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

Percentage Accurate: 67.5% → 90.8%

Time: 16.3s

Alternatives: 23

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t - x}}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-246}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a + y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+291}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) (- t x)))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-246)
       t_2
       (if (<= t_2 0.0)
         (+ t (/ (+ (* (- t x) a) (* y (- x t))) z))
         (if (<= t_2 5e+291) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-246) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + ((((t - x) * a) + (y * (x - t))) / z);
	} else if (t_2 <= 5e+291) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -1e-246) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + ((((t - x) * a) + (y * (x - t))) / z);
	} else if (t_2 <= 5e+291) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / (t - x)))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-246:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t + ((((t - x) * a) + (y * (x - t))) / z)
	elif t_2 <= 5e+291:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e-246)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(Float64(t - x) * a) + Float64(y * Float64(x - t))) / z));
	elseif (t_2 <= 5e+291)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / ((a - z) / (t - x)));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-246)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t + ((((t - x) * a) + (y * (x - t))) / z);
	elseif (t_2 <= 5e+291)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e-246], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(N[(t - x), $MachinePrecision] * a), $MachinePrecision] + N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+291], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 5.0000000000000001e291 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 44.9%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

      1. clear-num 87.8%

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

      2. un-div-inv 88.0%

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

   6. Applied egg-rr 88.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.99999999999999956e-247 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 5.0000000000000001e291

   1. Initial program 97.0%

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

   if -9.99999999999999956e-247 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.0%

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

      1. associate-/l* 3.8%

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

   3. Simplified 3.8%

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

   5. Taylor expanded in z around -inf 99.5%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -\infty:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-246}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a + y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 5 \cdot 10^{+291}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-246} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a + y \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (or (<= t_1 -1e-246) (not (<= t_1 0.0)))
     (fma (- t x) (/ (- y z) (- a z)) x)
     (+ t (/ (+ (* (- t x) a) (* y (- x t))) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if ((t_1 <= -1e-246) || !(t_1 <= 0.0)) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else {
		tmp = t + ((((t - x) * a) + (y * (x - t))) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if ((t_1 <= -1e-246) || !(t_1 <= 0.0))
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	else
		tmp = Float64(t + Float64(Float64(Float64(Float64(t - x) * a) + Float64(y * Float64(x - t))) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-246], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t + N[(N[(N[(N[(t - x), $MachinePrecision] * a), $MachinePrecision] + N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.99999999999999956e-247 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 73.8%

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

      1. +-commutative 73.8%

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

      2. *-commutative 73.8%

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

      3. associate-/l* 92.2%

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

      4. fma-define 92.2%

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

   3. Simplified 92.2%

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

   if -9.99999999999999956e-247 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.0%

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

      1. associate-/l* 3.8%

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

   3. Simplified 3.8%

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

   5. Taylor expanded in z around -inf 99.5%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-246} \lor \neg \left(x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0\right):\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot a + y \cdot \left(x - t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t - x}}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-246}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+291}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) (- t x)))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-246)
       t_2
       (if (<= t_2 0.0)
         (+ t (/ (* (- y a) (- x t)) z))
         (if (<= t_2 5e+291) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-246) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else if (t_2 <= 5e+291) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -1e-246) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else if (t_2 <= 5e+291) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / (t - x)))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-246:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t + (((y - a) * (x - t)) / z)
	elif t_2 <= 5e+291:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e-246)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	elseif (t_2 <= 5e+291)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / ((a - z) / (t - x)));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-246)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t + (((y - a) * (x - t)) / z);
	elseif (t_2 <= 5e+291)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e-246], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+291], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 5.0000000000000001e291 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 44.9%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

      1. clear-num 87.8%

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

      2. un-div-inv 88.0%

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

   6. Applied egg-rr 88.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.99999999999999956e-247 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 5.0000000000000001e291

   1. Initial program 97.0%

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

   if -9.99999999999999956e-247 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.0%

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

      1. associate-/l* 3.8%

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

   3. Simplified 3.8%

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

   5. Taylor expanded in z around inf 99.4%

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

      1. associate--l+ 99.4%

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

      2. associate-*r/ 99.4%

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

      3. associate-*r/ 99.4%

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

      4. mul-1-neg 99.4%

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

      5. div-sub 99.5%

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

      6. mul-1-neg 99.5%

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

      7. distribute-lft-out-- 99.5%

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

      8. associate-*r/ 99.5%

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

      9. mul-1-neg 99.5%

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

      10. unsub-neg 99.5%

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

      11. distribute-rgt-out-- 99.4%

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

   7. Simplified 99.4%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -\infty:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-246}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 5 \cdot 10^{+291}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-246}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+291}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z)))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-246)
       t_2
       (if (<= t_2 0.0)
         (+ t (/ (* (- y a) (- x t)) z))
         (if (<= t_2 5e+291) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-246) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else if (t_2 <= 5e+291) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -1e-246) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else if (t_2 <= 5e+291) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-246:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t + (((y - a) * (x - t)) / z)
	elif t_2 <= 5e+291:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e-246)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	elseif (t_2 <= 5e+291)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-246)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t + (((y - a) * (x - t)) / z);
	elseif (t_2 <= 5e+291)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e-246], t$95$2, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+291], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 5.0000000000000001e291 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 44.9%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.99999999999999956e-247 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 5.0000000000000001e291

