

      2. *-commutative 72.3%

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

      3. associate-*r/ 70.8%

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

      4. associate-/l* 72.2%

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

   4. Simplified 72.2%

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

   5. Taylor expanded in a around 0 55.2%

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

      1. associate-*r/ 55.2%

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

      2. associate-*r* 55.2%

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

      3. mul-1-neg 55.2%

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

   7. Simplified 55.2%

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

   8. Taylor expanded in t around inf 40.8%

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

      1. associate-*r* 40.8%

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

      2. neg-mul-1 40.8%

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

   10. Simplified 40.8%

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

   if 1.85000000000000007e-299 < a < 1.89999999999999999e-137

   1. Initial program 74.4%

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

   2. Taylor expanded in z around inf 82.7%

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

      1. +-commutative 82.7%

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

      2. associate--l+ 82.7%

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

      3. associate-*r/ 82.7%

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

      4. associate-*r/ 82.7%

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

      5. div-sub 82.7%

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

      6. distribute-lft-out-- 82.7%

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

      7. mul-1-neg 82.7%

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

      8. distribute-neg-frac 82.7%

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

      9. unsub-neg 82.7%

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

      10. distribute-rgt-out-- 82.7%

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

   4. Simplified 82.7%

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

   5. Taylor expanded in t around 0 40.0%

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

      1. *-commutative 40.0%

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

      2. associate-*l/ 42.6%

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

   7. Simplified 42.6%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -51000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-144}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-282}:\\ \;\;\;\;\frac{-y \cdot t}{z}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-299}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-137}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-53}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \end{array} \]

Alternative 9: 37.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -2.26 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-144}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-283}:\\ \;\;\;\;\frac{-y \cdot t}{z}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-302}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-159}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-53}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))))
   (if (<= a -2.26e+105)
     x
     (if (<= a -8e+16)
       t_1
       (if (<= a -6.4e-144)
         t
         (if (<= a -9.6e-283)
           (/ (- (* y t)) z)
           (if (<= a 3.7e-302)
             t
             (if (<= a 5.4e-159)
               (/ y (/ z x))
               (if (<= a 1.55e-53) t (if (<= a 2e+123) t_1 x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (a <= -2.26e+105) {
		tmp = x;
	} else if (a <= -8e+16) {
		tmp = t_1;
	} else if (a <= -6.4e-144) {
		tmp = t;
	} else if (a <= -9.6e-283) {
		tmp = -(y * t) / z;
	} else if (a <= 3.7e-302) {
		tmp = t;
	} else if (a <= 5.4e-159) {
		tmp = y / (z / x);
	} else if (a <= 1.55e-53) {
		tmp = t;
	} else if (a <= 2e+123) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / a)
    if (a <= (-2.26d+105)) then
        tmp = x
    else if (a <= (-8d+16)) then
        tmp = t_1
    else if (a <= (-6.4d-144)) then
        tmp = t
    else if (a <= (-9.6d-283)) then
        tmp = -(y * t) / z
    else if (a <= 3.7d-302) then
        tmp = t
    else if (a <= 5.4d-159) then
        tmp = y / (z / x)
    else if (a <= 1.55d-53) then
        tmp = t
    else if (a <= 2d+123) then
        tmp = t_1
    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 t_1 = y * ((t - x) / a);
	double tmp;
	if (a <= -2.26e+105) {
		tmp = x;
	} else if (a <= -8e+16) {
		tmp = t_1;
	} else if (a <= -6.4e-144) {
		tmp = t;
	} else if (a <= -9.6e-283) {
		tmp = -(y * t) / z;
	} else if (a <= 3.7e-302) {
		tmp = t;
	} else if (a <= 5.4e-159) {
		tmp = y / (z / x);
	} else if (a <= 1.55e-53) {
		tmp = t;
	} else if (a <= 2e+123) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	tmp = 0
	if a <= -2.26e+105:
		tmp = x
	elif a <= -8e+16:
		tmp = t_1
	elif a <= -6.4e-144:
		tmp = t
	elif a <= -9.6e-283:
		tmp = -(y * t) / z
	elif a <= 3.7e-302:
		tmp = t
	elif a <= 5.4e-159:
		tmp = y / (z / x)
	elif a <= 1.55e-53:
		tmp = t
	elif a <= 2e+123:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (a <= -2.26e+105)
		tmp = x;
	elseif (a <= -8e+16)
		tmp = t_1;
	elseif (a <= -6.4e-144)
		tmp = t;
	elseif (a <= -9.6e-283)
		tmp = Float64(Float64(-Float64(y * t)) / z);
	elseif (a <= 3.7e-302)
		tmp = t;
	elseif (a <= 5.4e-159)
		tmp = Float64(y / Float64(z / x));
	elseif (a <= 1.55e-53)
		tmp = t;
	elseif (a <= 2e+123)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	tmp = 0.0;
	if (a <= -2.26e+105)
		tmp = x;
	elseif (a <= -8e+16)
		tmp = t_1;
	elseif (a <= -6.4e-144)
		tmp = t;
	elseif (a <= -9.6e-283)
		tmp = -(y * t) / z;
	elseif (a <= 3.7e-302)
		tmp = t;
	elseif (a <= 5.4e-159)
		tmp = y / (z / x);
	elseif (a <= 1.55e-53)
		tmp = t;
	elseif (a <= 2e+123)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.26e+105], x, If[LessEqual[a, -8e+16], t$95$1, If[LessEqual[a, -6.4e-144], t, If[LessEqual[a, -9.6e-283], N[((-N[(y * t), $MachinePrecision]) / z), $MachinePrecision], If[LessEqual[a, 3.7e-302], t, If[LessEqual[a, 5.4e-159], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.55e-53], t, If[LessEqual[a, 2e+123], t$95$1, x]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.2600000000000001e105 or 1.99999999999999996e123 < a

   1. Initial program 91.9%

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

   2. Taylor expanded in a around inf 61.7%

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

   if -2.2600000000000001e105 < a < -8e16 or 1.55000000000000008e-53 < a < 1.99999999999999996e123

   1. Initial program 87.3%

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

   2. Taylor expanded in a around inf 69.7%

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

   3. Taylor expanded in y around inf 52.1%

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

      1. div-sub 52.1%

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

      2. *-commutative 52.1%

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

   5. Simplified 52.1%

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

   if -8e16 < a < -6.39999999999999946e-144 or -9.5999999999999999e-283 < a < 3.7e-302 or 5.4000000000000001e-159 < a < 1.55000000000000008e-53

   1. Initial program 63.2%

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

   2. Taylor expanded in z around inf 48.8%

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

   if -6.39999999999999946e-144 < a < -9.5999999999999999e-283

   1. Initial program 75.9%

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

   2. Taylor expanded in y around inf 72.3%

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

      1. div-sub 72.3%

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

      2. *-commutative 72.3%

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

      3. associate-*r/ 70.8%

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

      4. associate-/l* 72.2%

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

   4. Simplified 72.2%

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

   5. Taylor expanded in a around 0 55.2%

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

      1. associate-*r/ 55.2%

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

      2. associate-*r* 55.2%

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

      3. mul-1-neg 55.2%

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

   7. Simplified 55.2%

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

   8. Taylor expanded in t around inf 40.8%

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

      1. associate-*r* 40.8%

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

      2. neg-mul-1 40.8%

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

   10. Simplified 40.8%

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

   if 3.7e-302 < a < 5.4000000000000001e-159

   1. Initial program 73.0%

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

   2. Taylor expanded in y around inf 72.4%

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

      1. div-sub 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r/ 70.6%

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

      4. associate-/l* 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in a around 0 61.0%

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

      1. associate-*r/ 61.0%

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

      2. associate-*r* 61.0%

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

      3. mul-1-neg 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in t around 0 42.0%