   1. Initial program 97.0%

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

   if -9.99999999999999956e-247 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 4.0%

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

      1. associate-/l* 3.8%

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

   3. Simplified 3.8%

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

   5. Taylor expanded in z around inf 99.4%

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

      1. associate--l+ 99.4%

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

      2. associate-*r/ 99.4%

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

      3. associate-*r/ 99.4%

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

      4. mul-1-neg 99.4%

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

      5. div-sub 99.5%

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

      6. mul-1-neg 99.5%

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

      7. distribute-lft-out-- 99.5%

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

      8. associate-*r/ 99.5%

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

      9. mul-1-neg 99.5%

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

      10. unsub-neg 99.5%

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

      11. distribute-rgt-out-- 99.4%

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

   7. Simplified 99.4%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -\infty:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-246}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 0:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 5 \cdot 10^{+291}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-129}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-49}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-7}:\\ \;\;\;\;x + z \cdot \frac{x - t}{a}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -3.3e+41)
     t_1
     (if (<= z -5.5e-70)
       (* y (/ (- t x) (- a z)))
       (if (<= z 1.85e-129)
         (+ x (* y (/ (- t x) a)))
         (if (<= z 2.7e-49)
           (/ (* y (- t x)) (- a z))
           (if (<= z 9.2e-7)
             (+ x (* z (/ (- x t) a)))
             (if (<= z 5.8e+140) (* y (/ (- x t) z)) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -3.3e+41) {
		tmp = t_1;
	} else if (z <= -5.5e-70) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.85e-129) {
		tmp = x + (y * ((t - x) / a));
	} else if (z <= 2.7e-49) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 9.2e-7) {
		tmp = x + (z * ((x - t) / a));
	} else if (z <= 5.8e+140) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-3.3d+41)) then
        tmp = t_1
    else if (z <= (-5.5d-70)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 1.85d-129) then
        tmp = x + (y * ((t - x) / a))
    else if (z <= 2.7d-49) then
        tmp = (y * (t - x)) / (a - z)
    else if (z <= 9.2d-7) then
        tmp = x + (z * ((x - t) / a))
    else if (z <= 5.8d+140) then
        tmp = y * ((x - t) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -3.3e+41) {
		tmp = t_1;
	} else if (z <= -5.5e-70) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 1.85e-129) {
		tmp = x + (y * ((t - x) / a));
	} else if (z <= 2.7e-49) {
		tmp = (y * (t - x)) / (a - z);
	} else if (z <= 9.2e-7) {
		tmp = x + (z * ((x - t) / a));
	} else if (z <= 5.8e+140) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -3.3e+41:
		tmp = t_1
	elif z <= -5.5e-70:
		tmp = y * ((t - x) / (a - z))
	elif z <= 1.85e-129:
		tmp = x + (y * ((t - x) / a))
	elif z <= 2.7e-49:
		tmp = (y * (t - x)) / (a - z)
	elif z <= 9.2e-7:
		tmp = x + (z * ((x - t) / a))
	elif z <= 5.8e+140:
		tmp = y * ((x - t) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -3.3e+41)
		tmp = t_1;
	elseif (z <= -5.5e-70)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 1.85e-129)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (z <= 2.7e-49)
		tmp = Float64(Float64(y * Float64(t - x)) / Float64(a - z));
	elseif (z <= 9.2e-7)
		tmp = Float64(x + Float64(z * Float64(Float64(x - t) / a)));
	elseif (z <= 5.8e+140)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -3.3e+41)
		tmp = t_1;
	elseif (z <= -5.5e-70)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 1.85e-129)
		tmp = x + (y * ((t - x) / a));
	elseif (z <= 2.7e-49)
		tmp = (y * (t - x)) / (a - z);
	elseif (z <= 9.2e-7)
		tmp = x + (z * ((x - t) / a));
	elseif (z <= 5.8e+140)
		tmp = y * ((x - t) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+41], t$95$1, If[LessEqual[z, -5.5e-70], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e-129], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e-49], N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-7], N[(x + N[(z * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+140], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.3e41 or 5.7999999999999998e140 < z

   1. Initial program 45.5%

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

      1. associate-/l* 71.5%

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

   3. Simplified 71.5%

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

   5. Taylor expanded in x around 0 37.0%

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

      1. associate-/l* 65.9%

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

   7. Simplified 65.9%

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

   if -3.3e41 < z < -5.5000000000000001e-70

   1. Initial program 76.9%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in y around inf 71.8%

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

      1. div-sub 71.8%

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

   7. Simplified 71.8%

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

   if -5.5000000000000001e-70 < z < 1.8500000000000001e-129

   1. Initial program 89.1%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in z around 0 74.7%

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

      1. associate-/l* 81.4%

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

   7. Simplified 81.4%

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

   if 1.8500000000000001e-129 < z < 2.7e-49

   1. Initial program 83.9%

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

      1. associate-/l* 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in y around -inf 74.0%

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

   if 2.7e-49 < z < 9.1999999999999998e-7

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 71.5%

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

      1. mul-1-neg 71.5%

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

      2. unsub-neg 71.5%

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

      3. associate-/l* 80.6%

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

   7. Simplified 80.6%

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

   8. Taylor expanded in z around 0 72.7%

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

      1. associate-/l* 72.9%

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

   10. Simplified 72.9%

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

   if 9.1999999999999998e-7 < z < 5.7999999999999998e140

   1. Initial program 52.3%

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

      1. associate-/l* 64.5%

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

   3. Simplified 64.5%

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

   5. Taylor expanded in y around inf 51.7%

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

      1. div-sub 51.7%

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

   7. Simplified 51.7%

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

   8. Taylor expanded in a around 0 44.0%

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

      1. mul-1-neg 44.0%

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

      2. associate-/l* 52.4%

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

      3. distribute-rgt-neg-in 52.4%

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

      4. distribute-neg-frac2 52.4%

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

   10. Simplified 52.4%

       \[\leadsto \color{blue}{y \cdot \frac{t - x}{-z}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-129}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-49}:\\ \;\;\;\;\frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-7}:\\ \;\;\;\;x + z \cdot \frac{x - t}{a}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -1.9e+84)
     t_2
     (if (<= t -3.8e+36)
       t_1
       (if (<= t -1.3e-36)
         t_2
         (if (<= t -1.45e-163)
           t_1
           (if (<= t -1.9e-236)
             (* x (/ y z))
             (if (<= t 7.8e+24) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.9e+84) {
		tmp = t_2;
	} else if (t <= -3.8e+36) {
		tmp = t_1;
	} else if (t <= -1.3e-36) {
		tmp = t_2;
	} else if (t <= -1.45e-163) {
		tmp = t_1;
	} else if (t <= -1.9e-236) {
		tmp = x * (y / z);
	} else if (t <= 7.8e+24) {
		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 = x - (x * (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-1.9d+84)) then
        tmp = t_2
    else if (t <= (-3.8d+36)) then
        tmp = t_1
    else if (t <= (-1.3d-36)) then
        tmp = t_2
    else if (t <= (-1.45d-163)) then
        tmp = t_1
    else if (t <= (-1.9d-236)) then
        tmp = x * (y / z)
    else if (t <= 7.8d+24) 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 = x - (x * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.9e+84) {
		tmp = t_2;
	} else if (t <= -3.8e+36) {
		tmp = t_1;
	} else if (t <= -1.3e-36) {
		tmp = t_2;
	} else if (t <= -1.45e-163) {
		tmp = t_1;
	} else if (t <= -1.9e-236) {
		tmp = x * (y / z);
	} else if (t <= 7.8e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -1.9e+84:
		tmp = t_2
	elif t <= -3.8e+36:
		tmp = t_1
	elif t <= -1.3e-36:
		tmp = t_2
	elif t <= -1.45e-163:
		tmp = t_1
	elif t <= -1.9e-236:
		tmp = x * (y / z)
	elif t <= 7.8e+24:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -1.9e+84)
		tmp = t_2;
	elseif (t <= -3.8e+36)
		tmp = t_1;
	elseif (t <= -1.3e-36)
		tmp = t_2;
	elseif (t <= -1.45e-163)
		tmp = t_1;
	elseif (t <= -1.9e-236)
		tmp = Float64(x * Float64(y / z));
	elseif (t <= 7.8e+24)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -1.9e+84)
		tmp = t_2;
	elseif (t <= -3.8e+36)
		tmp = t_1;
	elseif (t <= -1.3e-36)
		tmp = t_2;
	elseif (t <= -1.45e-163)
		tmp = t_1;
	elseif (t <= -1.9e-236)
		tmp = x * (y / z);
	elseif (t <= 7.8e+24)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+84], t$95$2, If[LessEqual[t, -3.8e+36], t$95$1, If[LessEqual[t, -1.3e-36], t$95$2, If[LessEqual[t, -1.45e-163], t$95$1, If[LessEqual[t, -1.9e-236], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e+24], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9e84 or -3.80000000000000025e36 < t < -1.3e-36 or 7.7999999999999995e24 < t