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

      1. associate-/l* 45.3%

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

   10. Simplified 45.3%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.26 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-144}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-283}:\\ \;\;\;\;\frac{-y \cdot t}{z}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-302}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-159}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-53}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 37.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -1.62 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-144}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-282}:\\ \;\;\;\;\frac{-y \cdot t}{z}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-299}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-137}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.72 \cdot 10^{-53}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))))
   (if (<= a -1.62e+105)
     x
     (if (<= a -6e+16)
       t_1
       (if (<= a -6.8e-144)
         t
         (if (<= a -1e-282)
           (/ (- (* y t)) z)
           (if (<= a 8.2e-299)
             t
             (if (<= a 1.9e-137)
               (* (- y a) (/ x z))
               (if (<= a 1.72e-53) t (if (<= a 2.8e+122) t_1 x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (a <= -1.62e+105) {
		tmp = x;
	} else if (a <= -6e+16) {
		tmp = t_1;
	} else if (a <= -6.8e-144) {
		tmp = t;
	} else if (a <= -1e-282) {
		tmp = -(y * t) / z;
	} else if (a <= 8.2e-299) {
		tmp = t;
	} else if (a <= 1.9e-137) {
		tmp = (y - a) * (x / z);
	} else if (a <= 1.72e-53) {
		tmp = t;
	} else if (a <= 2.8e+122) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / a)
    if (a <= (-1.62d+105)) then
        tmp = x
    else if (a <= (-6d+16)) then
        tmp = t_1
    else if (a <= (-6.8d-144)) then
        tmp = t
    else if (a <= (-1d-282)) then
        tmp = -(y * t) / z
    else if (a <= 8.2d-299) then
        tmp = t
    else if (a <= 1.9d-137) then
        tmp = (y - a) * (x / z)
    else if (a <= 1.72d-53) then
        tmp = t
    else if (a <= 2.8d+122) then
        tmp = t_1
    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 t_1 = y * ((t - x) / a);
	double tmp;
	if (a <= -1.62e+105) {
		tmp = x;
	} else if (a <= -6e+16) {
		tmp = t_1;
	} else if (a <= -6.8e-144) {
		tmp = t;
	} else if (a <= -1e-282) {
		tmp = -(y * t) / z;
	} else if (a <= 8.2e-299) {
		tmp = t;
	} else if (a <= 1.9e-137) {
		tmp = (y - a) * (x / z);
	} else if (a <= 1.72e-53) {
		tmp = t;
	} else if (a <= 2.8e+122) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	tmp = 0
	if a <= -1.62e+105:
		tmp = x
	elif a <= -6e+16:
		tmp = t_1
	elif a <= -6.8e-144:
		tmp = t
	elif a <= -1e-282:
		tmp = -(y * t) / z
	elif a <= 8.2e-299:
		tmp = t
	elif a <= 1.9e-137:
		tmp = (y - a) * (x / z)
	elif a <= 1.72e-53:
		tmp = t
	elif a <= 2.8e+122:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (a <= -1.62e+105)
		tmp = x;
	elseif (a <= -6e+16)
		tmp = t_1;
	elseif (a <= -6.8e-144)
		tmp = t;
	elseif (a <= -1e-282)
		tmp = Float64(Float64(-Float64(y * t)) / z);
	elseif (a <= 8.2e-299)
		tmp = t;
	elseif (a <= 1.9e-137)
		tmp = Float64(Float64(y - a) * Float64(x / z));
	elseif (a <= 1.72e-53)
		tmp = t;
	elseif (a <= 2.8e+122)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	tmp = 0.0;
	if (a <= -1.62e+105)
		tmp = x;
	elseif (a <= -6e+16)
		tmp = t_1;
	elseif (a <= -6.8e-144)
		tmp = t;
	elseif (a <= -1e-282)
		tmp = -(y * t) / z;
	elseif (a <= 8.2e-299)
		tmp = t;
	elseif (a <= 1.9e-137)
		tmp = (y - a) * (x / z);
	elseif (a <= 1.72e-53)
		tmp = t;
	elseif (a <= 2.8e+122)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.62e+105], x, If[LessEqual[a, -6e+16], t$95$1, If[LessEqual[a, -6.8e-144], t, If[LessEqual[a, -1e-282], N[((-N[(y * t), $MachinePrecision]) / z), $MachinePrecision], If[LessEqual[a, 8.2e-299], t, If[LessEqual[a, 1.9e-137], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.72e-53], t, If[LessEqual[a, 2.8e+122], t$95$1, x]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.6200000000000001e105 or 2.8e122 < a

   1. Initial program 91.9%

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

   2. Taylor expanded in a around inf 61.7%

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

   if -1.6200000000000001e105 < a < -6e16 or 1.72e-53 < a < 2.8e122

   1. Initial program 87.3%

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

   2. Taylor expanded in a around inf 69.7%

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

   3. Taylor expanded in y around inf 52.1%

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

      1. div-sub 52.1%

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

      2. *-commutative 52.1%

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

   5. Simplified 52.1%

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

   if -6e16 < a < -6.80000000000000035e-144 or -1e-282 < a < 8.2000000000000002e-299 or 1.89999999999999999e-137 < a < 1.72e-53

   1. Initial program 61.0%

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

   2. Taylor expanded in z around inf 52.2%

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

   if -6.80000000000000035e-144 < a < -1e-282

   1. Initial program 75.9%

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

   2. Taylor expanded in y around inf 72.3%

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

      1. div-sub 72.3%

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

      2. *-commutative 72.3%

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

      3. associate-*r/ 70.8%

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

      4. associate-/l* 72.2%

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

   4. Simplified 72.2%

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

   5. Taylor expanded in a around 0 55.2%

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

      1. associate-*r/ 55.2%

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

      2. associate-*r* 55.2%

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

      3. mul-1-neg 55.2%

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

   7. Simplified 55.2%

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

   8. Taylor expanded in t around inf 40.8%

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

      1. associate-*r* 40.8%

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

      2. neg-mul-1 40.8%

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

   10. Simplified 40.8%

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

   if 8.2000000000000002e-299 < a < 1.89999999999999999e-137

   1. Initial program 74.4%

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

   2. Taylor expanded in z around inf 82.7%

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

      1. +-commutative 82.7%

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

      2. associate--l+ 82.7%

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

      3. associate-*r/ 82.7%

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

      4. associate-*r/ 82.7%

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

      5. div-sub 82.7%

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

      6. distribute-lft-out-- 82.7%

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

      7. mul-1-neg 82.7%

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

      8. distribute-neg-frac 82.7%

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

      9. unsub-neg 82.7%

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

      10. distribute-rgt-out-- 82.7%

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

   4. Simplified 82.7%

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

   5. Taylor expanded in t around 0 40.0%

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

      1. *-commutative 40.0%

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

      2. associate-*l/ 42.6%

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

   7. Simplified 42.6%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(y - a\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.62 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-144}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-282}:\\ \;\;\;\;\frac{-y \cdot t}{z}\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-299}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-137}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 1.72 \cdot 10^{-53}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 44.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{t - x}}\\ t_2 := x - \frac{z \cdot t}{a}\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-144}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-150}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-51}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a (- t x)))) (t_2 (- x (/ (* z t) a))))
   (if (<= a -2.6e+104)
     t_2
     (if (<= a -4e+17)
       t_1
       (if (<= a -5e+15)
         x
         (if (<= a -8.8e-144)
           t
           (if (<= a 2.9e-150)
             (/ (* y (- x t)) z)
             (if (<= a 1.05e-51) t (if (<= a 3.1e+114) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / (t - x));
	double t_2 = x - ((z * t) / a);
	double tmp;
	if (a <= -2.6e+104) {
		tmp = t_2;
	} else if (a <= -4e+17) {
		tmp = t_1;
	} else if (a <= -5e+15) {
		tmp = x;
	} else if (a <= -8.8e-144) {
		tmp = t;
	} else if (a <= 2.9e-150) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 1.05e-51) {
		tmp = t;
	} else if (a <= 3.1e+114) {
		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 = y / (a / (t - x))
    t_2 = x - ((z * t) / a)
    if (a <= (-2.6d+104)) then
        tmp = t_2
    else if (a <= (-4d+17)) then
        tmp = t_1
    else if (a <= (-5d+15)) then
        tmp = x
    else if (a <= (-8.8d-144)) then
        tmp = t
    else if (a <= 2.9d-150) then
        tmp = (y * (x - t)) / z
    else if (a <= 1.05d-51) then
        tmp = t
    else if (a <= 3.1d+114) 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 = y / (a / (t - x));
	double t_2 = x - ((z * t) / a);
	double tmp;
	if (a <= -2.6e+104) {
		tmp = t_2;
	} else if (a <= -4e+17) {
		tmp = t_1;
	} else if (a <= -5e+15) {
		tmp = x;
	} else if (a <= -8.8e-144) {
		tmp = t;
	} else if (a <= 2.9e-150) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 1.05e-51) {
		tmp = t;
	} else if (a <= 3.1e+114) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / (t - x))
	t_2 = x - ((z * t) / a)
	tmp = 0
	if a <= -2.6e+104:
		tmp = t_2
	elif a <= -4e+17:
		tmp = t_1
	elif a <= -5e+15:
		tmp = x
	elif a <= -8.8e-144:
		tmp = t
	elif a <= 2.9e-150:
		tmp = (y * (x - t)) / z
	elif a <= 1.05e-51:
		tmp = t
	elif a <= 3.1e+114:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / Float64(t - x)))
	t_2 = Float64(x - Float64(Float64(z * t) / a))
	tmp = 0.0
	if (a <= -2.6e+104)
		tmp = t_2;
	elseif (a <= -4e+17)
		tmp = t_1;
	elseif (a <= -5e+15)
		tmp = x;
	elseif (a <= -8.8e-144)
		tmp = t;
	elseif (a <= 2.9e-150)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (a <= 1.05e-51)
		tmp = t;
	elseif (a <= 3.1e+114)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a / (t - x));
	t_2 = x - ((z * t) / a);
	tmp = 0.0;
	if (a <= -2.6e+104)
		tmp = t_2;
	elseif (a <= -4e+17)
		tmp = t_1;
	elseif (a <= -5e+15)
		tmp = x;
	elseif (a <= -8.8e-144)
		tmp = t;
	elseif (a <= 2.9e-150)
		tmp = (y * (x - t)) / z;
	elseif (a <= 1.05e-51)
		tmp = t;
	elseif (a <= 3.1e+114)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.6e+104], t$95$2, If[LessEqual[a, -4e+17], t$95$1, If[LessEqual[a, -5e+15], x, If[LessEqual[a, -8.8e-144], t, If[LessEqual[a, 2.9e-150], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.05e-51], t, If[LessEqual[a, 3.1e+114], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.6e104 or 3.1e114 < a

   1. Initial program 92.5%

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

   2. Taylor expanded in a around inf 83.2%

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

   3. Taylor expanded in y around 0 60.9%

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

      1. +-commutative 60.9%

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

      2. *-commutative 60.9%

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

      3. mul-1-neg 60.9%

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

      4. unsub-neg 60.9%

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

      5. associate-/l* 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in t around inf 64.8%

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

   if -2.6e104 < a < -4e17 or 1.05000000000000001e-51 < a < 3.1e114

   1. Initial program 85.8%

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

   2. Taylor expanded in y around inf 59.3%

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

      1. div-sub 59.3%

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

      2. *-commutative 59.3%

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

      3. associate-*r/ 57.4%

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

      4. associate-/l* 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in a around inf 50.4%

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

      1. associate-/l* 52.1%

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

   7. Simplified 52.1%

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

   if -4e17 < a < -5e15

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 100.0%

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

   if -5e15 < a < -8.80000000000000025e-144 or 2.8999999999999998e-150 < a < 1.05000000000000001e-51

   1. Initial program 58.5%

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

   2. Taylor expanded in z around inf 50.4%

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

   if -8.80000000000000025e-144 < a < 2.8999999999999998e-150

   1. Initial program 75.6%

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

   2. Taylor expanded in y around inf 69.4%

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

      1. div-sub 69.4%

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

      2. *-commutative 69.4%

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

      3. associate-*r/ 68.1%

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

      4. associate-/l* 69.2%

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

   4. Simplified 69.2%

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

   5. Taylor expanded in a around 0 56.4%

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

      1. associate-*r/ 56.4%

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

      2. associate-*r* 56.4%

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

      3. mul-1-neg 56.4%

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

   7. Simplified 56.4%

      \[\leadsto \color{blue}{\frac{\left(-y\right) \cdot \left(t - x\right)}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;a \leq -4 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-144}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-150}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-51}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+114}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \end{array} \]

Alternative 12: 35.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-144}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-283}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-310}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-160}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-34}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{+119}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.5e+16)
   x
   (if (<= a -6.4e-144)
     t
     (if (<= a -8.8e-283)
       (/ (- y) (/ z t))
       (if (<= a -5e-310)
         t
         (if (<= a 2.4e-160)
           (/ y (/ z x))
           (if (<= a 2.2e-34) t (if (<= a 6.1e+119) (/ (* y t) a) x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e+16) {
		tmp = x;
	} else if (a <= -6.4e-144) {
		tmp = t;
	} else if (a <= -8.8e-283) {
		tmp = -y / (z / t);
	} else if (a <= -5e-310) {
		tmp = t;
	} else if (a <= 2.4e-160) {
		tmp = y / (z / x);
	} else if (a <= 2.2e-34) {
		tmp = t;
	} else if (a <= 6.1e+119) {
		tmp = (y * t) / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.5d+16)) then
        tmp = x
    else if (a <= (-6.4d-144)) then
        tmp = t
    else if (a <= (-8.8d-283)) then
        tmp = -y / (z / t)
    else if (a <= (-5d-310)) then
        tmp = t
    else if (a <= 2.4d-160) then
        tmp = y / (z / x)
    else if (a <= 2.2d-34) then
        tmp = t
    else if (a <= 6.1d+119) then
        tmp = (y * t) / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e+16) {
		tmp = x;
	} else if (a <= -6.4e-144) {
		tmp = t;
	} else if (a <= -8.8e-283) {
		tmp = -y / (z / t);
	} else if (a <= -5e-310) {
		tmp = t;
	} else if (a <= 2.4e-160) {
		tmp = y / (z / x);
	} else if (a <= 2.2e-34) {
		tmp = t;
	} else if (a <= 6.1e+119) {
		tmp = (y * t) / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.5e+16:
		tmp = x
	elif a <= -6.4e-144:
		tmp = t
	elif a <= -8.8e-283:
		tmp = -y / (z / t)
	elif a <= -5e-310:
		tmp = t
	elif a <= 2.4e-160:
		tmp = y / (z / x)
	elif a <= 2.2e-34:
		tmp = t
	elif a <= 6.1e+119:
		tmp = (y * t) / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.5e+16)
		tmp = x;
	elseif (a <= -6.4e-144)
		tmp = t;
	elseif (a <= -8.8e-283)
		tmp = Float64(Float64(-y) / Float64(z / t));
	elseif (a <= -5e-310)
		tmp = t;
	elseif (a <= 2.4e-160)
		tmp = Float64(y / Float64(z / x));
	elseif (a <= 2.2e-34)
		tmp = t;
	elseif (a <= 6.1e+119)
		tmp = Float64(Float64(y * t) / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.5e+16)
		tmp = x;
	elseif (a <= -6.4e-144)
		tmp = t;
	elseif (a <= -8.8e-283)
		tmp = -y / (z / t);
	elseif (a <= -5e-310)
		tmp = t;
	elseif (a <= 2.4e-160)
		tmp = y / (z / x);
	elseif (a <= 2.2e-34)
		tmp = t;
	elseif (a <= 6.1e+119)
		tmp = (y * t) / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.5e+16], x, If[LessEqual[a, -6.4e-144], t, If[LessEqual[a, -8.8e-283], N[((-y) / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5e-310], t, If[LessEqual[a, 2.4e-160], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e-34], t, If[LessEqual[a, 6.1e+119], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.5e16 or 6.1e119 < a

   1. Initial program 91.7%

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

   2. Taylor expanded in a around inf 53.3%

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

   if -2.5e16 < a < -6.39999999999999946e-144 or -8.7999999999999992e-283 < a < -4.999999999999985e-310 or 2.39999999999999991e-160 < a < 2.1999999999999999e-34

   1. Initial program 64.2%

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

   2. Taylor expanded in z around inf 48.8%

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

   if -6.39999999999999946e-144 < a < -8.7999999999999992e-283

   1. Initial program 75.9%

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

   2. Taylor expanded in y around inf 72.3%

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

      1. div-sub 72.3%

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

      2. *-commutative 72.3%

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

      3. associate-*r/ 70.8%

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

      4. associate-/l* 72.2%

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

   4. Simplified 72.2%

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

   5. Taylor expanded in a around 0 55.2%

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

      1. associate-*r/ 55.2%

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

      2. associate-*r* 55.2%

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

      3. mul-1-neg 55.2%

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

   7. Simplified 55.2%

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

   8. Taylor expanded in t around inf 40.8%

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

      1. mul-1-neg 40.8%

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

      2. associate-/l* 37.1%

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

   10. Simplified 37.1%

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

   if -4.999999999999985e-310 < a < 2.39999999999999991e-160

   1. Initial program 73.0%

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

   2. Taylor expanded in y around inf 72.4%

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

      1. div-sub 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r/ 70.6%

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

      4. associate-/l* 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in a around 0 61.0%

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

      1. associate-*r/ 61.0%

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

      2. associate-*r* 61.0%

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

      3. mul-1-neg 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in t around 0 42.0%

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

      1. associate-/l* 45.3%

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

   10. Simplified 45.3%

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

   if 2.1999999999999999e-34 < a < 6.1e119

   1. Initial program 83.7%

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

   2. Taylor expanded in a around inf 70.6%

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

   3. Taylor expanded in t around inf 37.0%

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

      1. div-sub 37.0%

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

   5. Simplified 37.0%

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

   6. Taylor expanded in y around inf 39.6%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-144}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-283}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-310}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-160}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-34}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{+119}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 35.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-143}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-283}:\\ \;\;\;\;\frac{-y \cdot t}{z}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-306}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-162}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-35}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+119}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e+14)
   x
   (if (<= a -1.2e-143)
     t
     (if (<= a -5.2e-283)
       (/ (- (* y t)) z)
       (if (<= a 8e-306)
         t
         (if (<= a 9.5e-162)
           (/ y (/ z x))
           (if (<= a 1.1e-35) t (if (<= a 5.8e+119) (/ (* y t) a) x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e+14) {
		tmp = x;
	} else if (a <= -1.2e-143) {
		tmp = t;
	} else if (a <= -5.2e-283) {
		tmp = -(y * t) / z;
	} else if (a <= 8e-306) {
		tmp = t;
	} else if (a <= 9.5e-162) {
		tmp = y / (z / x);
	} else if (a <= 1.1e-35) {
		tmp = t;
	} else if (a <= 5.8e+119) {
		tmp = (y * t) / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.2d+14)) then
        tmp = x
    else if (a <= (-1.2d-143)) then
        tmp = t
    else if (a <= (-5.2d-283)) then
        tmp = -(y * t) / z
    else if (a <= 8d-306) then
        tmp = t
    else if (a <= 9.5d-162) then
        tmp = y / (z / x)
    else if (a <= 1.1d-35) then
        tmp = t
    else if (a <= 5.8d+119) then
        tmp = (y * t) / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e+14) {
		tmp = x;
	} else if (a <= -1.2e-143) {
		tmp = t;
	} else if (a <= -5.2e-283) {
		tmp = -(y * t) / z;
	} else if (a <= 8e-306) {
		tmp = t;
	} else if (a <= 9.5e-162) {
		tmp = y / (z / x);
	} else if (a <= 1.1e-35) {
		tmp = t;
	} else if (a <= 5.8e+119) {
		tmp = (y * t) / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e+14:
		tmp = x
	elif a <= -1.2e-143:
		tmp = t
	elif a <= -5.2e-283:
		tmp = -(y * t) / z
	elif a <= 8e-306:
		tmp = t
	elif a <= 9.5e-162:
		tmp = y / (z / x)
	elif a <= 1.1e-35:
		tmp = t
	elif a <= 5.8e+119:
		tmp = (y * t) / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e+14)
		tmp = x;
	elseif (a <= -1.2e-143)
		tmp = t;
	elseif (a <= -5.2e-283)
		tmp = Float64(Float64(-Float64(y * t)) / z);
	elseif (a <= 8e-306)
		tmp = t;
	elseif (a <= 9.5e-162)
		tmp = Float64(y / Float64(z / x));
	elseif (a <= 1.1e-35)
		tmp = t;
	elseif (a <= 5.8e+119)
		tmp = Float64(Float64(y * t) / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.2e+14)
		tmp = x;
	elseif (a <= -1.2e-143)
		tmp = t;
	elseif (a <= -5.2e-283)
		tmp = -(y * t) / z;
	elseif (a <= 8e-306)
		tmp = t;
	elseif (a <= 9.5e-162)
		tmp = y / (z / x);
	elseif (a <= 1.1e-35)
		tmp = t;
	elseif (a <= 5.8e+119)
		tmp = (y * t) / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e+14], x, If[LessEqual[a, -1.2e-143], t, If[LessEqual[a, -5.2e-283], N[((-N[(y * t), $MachinePrecision]) / z), $MachinePrecision], If[LessEqual[a, 8e-306], t, If[LessEqual[a, 9.5e-162], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.1e-35], t, If[LessEqual[a, 5.8e+119], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.2e14 or 5.80000000000000014e119 < a