   1. Initial program 61.8%

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

      1. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in x around 0 52.0%

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

      1. associate-/l* 76.3%

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

   7. Simplified 76.3%

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

   if -1.9e84 < t < -3.80000000000000025e36 or -1.3e-36 < t < -1.4500000000000001e-163 or -1.9e-236 < t < 7.7999999999999995e24

   1. Initial program 79.8%

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

      1. associate-/l* 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in z around 0 58.2%

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

   6. Taylor expanded in t around 0 54.7%

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

      1. mul-1-neg 54.7%

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

      2. associate-/l* 57.9%

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

   8. Simplified 57.9%

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

   if -1.4500000000000001e-163 < t < -1.9e-236

   1. Initial program 64.9%

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

      1. associate-/l* 67.5%

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

   3. Simplified 67.5%

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

      1. clear-num 68.6%

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

      2. un-div-inv 68.7%

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

   6. Applied egg-rr 68.7%

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

   7. Taylor expanded in a around 0 46.2%

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

      1. mul-1-neg 46.2%

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

      2. unsub-neg 46.2%

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

      3. associate-/l* 49.4%

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

      4. div-sub 49.4%

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

      5. *-inverses 49.4%

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

   9. Simplified 49.4%

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

   10. Taylor expanded in x around -inf 56.3%

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

       1. associate-/l* 63.1%

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

   12. Simplified 63.1%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+84}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+36}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-36}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-163}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+24}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_3 := y \cdot \frac{x - t}{z}\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+146}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-73}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+139}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a))))
        (t_2 (* t (- 1.0 (/ y z))))
        (t_3 (* y (/ (- x t) z))))
   (if (<= z -1.9e+146)
     t_2
     (if (<= z -1.15e+112)
       t_1
       (if (<= z -1.08e+15)
         t_2
         (if (<= z -2.1e-73)
           t_3
           (if (<= z 2.85e-129)
             t_1
             (if (<= z 2.1e+139) t_3 (* t (/ z (- z a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = t * (1.0 - (y / z));
	double t_3 = y * ((x - t) / z);
	double tmp;
	if (z <= -1.9e+146) {
		tmp = t_2;
	} else if (z <= -1.15e+112) {
		tmp = t_1;
	} else if (z <= -1.08e+15) {
		tmp = t_2;
	} else if (z <= -2.1e-73) {
		tmp = t_3;
	} else if (z <= 2.85e-129) {
		tmp = t_1;
	} else if (z <= 2.1e+139) {
		tmp = t_3;
	} else {
		tmp = t * (z / (z - 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    t_2 = t * (1.0d0 - (y / z))
    t_3 = y * ((x - t) / z)
    if (z <= (-1.9d+146)) then
        tmp = t_2
    else if (z <= (-1.15d+112)) then
        tmp = t_1
    else if (z <= (-1.08d+15)) then
        tmp = t_2
    else if (z <= (-2.1d-73)) then
        tmp = t_3
    else if (z <= 2.85d-129) then
        tmp = t_1
    else if (z <= 2.1d+139) then
        tmp = t_3
    else
        tmp = t * (z / (z - 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 + (t * (y / a));
	double t_2 = t * (1.0 - (y / z));
	double t_3 = y * ((x - t) / z);
	double tmp;
	if (z <= -1.9e+146) {
		tmp = t_2;
	} else if (z <= -1.15e+112) {
		tmp = t_1;
	} else if (z <= -1.08e+15) {
		tmp = t_2;
	} else if (z <= -2.1e-73) {
		tmp = t_3;
	} else if (z <= 2.85e-129) {
		tmp = t_1;
	} else if (z <= 2.1e+139) {
		tmp = t_3;
	} else {
		tmp = t * (z / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	t_2 = t * (1.0 - (y / z))
	t_3 = y * ((x - t) / z)
	tmp = 0
	if z <= -1.9e+146:
		tmp = t_2
	elif z <= -1.15e+112:
		tmp = t_1
	elif z <= -1.08e+15:
		tmp = t_2
	elif z <= -2.1e-73:
		tmp = t_3
	elif z <= 2.85e-129:
		tmp = t_1
	elif z <= 2.1e+139:
		tmp = t_3
	else:
		tmp = t * (z / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	t_2 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_3 = Float64(y * Float64(Float64(x - t) / z))
	tmp = 0.0
	if (z <= -1.9e+146)
		tmp = t_2;
	elseif (z <= -1.15e+112)
		tmp = t_1;
	elseif (z <= -1.08e+15)
		tmp = t_2;
	elseif (z <= -2.1e-73)
		tmp = t_3;
	elseif (z <= 2.85e-129)
		tmp = t_1;
	elseif (z <= 2.1e+139)
		tmp = t_3;
	else
		tmp = Float64(t * Float64(z / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	t_2 = t * (1.0 - (y / z));
	t_3 = y * ((x - t) / z);
	tmp = 0.0;
	if (z <= -1.9e+146)
		tmp = t_2;
	elseif (z <= -1.15e+112)
		tmp = t_1;
	elseif (z <= -1.08e+15)
		tmp = t_2;
	elseif (z <= -2.1e-73)
		tmp = t_3;
	elseif (z <= 2.85e-129)
		tmp = t_1;
	elseif (z <= 2.1e+139)
		tmp = t_3;
	else
		tmp = t * (z / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+146], t$95$2, If[LessEqual[z, -1.15e+112], t$95$1, If[LessEqual[z, -1.08e+15], t$95$2, If[LessEqual[z, -2.1e-73], t$95$3, If[LessEqual[z, 2.85e-129], t$95$1, If[LessEqual[z, 2.1e+139], t$95$3, N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8999999999999999e146 or -1.15e112 < z < -1.08e15