   1. Initial program 91.7%

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

   2. Taylor expanded in a around inf 53.3%

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

   if -1.2e14 < a < -1.1999999999999999e-143 or -5.2000000000000002e-283 < a < 8.00000000000000022e-306 or 9.5000000000000004e-162 < a < 1.09999999999999997e-35

   1. Initial program 64.2%

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

   2. Taylor expanded in z around inf 48.8%

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

   if -1.1999999999999999e-143 < a < -5.2000000000000002e-283

   1. Initial program 75.9%

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

   2. Taylor expanded in y around inf 72.3%

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

      1. div-sub 72.3%

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

      2. *-commutative 72.3%

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

      3. associate-*r/ 70.8%

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

      4. associate-/l* 72.2%

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

   4. Simplified 72.2%

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

   5. Taylor expanded in a around 0 55.2%

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

      1. associate-*r/ 55.2%

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

      2. associate-*r* 55.2%

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

      3. mul-1-neg 55.2%

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

   7. Simplified 55.2%

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

   8. Taylor expanded in t around inf 40.8%

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

      1. associate-*r* 40.8%

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

      2. neg-mul-1 40.8%

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

   10. Simplified 40.8%

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

   if 8.00000000000000022e-306 < a < 9.5000000000000004e-162

   1. Initial program 73.0%

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

   2. Taylor expanded in y around inf 72.4%

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

      1. div-sub 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r/ 70.6%

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

      4. associate-/l* 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in a around 0 61.0%

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

      1. associate-*r/ 61.0%

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

      2. associate-*r* 61.0%

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

      3. mul-1-neg 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in t around 0 42.0%

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

      1. associate-/l* 45.3%

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

   10. Simplified 45.3%

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

   if 1.09999999999999997e-35 < a < 5.80000000000000014e119

   1. Initial program 83.7%

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

   2. Taylor expanded in a around inf 70.6%

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

   3. Taylor expanded in t around inf 37.0%

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

      1. div-sub 37.0%

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

   5. Simplified 37.0%

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

   6. Taylor expanded in y around inf 39.6%

      \[\leadsto \color{blue}{\frac{y \cdot t}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-143}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-283}:\\ \;\;\;\;\frac{-y \cdot t}{z}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-306}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-162}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-35}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+119}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 43.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{z \cdot t}{a}\\ t_2 := \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+107}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* z t) a))) (t_2 (* (- y a) (/ x z))))
   (if (<= z -2.1e+107)
     t
     (if (<= z -3.35e+16)
       t_2
       (if (<= z -5.8e-42)
         t_1
         (if (<= z -9.2e-51)
           t_2
           (if (<= z 5.2e-69)
             (/ y (/ a (- t x)))
             (if (<= z 2.35e+73) t_1 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z * t) / a);
	double t_2 = (y - a) * (x / z);
	double tmp;
	if (z <= -2.1e+107) {
		tmp = t;
	} else if (z <= -3.35e+16) {
		tmp = t_2;
	} else if (z <= -5.8e-42) {
		tmp = t_1;
	} else if (z <= -9.2e-51) {
		tmp = t_2;
	} else if (z <= 5.2e-69) {
		tmp = y / (a / (t - x));
	} else if (z <= 2.35e+73) {
		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) :: t_2
    real(8) :: tmp
    t_1 = x - ((z * t) / a)
    t_2 = (y - a) * (x / z)
    if (z <= (-2.1d+107)) then
        tmp = t
    else if (z <= (-3.35d+16)) then
        tmp = t_2
    else if (z <= (-5.8d-42)) then
        tmp = t_1
    else if (z <= (-9.2d-51)) then
        tmp = t_2
    else if (z <= 5.2d-69) then
        tmp = y / (a / (t - x))
    else if (z <= 2.35d+73) 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 - ((z * t) / a);
	double t_2 = (y - a) * (x / z);
	double tmp;
	if (z <= -2.1e+107) {
		tmp = t;
	} else if (z <= -3.35e+16) {
		tmp = t_2;
	} else if (z <= -5.8e-42) {
		tmp = t_1;
	} else if (z <= -9.2e-51) {
		tmp = t_2;
	} else if (z <= 5.2e-69) {
		tmp = y / (a / (t - x));
	} else if (z <= 2.35e+73) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((z * t) / a)
	t_2 = (y - a) * (x / z)
	tmp = 0
	if z <= -2.1e+107:
		tmp = t
	elif z <= -3.35e+16:
		tmp = t_2
	elif z <= -5.8e-42:
		tmp = t_1
	elif z <= -9.2e-51:
		tmp = t_2
	elif z <= 5.2e-69:
		tmp = y / (a / (t - x))
	elif z <= 2.35e+73:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(z * t) / a))
	t_2 = Float64(Float64(y - a) * Float64(x / z))
	tmp = 0.0
	if (z <= -2.1e+107)
		tmp = t;
	elseif (z <= -3.35e+16)
		tmp = t_2;
	elseif (z <= -5.8e-42)
		tmp = t_1;
	elseif (z <= -9.2e-51)
		tmp = t_2;
	elseif (z <= 5.2e-69)
		tmp = Float64(y / Float64(a / Float64(t - x)));
	elseif (z <= 2.35e+73)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((z * t) / a);
	t_2 = (y - a) * (x / z);
	tmp = 0.0;
	if (z <= -2.1e+107)
		tmp = t;
	elseif (z <= -3.35e+16)
		tmp = t_2;
	elseif (z <= -5.8e-42)
		tmp = t_1;
	elseif (z <= -9.2e-51)
		tmp = t_2;
	elseif (z <= 5.2e-69)
		tmp = y / (a / (t - x));
	elseif (z <= 2.35e+73)
		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[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+107], t, If[LessEqual[z, -3.35e+16], t$95$2, If[LessEqual[z, -5.8e-42], t$95$1, If[LessEqual[z, -9.2e-51], t$95$2, If[LessEqual[z, 5.2e-69], N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e+73], t$95$1, t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.1e107 or 2.3500000000000001e73 < z

   1. Initial program 62.6%

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

   2. Taylor expanded in z around inf 56.8%

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

   if -2.1e107 < z < -3.35e16 or -5.8000000000000006e-42 < z < -9.20000000000000007e-51

   1. Initial program 67.6%

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

   2. Taylor expanded in z around inf 62.9%

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

      1. +-commutative 62.9%

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

      2. associate--l+ 62.9%

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

      3. associate-*r/ 62.9%

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

      4. associate-*r/ 62.9%

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

      5. div-sub 67.7%

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

      6. distribute-lft-out-- 67.7%

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

      7. mul-1-neg 67.7%

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

      8. distribute-neg-frac 67.7%

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

      9. unsub-neg 67.7%

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

      10. distribute-rgt-out-- 72.5%

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

   4. Simplified 72.5%

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

   5. Taylor expanded in t around 0 50.1%

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

      1. *-commutative 50.1%

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

      2. associate-*l/ 50.2%

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

   7. Simplified 50.2%

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

   if -3.35e16 < z < -5.8000000000000006e-42 or 5.2000000000000004e-69 < z < 2.3500000000000001e73

   1. Initial program 84.0%

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

   2. Taylor expanded in a around inf 52.7%

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

   3. Taylor expanded in y around 0 45.5%

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

      1. +-commutative 45.5%

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

      2. *-commutative 45.5%

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

      3. mul-1-neg 45.5%

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

      4. unsub-neg 45.5%

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

      5. associate-/l* 45.5%

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

   5. Simplified 45.5%

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

   6. Taylor expanded in t around inf 43.6%

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

   if -9.20000000000000007e-51 < z < 5.2000000000000004e-69

   1. Initial program 92.2%

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

   2. Taylor expanded in y around inf 61.4%

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

      1. div-sub 61.4%

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

      2. *-commutative 61.4%

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

      3. associate-*r/ 58.9%

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

      4. associate-/l* 61.5%

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

   4. Simplified 61.5%

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

   5. Taylor expanded in a around inf 47.7%

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

      1. associate-/l* 51.3%

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

   7. Simplified 51.3%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+107}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{+16}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-42}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-51}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 43.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{z \cdot t}{a}\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{+111}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+15}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-51}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* z t) a))))
   (if (<= z -9.6e+111)
     t
     (if (<= z -1.1e+15)
       (/ (- y a) (/ z x))
       (if (<= z -3.5e-41)
         t_1
         (if (<= z -4.4e-51)
           (* (- y a) (/ x z))
           (if (<= z 2.8e-69)
             (/ y (/ a (- t x)))
             (if (<= z 1.1e+73) t_1 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((z * t) / a);
	double tmp;
	if (z <= -9.6e+111) {
		tmp = t;
	} else if (z <= -1.1e+15) {
		tmp = (y - a) / (z / x);
	} else if (z <= -3.5e-41) {
		tmp = t_1;
	} else if (z <= -4.4e-51) {
		tmp = (y - a) * (x / z);
	} else if (z <= 2.8e-69) {
		tmp = y / (a / (t - x));
	} else if (z <= 1.1e+73) {
		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 - ((z * t) / a)
    if (z <= (-9.6d+111)) then
        tmp = t
    else if (z <= (-1.1d+15)) then
        tmp = (y - a) / (z / x)
    else if (z <= (-3.5d-41)) then
        tmp = t_1
    else if (z <= (-4.4d-51)) then
        tmp = (y - a) * (x / z)
    else if (z <= 2.8d-69) then
        tmp = y / (a / (t - x))
    else if (z <= 1.1d+73) 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 - ((z * t) / a);
	double tmp;
	if (z <= -9.6e+111) {
		tmp = t;
	} else if (z <= -1.1e+15) {
		tmp = (y - a) / (z / x);
	} else if (z <= -3.5e-41) {
		tmp = t_1;
	} else if (z <= -4.4e-51) {
		tmp = (y - a) * (x / z);
	} else if (z <= 2.8e-69) {
		tmp = y / (a / (t - x));
	} else if (z <= 1.1e+73) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((z * t) / a)
	tmp = 0
	if z <= -9.6e+111:
		tmp = t
	elif z <= -1.1e+15:
		tmp = (y - a) / (z / x)
	elif z <= -3.5e-41:
		tmp = t_1
	elif z <= -4.4e-51:
		tmp = (y - a) * (x / z)
	elif z <= 2.8e-69:
		tmp = y / (a / (t - x))
	elif z <= 1.1e+73:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(z * t) / a))
	tmp = 0.0
	if (z <= -9.6e+111)
		tmp = t;
	elseif (z <= -1.1e+15)
		tmp = Float64(Float64(y - a) / Float64(z / x));
	elseif (z <= -3.5e-41)
		tmp = t_1;
	elseif (z <= -4.4e-51)
		tmp = Float64(Float64(y - a) * Float64(x / z));
	elseif (z <= 2.8e-69)
		tmp = Float64(y / Float64(a / Float64(t - x)));
	elseif (z <= 1.1e+73)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((z * t) / a);
	tmp = 0.0;
	if (z <= -9.6e+111)
		tmp = t;
	elseif (z <= -1.1e+15)
		tmp = (y - a) / (z / x);
	elseif (z <= -3.5e-41)
		tmp = t_1;
	elseif (z <= -4.4e-51)
		tmp = (y - a) * (x / z);
	elseif (z <= 2.8e-69)
		tmp = y / (a / (t - x));
	elseif (z <= 1.1e+73)
		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[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.6e+111], t, If[LessEqual[z, -1.1e+15], N[(N[(y - a), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-41], t$95$1, If[LessEqual[z, -4.4e-51], N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-69], N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+73], t$95$1, t]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -9.60000000000000023e111 or 1.1e73 < z

   1. Initial program 62.6%

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

   2. Taylor expanded in z around inf 56.8%

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

   if -9.60000000000000023e111 < z < -1.1e15

   1. Initial program 73.1%

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

   2. Taylor expanded in z around inf 62.3%

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

      1. +-commutative 62.3%

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

      2. associate--l+ 62.3%

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

      3. associate-*r/ 62.3%

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

      4. associate-*r/ 62.3%

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

      5. div-sub 62.3%

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

      6. distribute-lft-out-- 62.3%

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

      7. mul-1-neg 62.3%

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

      8. distribute-neg-frac 62.3%

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

      9. unsub-neg 62.3%

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

      10. distribute-rgt-out-- 67.9%

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

   4. Simplified 67.9%

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

   5. Taylor expanded in t around 0 41.8%

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

      1. associate-/l* 42.0%

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

   7. Simplified 42.0%

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

   if -1.1e15 < z < -3.5e-41 or 2.79999999999999979e-69 < z < 1.1e73

   1. Initial program 84.0%

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

   2. Taylor expanded in a around inf 52.7%

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

   3. Taylor expanded in y around 0 45.5%

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

      1. +-commutative 45.5%

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

      2. *-commutative 45.5%

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

      3. mul-1-neg 45.5%

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

      4. unsub-neg 45.5%

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

      5. associate-/l* 45.5%

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

   5. Simplified 45.5%

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

   6. Taylor expanded in t around inf 43.6%

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

   if -3.5e-41 < z < -4.4e-51

   1. Initial program 34.8%

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

   2. Taylor expanded in z around inf 66.7%

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

      1. +-commutative 66.7%

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

      2. associate--l+ 66.7%

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

      3. associate-*r/ 66.7%

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

      4. associate-*r/ 66.7%

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

      5. div-sub 100.0%

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

      6. distribute-lft-out-- 100.0%

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

      7. mul-1-neg 100.0%

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

      8. distribute-neg-frac 100.0%

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

      9. unsub-neg 100.0%

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

      10. distribute-rgt-out-- 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

   7. Simplified 100.0%

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

   if -4.4e-51 < z < 2.79999999999999979e-69

   1. Initial program 92.2%

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

   2. Taylor expanded in y around inf 61.4%

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

      1. div-sub 61.4%

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

      2. *-commutative 61.4%

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

      3. associate-*r/ 58.9%

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

      4. associate-/l* 61.5%

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

   4. Simplified 61.5%

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

   5. Taylor expanded in a around inf 47.7%

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

      1. associate-/l* 51.3%

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

   7. Simplified 51.3%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{t - x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+111}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+15}:\\ \;\;\;\;\frac{y - a}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-41}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-51}:\\ \;\;\;\;\left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16: 58.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 + \frac{z - y}{a}\right)\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+20}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -3700000 \lor \neg \left(a \leq 1.9 \cdot 10^{+123}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (+ 1.0 (/ (- z y) a)))))
   (if (<= a -5.6e+104)
     t_1
     (if (<= a -2e+20)
       (* (- t x) (/ y (- a z)))
       (if (or (<= a -3700000.0) (not (<= a 1.9e+123)))
         t_1
         (* t (/ (- y z) (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 + ((z - y) / a));
	double tmp;
	if (a <= -5.6e+104) {
		tmp = t_1;
	} else if (a <= -2e+20) {
		tmp = (t - x) * (y / (a - z));
	} else if ((a <= -3700000.0) || !(a <= 1.9e+123)) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 + ((z - y) / a))
    if (a <= (-5.6d+104)) then
        tmp = t_1
    else if (a <= (-2d+20)) then
        tmp = (t - x) * (y / (a - z))
    else if ((a <= (-3700000.0d0)) .or. (.not. (a <= 1.9d+123))) then
        tmp = t_1
    else
        tmp = t * ((y - z) / (a - 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 = x * (1.0 + ((z - y) / a));
	double tmp;
	if (a <= -5.6e+104) {
		tmp = t_1;
	} else if (a <= -2e+20) {
		tmp = (t - x) * (y / (a - z));
	} else if ((a <= -3700000.0) || !(a <= 1.9e+123)) {
		tmp = t_1;
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 + ((z - y) / a))
	tmp = 0
	if a <= -5.6e+104:
		tmp = t_1
	elif a <= -2e+20:
		tmp = (t - x) * (y / (a - z))
	elif (a <= -3700000.0) or not (a <= 1.9e+123):
		tmp = t_1
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 + Float64(Float64(z - y) / a)))
	tmp = 0.0
	if (a <= -5.6e+104)
		tmp = t_1;
	elseif (a <= -2e+20)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif ((a <= -3700000.0) || !(a <= 1.9e+123))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 + ((z - y) / a));
	tmp = 0.0;
	if (a <= -5.6e+104)
		tmp = t_1;
	elseif (a <= -2e+20)
		tmp = (t - x) * (y / (a - z));
	elseif ((a <= -3700000.0) || ~((a <= 1.9e+123)))
		tmp = t_1;
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 + N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.6e+104], t$95$1, If[LessEqual[a, -2e+20], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -3700000.0], N[Not[LessEqual[a, 1.9e+123]], $MachinePrecision]], t$95$1, N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.6e104 or -2e20 < a < -3.7e6 or 1.89999999999999997e123 < a