   1. Initial program 46.0%

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

      1. associate-/l* 81.2%

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

   3. Simplified 81.2%

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

      1. clear-num 81.2%

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

      2. un-div-inv 81.3%

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

   6. Applied egg-rr 81.3%

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

   7. Taylor expanded in a around 0 36.6%

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

      1. mul-1-neg 36.6%

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

      2. unsub-neg 36.6%

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

      3. associate-/l* 64.0%

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

      4. div-sub 64.0%

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

      5. *-inverses 64.0%

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

   9. Simplified 64.0%

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

   10. Taylor expanded in x around 0 60.7%

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

       1. mul-1-neg 60.7%

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

       2. sub-neg 60.7%

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

       3. metadata-eval 60.7%

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

       4. distribute-rgt-neg-in 60.7%

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

       5. +-commutative 60.7%

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

       6. distribute-neg-in 60.7%

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

       7. metadata-eval 60.7%

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

       8. sub-neg 60.7%

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

   12. Simplified 60.7%

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

   if -1.8999999999999999e146 < z < -1.15e112 or -2.0999999999999999e-73 < z < 2.85e-129

   1. Initial program 85.6%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in z around 0 73.0%

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

   6. Taylor expanded in t around inf 64.1%

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

      1. associate-/l* 65.4%

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

   8. Simplified 65.4%

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

   if -1.08e15 < z < -2.0999999999999999e-73 or 2.85e-129 < z < 2.0999999999999999e139

   1. Initial program 77.1%

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

      1. associate-/l* 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in y around inf 59.7%

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

      1. div-sub 59.7%

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

   7. Simplified 59.7%

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

   8. Taylor expanded in a around 0 51.9%

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

      1. mul-1-neg 51.9%

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

      2. associate-/l* 53.9%

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

      3. distribute-rgt-neg-in 53.9%

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

      4. distribute-neg-frac2 53.9%

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

   10. Simplified 53.9%

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

   if 2.0999999999999999e139 < z

   1. Initial program 39.1%

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

      1. associate-/l* 57.7%

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

   3. Simplified 57.7%

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

   5. Taylor expanded in y around 0 27.1%

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

      1. mul-1-neg 27.1%

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

      2. unsub-neg 27.1%

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

      3. associate-/l* 44.6%

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

   7. Simplified 44.6%

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

   8. Taylor expanded in x around 0 31.3%

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

      1. mul-1-neg 31.3%

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

      2. associate-/l* 58.0%

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

   10. Simplified 58.0%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+146}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+112}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-129}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{-17}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-257}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -1.9e+84)
     t_2
     (if (<= t -7.5e+36)
       t_1
       (if (<= t -5.3e-17)
         t_2
         (if (<= t -2.5e-257)
           (* y (/ (- t x) (- a z)))
           (if (<= t 7.8e+24) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.9e+84) {
		tmp = t_2;
	} else if (t <= -7.5e+36) {
		tmp = t_1;
	} else if (t <= -5.3e-17) {
		tmp = t_2;
	} else if (t <= -2.5e-257) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 7.8e+24) {
		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 = x - (x * (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-1.9d+84)) then
        tmp = t_2
    else if (t <= (-7.5d+36)) then
        tmp = t_1
    else if (t <= (-5.3d-17)) then
        tmp = t_2
    else if (t <= (-2.5d-257)) then
        tmp = y * ((t - x) / (a - z))
    else if (t <= 7.8d+24) 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 = x - (x * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.9e+84) {
		tmp = t_2;
	} else if (t <= -7.5e+36) {
		tmp = t_1;
	} else if (t <= -5.3e-17) {
		tmp = t_2;
	} else if (t <= -2.5e-257) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 7.8e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -1.9e+84:
		tmp = t_2
	elif t <= -7.5e+36:
		tmp = t_1
	elif t <= -5.3e-17:
		tmp = t_2
	elif t <= -2.5e-257:
		tmp = y * ((t - x) / (a - z))
	elif t <= 7.8e+24:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -1.9e+84)
		tmp = t_2;
	elseif (t <= -7.5e+36)
		tmp = t_1;
	elseif (t <= -5.3e-17)
		tmp = t_2;
	elseif (t <= -2.5e-257)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (t <= 7.8e+24)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -1.9e+84)
		tmp = t_2;
	elseif (t <= -7.5e+36)
		tmp = t_1;
	elseif (t <= -5.3e-17)
		tmp = t_2;
	elseif (t <= -2.5e-257)
		tmp = y * ((t - x) / (a - z));
	elseif (t <= 7.8e+24)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+84], t$95$2, If[LessEqual[t, -7.5e+36], t$95$1, If[LessEqual[t, -5.3e-17], t$95$2, If[LessEqual[t, -2.5e-257], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e+24], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9e84 or -7.50000000000000054e36 < t < -5.2999999999999998e-17 or 7.7999999999999995e24 < t