   1. Initial program 92.4%

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

   2. Taylor expanded in a around inf 81.8%

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

   3. Taylor expanded in x around inf 70.1%

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

      1. *-commutative 70.1%

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

      2. div-sub 70.1%

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

      3. mul-1-neg 70.1%

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

      4. unsub-neg 70.1%

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

      5. div-sub 70.1%

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

   5. Simplified 70.1%

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

   if -5.6e104 < a < -2e20

   1. Initial program 89.1%

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

   2. Taylor expanded in y around inf 61.9%

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

      1. div-sub 62.0%

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

      2. *-commutative 62.0%

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

      3. associate-*r/ 56.9%

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

      4. associate-/l* 62.1%

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

   4. Simplified 62.1%

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

   5. Taylor expanded in y around 0 56.9%

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

      1. associate-*l/ 62.1%

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

   7. Simplified 62.1%

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

   if -3.7e6 < a < 1.89999999999999997e123

   1. Initial program 71.3%

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

   2. Taylor expanded in t around inf 66.8%

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

      1. div-sub 66.9%

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

   4. Simplified 66.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \left(1 + \frac{z - y}{a}\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{+20}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq -3700000 \lor \neg \left(a \leq 1.9 \cdot 10^{+123}\right):\\ \;\;\;\;x \cdot \left(1 + \frac{z - y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 17: 36.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.72 \cdot 10^{-307}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-161}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-33}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{+119}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.6e+16)
   x
   (if (<= a -1.72e-307)
     t
     (if (<= a 1.45e-161)
       (/ y (/ z x))
       (if (<= a 8.5e-33) t (if (<= a 6.1e+119) (/ (* y t) a) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e+16) {
		tmp = x;
	} else if (a <= -1.72e-307) {
		tmp = t;
	} else if (a <= 1.45e-161) {
		tmp = y / (z / x);
	} else if (a <= 8.5e-33) {
		tmp = t;
	} else if (a <= 6.1e+119) {
		tmp = (y * t) / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.6d+16)) then
        tmp = x
    else if (a <= (-1.72d-307)) then
        tmp = t
    else if (a <= 1.45d-161) then
        tmp = y / (z / x)
    else if (a <= 8.5d-33) then
        tmp = t
    else if (a <= 6.1d+119) then
        tmp = (y * t) / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e+16) {
		tmp = x;
	} else if (a <= -1.72e-307) {
		tmp = t;
	} else if (a <= 1.45e-161) {
		tmp = y / (z / x);
	} else if (a <= 8.5e-33) {
		tmp = t;
	} else if (a <= 6.1e+119) {
		tmp = (y * t) / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.6e+16:
		tmp = x
	elif a <= -1.72e-307:
		tmp = t
	elif a <= 1.45e-161:
		tmp = y / (z / x)
	elif a <= 8.5e-33:
		tmp = t
	elif a <= 6.1e+119:
		tmp = (y * t) / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.6e+16)
		tmp = x;
	elseif (a <= -1.72e-307)
		tmp = t;
	elseif (a <= 1.45e-161)
		tmp = Float64(y / Float64(z / x));
	elseif (a <= 8.5e-33)
		tmp = t;
	elseif (a <= 6.1e+119)
		tmp = Float64(Float64(y * t) / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.6e+16)
		tmp = x;
	elseif (a <= -1.72e-307)
		tmp = t;
	elseif (a <= 1.45e-161)
		tmp = y / (z / x);
	elseif (a <= 8.5e-33)
		tmp = t;
	elseif (a <= 6.1e+119)
		tmp = (y * t) / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.6e+16], x, If[LessEqual[a, -1.72e-307], t, If[LessEqual[a, 1.45e-161], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e-33], t, If[LessEqual[a, 6.1e+119], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.6e16 or 6.1e119 < a

   1. Initial program 91.7%

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

   2. Taylor expanded in a around inf 53.3%

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

   if -3.6e16 < a < -1.72000000000000008e-307 or 1.45e-161 < a < 8.49999999999999945e-33

   1. Initial program 67.5%

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

   2. Taylor expanded in z around inf 40.5%

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

   if -1.72000000000000008e-307 < a < 1.45e-161

   1. Initial program 73.0%

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

   2. Taylor expanded in y around inf 72.4%

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

      1. div-sub 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r/ 70.6%

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

      4. associate-/l* 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in a around 0 61.0%

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

      1. associate-*r/ 61.0%

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

      2. associate-*r* 61.0%

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

      3. mul-1-neg 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in t around 0 42.0%

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

      1. associate-/l* 45.3%

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

   10. Simplified 45.3%

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

   if 8.49999999999999945e-33 < a < 6.1e119

   1. Initial program 83.7%

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

   2. Taylor expanded in a around inf 70.6%

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

   3. Taylor expanded in t around inf 37.0%

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

      1. div-sub 37.0%

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

   5. Simplified 37.0%

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

   6. Taylor expanded in y around inf 39.6%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.72 \cdot 10^{-307}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-161}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-33}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{+119}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 68.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2900:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-239}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-39}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2900.0)
   (- x (/ (- x t) (/ a y)))
   (if (<= a -1.8e-239)
     (* t (/ (- y z) (- a z)))
     (if (<= a 8.6e-39) (+ t (* y (/ (- x t) z))) (+ x (/ y (/ a (- t x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2900.0) {
		tmp = x - ((x - t) / (a / y));
	} else if (a <= -1.8e-239) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 8.6e-39) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (y / (a / (t - 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 <= (-2900.0d0)) then
        tmp = x - ((x - t) / (a / y))
    else if (a <= (-1.8d-239)) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 8.6d-39) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + (y / (a / (t - 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 <= -2900.0) {
		tmp = x - ((x - t) / (a / y));
	} else if (a <= -1.8e-239) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 8.6e-39) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2900.0:
		tmp = x - ((x - t) / (a / y))
	elif a <= -1.8e-239:
		tmp = t * ((y - z) / (a - z))
	elif a <= 8.6e-39:
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2900.0)
		tmp = Float64(x - Float64(Float64(x - t) / Float64(a / y)));
	elseif (a <= -1.8e-239)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 8.6e-39)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2900.0)
		tmp = x - ((x - t) / (a / y));
	elseif (a <= -1.8e-239)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 8.6e-39)
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2900.0], N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.8e-239], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.6e-39], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2900

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

      2. associate-*l/ 79.8%

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

      3. associate-*r/ 95.2%

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

      4. clear-num 94.1%

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

      5. un-div-inv 94.1%

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

   3. Applied egg-rr 94.1%

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

   4. Taylor expanded in z around 0 73.9%

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

   if -2900 < a < -1.8000000000000001e-239

   1. Initial program 64.1%

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

   2. Taylor expanded in t around inf 72.9%

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

      1. div-sub 72.9%

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

   4. Simplified 72.9%

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

   if -1.8000000000000001e-239 < a < 8.5999999999999999e-39

   1. Initial program 70.1%

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

   2. Taylor expanded in z around inf 89.2%

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

      1. +-commutative 89.2%

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

      2. associate--l+ 89.2%

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

      3. associate-*r/ 89.2%

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

      4. associate-*r/ 89.2%

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

      5. div-sub 89.2%

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

      6. distribute-lft-out-- 89.2%

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

      7. mul-1-neg 89.2%

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

      8. distribute-neg-frac 89.2%

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

      9. unsub-neg 89.2%

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

      10. distribute-rgt-out-- 89.2%

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

   4. Simplified 89.2%

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

   5. Taylor expanded in y around inf 83.7%

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

      1. associate-*r/ 83.6%

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

   7. Simplified 83.6%

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

   if 8.5999999999999999e-39 < a

   1. Initial program 89.3%

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

   2. Taylor expanded in z around 0 62.8%

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

      1. +-commutative 62.8%

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

      2. associate-/l* 74.7%

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

   4. Simplified 74.7%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2900:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-239}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-39}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 19: 71.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -51000 \lor \neg \left(a \leq 1.55 \cdot 10^{-40}\right):\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -51000.0) (not (<= a 1.55e-40)))
   (+ x (* (- z y) (/ (- x t) a)))
   (+ t (/ (* y (- x t)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -51000.0) || !(a <= 1.55e-40)) {
		tmp = x + ((z - y) * ((x - t) / a));
	} else {
		tmp = t + ((y * (x - t)) / 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 ((a <= (-51000.0d0)) .or. (.not. (a <= 1.55d-40))) then
        tmp = x + ((z - y) * ((x - t) / a))
    else
        tmp = t + ((y * (x - t)) / 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 ((a <= -51000.0) || !(a <= 1.55e-40)) {
		tmp = x + ((z - y) * ((x - t) / a));
	} else {
		tmp = t + ((y * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -51000.0) or not (a <= 1.55e-40):
		tmp = x + ((z - y) * ((x - t) / a))
	else:
		tmp = t + ((y * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -51000.0) || !(a <= 1.55e-40))
		tmp = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / a)));
	else
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -51000.0) || ~((a <= 1.55e-40)))
		tmp = x + ((z - y) * ((x - t) / a));
	else
		tmp = t + ((y * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -51000.0], N[Not[LessEqual[a, 1.55e-40]], $MachinePrecision]], N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -51000 or 1.55000000000000005e-40 < a

   1. Initial program 90.1%

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

   2. Taylor expanded in a around inf 77.2%

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

   if -51000 < a < 1.55000000000000005e-40

   1. Initial program 67.6%

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

   2. Taylor expanded in z around inf 82.2%

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

      1. +-commutative 82.2%

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

      2. associate--l+ 82.2%

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

      3. associate-*r/ 82.2%

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

      4. associate-*r/ 82.2%

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

      5. div-sub 83.0%

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

      6. distribute-lft-out-- 83.0%

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

      7. mul-1-neg 83.0%

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

      8. distribute-neg-frac 83.0%

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

      9. unsub-neg 83.0%

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

      10. distribute-rgt-out-- 83.0%

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

   4. Simplified 83.0%

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

   5. Taylor expanded in y around inf 76.8%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -51000 \lor \neg \left(a \leq 1.55 \cdot 10^{-40}\right):\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \end{array} \]

Alternative 20: 76.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.3e+103)
   (* t (/ (- y z) (- a z)))
   (if (<= z 1.5e+73)
     (- x (/ (- x t) (/ (- a z) y)))
     (+ t (* y (/ (- x t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.3e+103) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 1.5e+73) {
		tmp = x - ((x - t) / ((a - z) / y));
	} else {
		tmp = t + (y * ((x - t) / 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 <= (-6.3d+103)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 1.5d+73) then
        tmp = x - ((x - t) / ((a - z) / y))
    else
        tmp = t + (y * ((x - t) / 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 <= -6.3e+103) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 1.5e+73) {
		tmp = x - ((x - t) / ((a - z) / y));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.3e+103:
		tmp = t * ((y - z) / (a - z))
	elif z <= 1.5e+73:
		tmp = x - ((x - t) / ((a - z) / y))
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.3e+103)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 1.5e+73)
		tmp = Float64(x - Float64(Float64(x - t) / Float64(Float64(a - z) / y)));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.3e+103)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 1.5e+73)
		tmp = x - ((x - t) / ((a - z) / y));
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.3e+103], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+73], N[(x - N[(N[(x - t), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.29999999999999969e103