   1. Initial program 61.5%

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

      1. associate-/l* 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in x around 0 53.7%

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

      1. associate-/l* 79.3%

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

   7. Simplified 79.3%

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

   if -1.9e84 < t < -7.50000000000000054e36 or -2.49999999999999994e-257 < t < 7.7999999999999995e24

   1. Initial program 82.1%

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

      1. associate-/l* 79.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in z around 0 57.6%

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

   6. Taylor expanded in t around 0 54.0%

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

      1. mul-1-neg 54.0%

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

      2. associate-/l* 56.1%

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

   8. Simplified 56.1%

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

   if -5.2999999999999998e-17 < t < -2.49999999999999994e-257

   1. Initial program 69.3%

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

      1. associate-/l* 73.7%

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

   3. Simplified 73.7%

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

   5. Taylor expanded in y around inf 59.7%

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

      1. div-sub 59.6%

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

   7. Simplified 59.6%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+84}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+36}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-257}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+24}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))) (t_2 (+ x (* t (/ y a)))))
   (if (<= a -3.5e+90)
     t_2
     (if (<= a -1.35e+60)
       t_1
       (if (<= a -2.65e-30)
         (+ x (/ (* y t) a))
         (if (<= a -2.7e-35)
           (* t (/ z (- z a)))
           (if (<= a 3.4e-62) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -3.5e+90) {
		tmp = t_2;
	} else if (a <= -1.35e+60) {
		tmp = t_1;
	} else if (a <= -2.65e-30) {
		tmp = x + ((y * t) / a);
	} else if (a <= -2.7e-35) {
		tmp = t * (z / (z - a));
	} else if (a <= 3.4e-62) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    t_2 = x + (t * (y / a))
    if (a <= (-3.5d+90)) then
        tmp = t_2
    else if (a <= (-1.35d+60)) then
        tmp = t_1
    else if (a <= (-2.65d-30)) then
        tmp = x + ((y * t) / a)
    else if (a <= (-2.7d-35)) then
        tmp = t * (z / (z - a))
    else if (a <= 3.4d-62) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -3.5e+90) {
		tmp = t_2;
	} else if (a <= -1.35e+60) {
		tmp = t_1;
	} else if (a <= -2.65e-30) {
		tmp = x + ((y * t) / a);
	} else if (a <= -2.7e-35) {
		tmp = t * (z / (z - a));
	} else if (a <= 3.4e-62) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	t_2 = x + (t * (y / a))
	tmp = 0
	if a <= -3.5e+90:
		tmp = t_2
	elif a <= -1.35e+60:
		tmp = t_1
	elif a <= -2.65e-30:
		tmp = x + ((y * t) / a)
	elif a <= -2.7e-35:
		tmp = t * (z / (z - a))
	elif a <= 3.4e-62:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -3.5e+90)
		tmp = t_2;
	elseif (a <= -1.35e+60)
		tmp = t_1;
	elseif (a <= -2.65e-30)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (a <= -2.7e-35)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	elseif (a <= 3.4e-62)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	t_2 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -3.5e+90)
		tmp = t_2;
	elseif (a <= -1.35e+60)
		tmp = t_1;
	elseif (a <= -2.65e-30)
		tmp = x + ((y * t) / a);
	elseif (a <= -2.7e-35)
		tmp = t * (z / (z - a));
	elseif (a <= 3.4e-62)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e+90], t$95$2, If[LessEqual[a, -1.35e+60], t$95$1, If[LessEqual[a, -2.65e-30], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.7e-35], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e-62], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.4999999999999998e90 or 3.39999999999999988e-62 < a

   1. Initial program 65.2%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in z around 0 58.8%

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

   6. Taylor expanded in t around inf 57.9%

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

      1. associate-/l* 62.8%

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

   8. Simplified 62.8%

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

   if -3.4999999999999998e90 < a < -1.35e60 or -2.6999999999999997e-35 < a < 3.39999999999999988e-62