   1. Initial program 64.8%

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

   2. Taylor expanded in t around inf 76.0%

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

      1. div-sub 76.0%

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

   4. Simplified 76.0%

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

   if -6.29999999999999969e103 < z < 1.50000000000000005e73

   1. Initial program 87.6%

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

      1. *-commutative 87.6%

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

      2. associate-*l/ 84.3%

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

      3. associate-*r/ 90.2%

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

      4. clear-num 89.7%

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

      5. un-div-inv 90.1%

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

   3. Applied egg-rr 90.1%

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

   4. Taylor expanded in y around inf 80.5%

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

   if 1.50000000000000005e73 < z

   1. Initial program 59.6%

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

   2. Taylor expanded in z around inf 75.5%

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

      1. +-commutative 75.5%

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

      2. associate--l+ 75.5%

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

      3. associate-*r/ 75.5%

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

      4. associate-*r/ 75.5%

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

      5. div-sub 75.5%

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

      6. distribute-lft-out-- 75.5%

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

      7. mul-1-neg 75.5%

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

      8. distribute-neg-frac 75.5%

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

      9. unsub-neg 75.5%

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

      10. distribute-rgt-out-- 78.2%

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

   4. Simplified 78.2%

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

   5. Taylor expanded in y around inf 69.6%

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

      1. associate-*r/ 75.6%

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

   7. Simplified 75.6%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{+103}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]

Alternative 21: 72.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.000175:\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-42}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.000175)
   (- x (/ (- x t) (/ (- a z) y)))
   (if (<= a 3.6e-42)
     (+ t (/ (* (- y a) (- x t)) z))
     (+ x (* (- z y) (/ (- x t) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.000175) {
		tmp = x - ((x - t) / ((a - z) / y));
	} else if (a <= 3.6e-42) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else {
		tmp = x + ((z - y) * ((x - t) / 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 (a <= (-0.000175d0)) then
        tmp = x - ((x - t) / ((a - z) / y))
    else if (a <= 3.6d-42) then
        tmp = t + (((y - a) * (x - t)) / z)
    else
        tmp = x + ((z - y) * ((x - t) / 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 (a <= -0.000175) {
		tmp = x - ((x - t) / ((a - z) / y));
	} else if (a <= 3.6e-42) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else {
		tmp = x + ((z - y) * ((x - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.000175:
		tmp = x - ((x - t) / ((a - z) / y))
	elif a <= 3.6e-42:
		tmp = t + (((y - a) * (x - t)) / z)
	else:
		tmp = x + ((z - y) * ((x - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.000175)
		tmp = Float64(x - Float64(Float64(x - t) / Float64(Float64(a - z) / y)));
	elseif (a <= 3.6e-42)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	else
		tmp = Float64(x + Float64(Float64(z - y) * Float64(Float64(x - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -0.000175)
		tmp = x - ((x - t) / ((a - z) / y));
	elseif (a <= 3.6e-42)
		tmp = t + (((y - a) * (x - t)) / z);
	else
		tmp = x + ((z - y) * ((x - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.000175], N[(x - N[(N[(x - t), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e-42], N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - y), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.74999999999999998e-4

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l/ 79.0%

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

      3. associate-*r/ 94.0%

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

      4. clear-num 92.9%

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

      5. un-div-inv 92.9%

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

   3. Applied egg-rr 92.9%

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

   4. Taylor expanded in y around inf 76.7%

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

   if -1.74999999999999998e-4 < a < 3.6000000000000002e-42

   1. Initial program 67.9%

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

   2. Taylor expanded in z around inf 82.7%

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

      1. +-commutative 82.7%

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

      2. associate--l+ 82.7%

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

      3. associate-*r/ 82.7%

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

      4. associate-*r/ 82.7%

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

      5. div-sub 83.6%

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

      6. distribute-lft-out-- 83.6%

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

      7. mul-1-neg 83.6%

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

      8. distribute-neg-frac 83.6%

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

      9. unsub-neg 83.6%

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

      10. distribute-rgt-out-- 83.6%

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

   4. Simplified 83.6%

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

   if 3.6000000000000002e-42 < a

   1. Initial program 89.3%

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

   2. Taylor expanded in a around inf 77.5%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.000175:\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-42}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - y\right) \cdot \frac{x - t}{a}\\ \end{array} \]

Alternative 22: 58.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+107} \lor \neg \left(a \leq 4.9 \cdot 10^{+123}\right):\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.8e+107) (not (<= a 4.9e+123)))
   (- x (/ (* z t) a))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.8e+107) || !(a <= 4.9e+123)) {
		tmp = x - ((z * t) / a);
	} else {
		tmp = t * ((y - z) / (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 ((a <= (-7.8d+107)) .or. (.not. (a <= 4.9d+123))) then
        tmp = x - ((z * t) / a)
    else
        tmp = t * ((y - z) / (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 ((a <= -7.8e+107) || !(a <= 4.9e+123)) {
		tmp = x - ((z * t) / a);
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.8e+107) or not (a <= 4.9e+123):
		tmp = x - ((z * t) / a)
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.8e+107) || !(a <= 4.9e+123))
		tmp = Float64(x - Float64(Float64(z * t) / a));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7.8e+107) || ~((a <= 4.9e+123)))
		tmp = x - ((z * t) / a);
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7.8e+107], N[Not[LessEqual[a, 4.9e+123]], $MachinePrecision]], N[(x - N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.7999999999999997e107 or 4.89999999999999976e123 < a

   1. Initial program 91.9%

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

   2. Taylor expanded in a around inf 81.9%

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

   3. Taylor expanded in y around 0 61.6%

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

      1. +-commutative 61.6%

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

      2. *-commutative 61.6%

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

      3. mul-1-neg 61.6%

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

      4. unsub-neg 61.6%

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

      5. associate-/l* 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in t around inf 65.8%

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

   if -7.7999999999999997e107 < a < 4.89999999999999976e123

   1. Initial program 73.8%

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

   2. Taylor expanded in t around inf 64.1%

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

      1. div-sub 64.1%

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

   4. Simplified 64.1%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+107} \lor \neg \left(a \leq 4.9 \cdot 10^{+123}\right):\\ \;\;\;\;x - \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 23: 59.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+172} \lor \neg \left(a \leq 2.35 \cdot 10^{+123}\right):\\ \;\;\;\;x \cdot \left(1 + \frac{z - y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.4e+172) (not (<= a 2.35e+123)))
   (* x (+ 1.0 (/ (- z y) a)))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.4e+172) || !(a <= 2.35e+123)) {
		tmp = x * (1.0 + ((z - y) / a));
	} else {
		tmp = t * ((y - z) / (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 ((a <= (-4.4d+172)) .or. (.not. (a <= 2.35d+123))) then
        tmp = x * (1.0d0 + ((z - y) / a))
    else
        tmp = t * ((y - z) / (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 ((a <= -4.4e+172) || !(a <= 2.35e+123)) {
		tmp = x * (1.0 + ((z - y) / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.4e+172) or not (a <= 2.35e+123):
		tmp = x * (1.0 + ((z - y) / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.4e+172) || !(a <= 2.35e+123))
		tmp = Float64(x * Float64(1.0 + Float64(Float64(z - y) / a)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.4e+172) || ~((a <= 2.35e+123)))
		tmp = x * (1.0 + ((z - y) / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.4e+172], N[Not[LessEqual[a, 2.35e+123]], $MachinePrecision]], N[(x * N[(1.0 + N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.4000000000000002e172 or 2.3499999999999999e123 < a

   1. Initial program 92.6%

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

   2. Taylor expanded in a around inf 86.7%

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

   3. Taylor expanded in x around inf 74.8%

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

      1. *-commutative 74.8%

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

      2. div-sub 74.8%

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

      3. mul-1-neg 74.8%

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

      4. unsub-neg 74.8%

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

      5. div-sub 74.8%

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

   5. Simplified 74.8%

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

   if -4.4000000000000002e172 < a < 2.3499999999999999e123

   1. Initial program 74.8%

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

   2. Taylor expanded in t around inf 62.9%

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

      1. div-sub 62.9%

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

   4. Simplified 62.9%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{+172} \lor \neg \left(a \leq 2.35 \cdot 10^{+123}\right):\\ \;\;\;\;x \cdot \left(1 + \frac{z - y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 24: 63.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4100 \lor \neg \left(a \leq 8 \cdot 10^{-39}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4100.0) (not (<= a 8e-39)))
   (+ x (/ y (/ a (- t x))))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4100.0) || !(a <= 8e-39)) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t * ((y - z) / (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 ((a <= (-4100.0d0)) .or. (.not. (a <= 8d-39))) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t * ((y - z) / (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 ((a <= -4100.0) || !(a <= 8e-39)) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4100.0) or not (a <= 8e-39):
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4100.0) || !(a <= 8e-39))
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4100.0) || ~((a <= 8e-39)))
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4100.0], N[Not[LessEqual[a, 8e-39]], $MachinePrecision]], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4100 or 7.99999999999999943e-39 < a

   1. Initial program 90.1%

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

   2. Taylor expanded in z around 0 64.8%

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

      1. +-commutative 64.8%

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

      2. associate-/l* 73.8%

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

   4. Simplified 73.8%

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

   if -4100 < a < 7.99999999999999943e-39

   1. Initial program 67.6%

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

   2. Taylor expanded in t around inf 70.9%

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

      1. div-sub 70.9%

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

   4. Simplified 70.9%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4100 \lor \neg \left(a \leq 8 \cdot 10^{-39}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 25: 63.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -750:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -750.0)
   (- x (/ (- x t) (/ a y)))
   (if (<= a 1.8e-39) (* t (/ (- y z) (- a z))) (+ x (/ y (/ a (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -750.0) {
		tmp = x - ((x - t) / (a / y));
	} else if (a <= 1.8e-39) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - 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 <= (-750.0d0)) then
        tmp = x - ((x - t) / (a / y))
    else if (a <= 1.8d-39) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y / (a / (t - 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 <= -750.0) {
		tmp = x - ((x - t) / (a / y));
	} else if (a <= 1.8e-39) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -750.0:
		tmp = x - ((x - t) / (a / y))
	elif a <= 1.8e-39:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -750.0)
		tmp = Float64(x - Float64(Float64(x - t) / Float64(a / y)));
	elseif (a <= 1.8e-39)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -750.0)
		tmp = x - ((x - t) / (a / y));
	elseif (a <= 1.8e-39)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -750.0], N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e-39], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -750

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

      2. associate-*l/ 79.8%

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

      3. associate-*r/ 95.2%

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

      4. clear-num 94.1%

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

      5. un-div-inv 94.1%

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

   3. Applied egg-rr 94.1%

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

   4. Taylor expanded in z around 0 73.9%

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

   if -750 < a < 1.8e-39

   1. Initial program 67.6%

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

   2. Taylor expanded in t around inf 70.9%

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

      1. div-sub 70.9%

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

   4. Simplified 70.9%

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

   if 1.8e-39 < a

   1. Initial program 89.3%

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

   2. Taylor expanded in z around 0 62.8%

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

      1. +-commutative 62.8%

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

      2. associate-/l* 74.7%

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

   4. Simplified 74.7%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -750:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 26: 67.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6500:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-40}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6500.0)
   (- x (/ (- x t) (/ a y)))
   (if (<= a 6.5e-40) (+ t (/ (* y (- x t)) z)) (+ x (/ y (/ a (- t x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6500.0) {
		tmp = x - ((x - t) / (a / y));
	} else if (a <= 6.5e-40) {
		tmp = t + ((y * (x - t)) / z);
	} else {
		tmp = x + (y / (a / (t - 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 <= (-6500.0d0)) then
        tmp = x - ((x - t) / (a / y))
    else if (a <= 6.5d-40) then
        tmp = t + ((y * (x - t)) / z)
    else
        tmp = x + (y / (a / (t - 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 <= -6500.0) {
		tmp = x - ((x - t) / (a / y));
	} else if (a <= 6.5e-40) {
		tmp = t + ((y * (x - t)) / z);
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6500.0:
		tmp = x - ((x - t) / (a / y))
	elif a <= 6.5e-40:
		tmp = t + ((y * (x - t)) / z)
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6500.0)
		tmp = Float64(x - Float64(Float64(x - t) / Float64(a / y)));
	elseif (a <= 6.5e-40)
		tmp = Float64(t + Float64(Float64(y * Float64(x - t)) / z));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6500.0)
		tmp = x - ((x - t) / (a / y));
	elseif (a <= 6.5e-40)
		tmp = t + ((y * (x - t)) / z);
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6500.0], N[(x - N[(N[(x - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-40], N[(t + N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -6500

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

      2. associate-*l/ 79.8%

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

      3. associate-*r/ 95.2%

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

      4. clear-num 94.1%

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

      5. un-div-inv 94.1%

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

   3. Applied egg-rr 94.1%

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

   4. Taylor expanded in z around 0 73.9%

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

   if -6500 < a < 6.4999999999999999e-40

   1. Initial program 67.6%

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

   2. Taylor expanded in z around inf 82.2%

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

      1. +-commutative 82.2%

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

      2. associate--l+ 82.2%

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

      3. associate-*r/ 82.2%

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

      4. associate-*r/ 82.2%

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

      5. div-sub 83.0%

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

      6. distribute-lft-out-- 83.0%

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

      7. mul-1-neg 83.0%

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

      8. distribute-neg-frac 83.0%

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

      9. unsub-neg 83.0%

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

      10. distribute-rgt-out-- 83.0%

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

   4. Simplified 83.0%

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

   5. Taylor expanded in y around inf 76.8%

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

   if 6.4999999999999999e-40 < a

   1. Initial program 89.3%

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

   2. Taylor expanded in z around 0 62.8%

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

      1. +-commutative 62.8%

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

      2. associate-/l* 74.7%

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

   4. Simplified 74.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6500:\\ \;\;\;\;x - \frac{x - t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-40}:\\ \;\;\;\;t + \frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]

Alternative 27: 36.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-295}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-216}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+111}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.7e+16)
   x
   (if (<= a 1.55e-295)
     t
     (if (<= a 6.8e-216) (* t (/ y a)) (if (<= a 3.6e+111) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e+16) {
		tmp = x;
	} else if (a <= 1.55e-295) {
		tmp = t;
	} else if (a <= 6.8e-216) {
		tmp = t * (y / a);
	} else if (a <= 3.6e+111) {
		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 <= (-3.7d+16)) then
        tmp = x
    else if (a <= 1.55d-295) then
        tmp = t
    else if (a <= 6.8d-216) then
        tmp = t * (y / a)
    else if (a <= 3.6d+111) 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 <= -3.7e+16) {
		tmp = x;
	} else if (a <= 1.55e-295) {
		tmp = t;
	} else if (a <= 6.8e-216) {
		tmp = t * (y / a);
	} else if (a <= 3.6e+111) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.7e+16:
		tmp = x
	elif a <= 1.55e-295:
		tmp = t
	elif a <= 6.8e-216:
		tmp = t * (y / a)
	elif a <= 3.6e+111:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.7e+16)
		tmp = x;
	elseif (a <= 1.55e-295)
		tmp = t;
	elseif (a <= 6.8e-216)
		tmp = Float64(t * Float64(y / a));
	elseif (a <= 3.6e+111)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.7e+16)
		tmp = x;
	elseif (a <= 1.55e-295)
		tmp = t;
	elseif (a <= 6.8e-216)
		tmp = t * (y / a);
	elseif (a <= 3.6e+111)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.7e+16], x, If[LessEqual[a, 1.55e-295], t, If[LessEqual[a, 6.8e-216], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e+111], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.7e16 or 3.6000000000000002e111 < a

   1. Initial program 92.0%

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

   2. Taylor expanded in a around inf 52.3%

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

   if -3.7e16 < a < 1.5500000000000001e-295 or 6.7999999999999995e-216 < a < 3.6000000000000002e111

   1. Initial program 71.0%

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

   2. Taylor expanded in z around inf 35.9%

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

   if 1.5500000000000001e-295 < a < 6.7999999999999995e-216

   1. Initial program 68.1%

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

   2. Taylor expanded in a around inf 34.4%

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

   3. Taylor expanded in t around inf 54.5%

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

      1. div-sub 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in y around inf 51.5%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-295}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-216}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+111}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 28: 37.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-302}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-161}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+113}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.8e+14)
   x
   (if (<= a 6.5e-302)
     t
     (if (<= a 1.55e-161) (/ y (/ z x)) (if (<= a 4e+113) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.8e+14) {
		tmp = x;
	} else if (a <= 6.5e-302) {
		tmp = t;
	} else if (a <= 1.55e-161) {
		tmp = y / (z / x);
	} else if (a <= 4e+113) {
		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 <= (-3.8d+14)) then
        tmp = x
    else if (a <= 6.5d-302) then
        tmp = t
    else if (a <= 1.55d-161) then
        tmp = y / (z / x)
    else if (a <= 4d+113) 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 <= -3.8e+14) {
		tmp = x;
	} else if (a <= 6.5e-302) {
		tmp = t;
	} else if (a <= 1.55e-161) {
		tmp = y / (z / x);
	} else if (a <= 4e+113) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.8e+14:
		tmp = x
	elif a <= 6.5e-302:
		tmp = t
	elif a <= 1.55e-161:
		tmp = y / (z / x)
	elif a <= 4e+113:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.8e+14)
		tmp = x;
	elseif (a <= 6.5e-302)
		tmp = t;
	elseif (a <= 1.55e-161)
		tmp = Float64(y / Float64(z / x));
	elseif (a <= 4e+113)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.8e+14)
		tmp = x;
	elseif (a <= 6.5e-302)
		tmp = t;
	elseif (a <= 1.55e-161)
		tmp = y / (z / x);
	elseif (a <= 4e+113)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.8e+14], x, If[LessEqual[a, 6.5e-302], t, If[LessEqual[a, 1.55e-161], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e+113], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.8e14 or 4e113 < a

   1. Initial program 92.0%

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

   2. Taylor expanded in a around inf 52.3%

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

   if -3.8e14 < a < 6.4999999999999995e-302 or 1.5499999999999999e-161 < a < 4e113

   1. Initial program 70.3%

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

   2. Taylor expanded in z around inf 37.0%

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

   if 6.4999999999999995e-302 < a < 1.5499999999999999e-161

   1. Initial program 73.0%

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

   2. Taylor expanded in y around inf 72.4%

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

      1. div-sub 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r/ 70.6%

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

      4. associate-/l* 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in a around 0 61.0%

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

      1. associate-*r/ 61.0%

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

      2. associate-*r* 61.0%

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

      3. mul-1-neg 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in t around 0 42.0%

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

      1. associate-/l* 45.3%

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

   10. Simplified 45.3%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-302}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-161}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+113}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 29: 38.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -50000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+111}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -50000000000000.0) x (if (<= a 3.6e+111) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -50000000000000.0) {
		tmp = x;
	} else if (a <= 3.6e+111) {
		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 <= (-50000000000000.0d0)) then
        tmp = x
    else if (a <= 3.6d+111) 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 <= -50000000000000.0) {
		tmp = x;
	} else if (a <= 3.6e+111) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -50000000000000.0:
		tmp = x
	elif a <= 3.6e+111:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -50000000000000.0)
		tmp = x;
	elseif (a <= 3.6e+111)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -50000000000000.0)
		tmp = x;
	elseif (a <= 3.6e+111)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -50000000000000.0], x, If[LessEqual[a, 3.6e+111], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -5e13 or 3.6000000000000002e111 < a

   1. Initial program 92.0%

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

   2. Taylor expanded in a around inf 52.3%

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

   if -5e13 < a < 3.6000000000000002e111

   1. Initial program 70.7%

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

   2. Taylor expanded in z around inf 34.9%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -50000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+111}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 30: 25.4% 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 79.1%

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

2. Taylor expanded in z around inf 25.7%

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

3. Final simplification 25.7%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023196 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))