   1. Initial program 73.8%

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

      1. associate-/l* 78.5%

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

   3. Simplified 78.5%

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

      1. clear-num 78.4%

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

      2. un-div-inv 78.7%

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

   6. Applied egg-rr 78.7%

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

   7. Taylor expanded in a around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. unsub-neg 58.3%

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

      3. associate-/l* 68.5%

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

      4. div-sub 68.5%

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

      5. *-inverses 68.5%

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

   9. Simplified 68.5%

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

   10. Taylor expanded in x around 0 53.3%

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

       1. mul-1-neg 53.3%

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

       2. sub-neg 53.3%

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

       3. metadata-eval 53.3%

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

       4. distribute-rgt-neg-in 53.3%

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

       5. +-commutative 53.3%

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

       6. distribute-neg-in 53.3%

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

       7. metadata-eval 53.3%

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

       8. sub-neg 53.3%

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

   12. Simplified 53.3%

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

   if -1.35e60 < a < -2.64999999999999987e-30

   1. Initial program 79.1%

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

      1. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in z around 0 66.4%

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

   6. Taylor expanded in t around inf 59.5%

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

   if -2.64999999999999987e-30 < a < -2.6999999999999997e-35

   1. Initial program 99.2%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.2%

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

      1. mul-1-neg 99.2%

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

      2. unsub-neg 99.2%

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

      3. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 99.2%

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

      1. mul-1-neg 99.2%

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

      2. associate-/l* 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+90}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{+60}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{-30}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+36}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-17}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -5e+85)
     t_1
     (if (<= t -3e+36)
       (+ x (* y (/ (- t x) a)))
       (if (<= t -9e-17)
         (/ (* (- y z) t) (- a z))
         (if (<= t 4.5e+24) (* x (+ (/ (- y z) (- z a)) 1.0)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -5e+85) {
		tmp = t_1;
	} else if (t <= -3e+36) {
		tmp = x + (y * ((t - x) / a));
	} else if (t <= -9e-17) {
		tmp = ((y - z) * t) / (a - z);
	} else if (t <= 4.5e+24) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (t <= (-5d+85)) then
        tmp = t_1
    else if (t <= (-3d+36)) then
        tmp = x + (y * ((t - x) / a))
    else if (t <= (-9d-17)) then
        tmp = ((y - z) * t) / (a - z)
    else if (t <= 4.5d+24) then
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -5e+85) {
		tmp = t_1;
	} else if (t <= -3e+36) {
		tmp = x + (y * ((t - x) / a));
	} else if (t <= -9e-17) {
		tmp = ((y - z) * t) / (a - z);
	} else if (t <= 4.5e+24) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -5e+85:
		tmp = t_1
	elif t <= -3e+36:
		tmp = x + (y * ((t - x) / a))
	elif t <= -9e-17:
		tmp = ((y - z) * t) / (a - z)
	elif t <= 4.5e+24:
		tmp = x * (((y - z) / (z - a)) + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -5e+85)
		tmp = t_1;
	elseif (t <= -3e+36)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (t <= -9e-17)
		tmp = Float64(Float64(Float64(y - z) * t) / Float64(a - z));
	elseif (t <= 4.5e+24)
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -5e+85)
		tmp = t_1;
	elseif (t <= -3e+36)
		tmp = x + (y * ((t - x) / a));
	elseif (t <= -9e-17)
		tmp = ((y - z) * t) / (a - z);
	elseif (t <= 4.5e+24)
		tmp = x * (((y - z) / (z - a)) + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e+85], t$95$1, If[LessEqual[t, -3e+36], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9e-17], N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+24], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.0000000000000001e85 or 4.50000000000000019e24 < t

   1. Initial program 59.7%

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

      1. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in x around 0 49.9%

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

      1. associate-/l* 77.6%

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

   7. Simplified 77.6%

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

   if -5.0000000000000001e85 < t < -3e36

   1. Initial program 91.6%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 75.6%

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

      1. associate-/l* 75.6%

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

   7. Simplified 75.6%

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

   if -3e36 < t < -8.99999999999999957e-17

   1. Initial program 83.9%

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

      1. associate-/l* 83.9%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in x around 0 99.4%

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

   if -8.99999999999999957e-17 < t < 4.50000000000000019e24

   1. Initial program 76.4%

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

      1. associate-/l* 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in x around inf 68.8%

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

      1. mul-1-neg 68.8%

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

      2. unsub-neg 68.8%

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

   7. Simplified 68.8%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y - z}{a - z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+36}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-17}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-66}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-67}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -3.5e+42)
     t_1
     (if (<= z -2.6e-66)
       (* y (/ (- t x) (- a z)))
       (if (<= z 8e-67)
         (+ x (* y (/ (- t x) a)))
         (if (<= z 2e+139) (* y (/ (- x t) z)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -3.5e+42) {
		tmp = t_1;
	} else if (z <= -2.6e-66) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 8e-67) {
		tmp = x + (y * ((t - x) / a));
	} else if (z <= 2e+139) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (z <= (-3.5d+42)) then
        tmp = t_1
    else if (z <= (-2.6d-66)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 8d-67) then
        tmp = x + (y * ((t - x) / a))
    else if (z <= 2d+139) then
        tmp = y * ((x - t) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -3.5e+42) {
		tmp = t_1;
	} else if (z <= -2.6e-66) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 8e-67) {
		tmp = x + (y * ((t - x) / a));
	} else if (z <= 2e+139) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -3.5e+42:
		tmp = t_1
	elif z <= -2.6e-66:
		tmp = y * ((t - x) / (a - z))
	elif z <= 8e-67:
		tmp = x + (y * ((t - x) / a))
	elif z <= 2e+139:
		tmp = y * ((x - t) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -3.5e+42)
		tmp = t_1;
	elseif (z <= -2.6e-66)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 8e-67)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (z <= 2e+139)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -3.5e+42)
		tmp = t_1;
	elseif (z <= -2.6e-66)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 8e-67)
		tmp = x + (y * ((t - x) / a));
	elseif (z <= 2e+139)
		tmp = y * ((x - t) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+42], t$95$1, If[LessEqual[z, -2.6e-66], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-67], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+139], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.50000000000000023e42 or 2.00000000000000007e139 < z

   1. Initial program 45.5%

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

      1. associate-/l* 71.5%

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

   3. Simplified 71.5%

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

   5. Taylor expanded in x around 0 37.0%

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

      1. associate-/l* 65.9%

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

   7. Simplified 65.9%

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

   if -3.50000000000000023e42 < z < -2.5999999999999999e-66

   1. Initial program 76.9%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in y around inf 71.8%

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

      1. div-sub 71.8%

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

   7. Simplified 71.8%

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

   if -2.5999999999999999e-66 < z < 7.99999999999999954e-67

   1. Initial program 88.5%

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

      1. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in z around 0 73.9%

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

      1. associate-/l* 79.6%

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

   7. Simplified 79.6%

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

   if 7.99999999999999954e-67 < z < 2.00000000000000007e139

   1. Initial program 68.9%

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

      1. associate-/l* 73.6%

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

   3. Simplified 73.6%

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

   5. Taylor expanded in y around inf 47.9%

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

      1. div-sub 47.9%

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

   7. Simplified 47.9%

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

   8. Taylor expanded in a around 0 44.5%

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

      1. mul-1-neg 44.5%

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

      2. associate-/l* 48.5%

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

      3. distribute-rgt-neg-in 48.5%

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

      4. distribute-neg-frac2 48.5%

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

   10. Simplified 48.5%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+42}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-66}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-67}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+206}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3e+206)
   x
   (if (<= a -3.4e+114)
     (* t (/ (- y z) a))
     (if (<= a -2.4e+108) x (if (<= a 1.08e+55) (* t (- 1.0 (/ y z))) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3e+206) {
		tmp = x;
	} else if (a <= -3.4e+114) {
		tmp = t * ((y - z) / a);
	} else if (a <= -2.4e+108) {
		tmp = x;
	} else if (a <= 1.08e+55) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3d+206)) then
        tmp = x
    else if (a <= (-3.4d+114)) then
        tmp = t * ((y - z) / a)
    else if (a <= (-2.4d+108)) then
        tmp = x
    else if (a <= 1.08d+55) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3e+206) {
		tmp = x;
	} else if (a <= -3.4e+114) {
		tmp = t * ((y - z) / a);
	} else if (a <= -2.4e+108) {
		tmp = x;
	} else if (a <= 1.08e+55) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3e+206:
		tmp = x
	elif a <= -3.4e+114:
		tmp = t * ((y - z) / a)
	elif a <= -2.4e+108:
		tmp = x
	elif a <= 1.08e+55:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3e+206)
		tmp = x;
	elseif (a <= -3.4e+114)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (a <= -2.4e+108)
		tmp = x;
	elseif (a <= 1.08e+55)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3e+206)
		tmp = x;
	elseif (a <= -3.4e+114)
		tmp = t * ((y - z) / a);
	elseif (a <= -2.4e+108)
		tmp = x;
	elseif (a <= 1.08e+55)
		tmp = t * (1.0 - (y / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3e+206], x, If[LessEqual[a, -3.4e+114], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.4e+108], x, If[LessEqual[a, 1.08e+55], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.0000000000000001e206 or -3.4000000000000001e114 < a < -2.40000000000000019e108 or 1.08000000000000004e55 < a

   1. Initial program 65.2%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in a around inf 53.6%

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

   if -3.0000000000000001e206 < a < -3.4000000000000001e114

   1. Initial program 73.9%

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

      1. associate-/l* 84.2%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in x around 0 41.4%

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

      1. associate-/l* 57.1%

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

   7. Simplified 57.1%

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

   8. Taylor expanded in a around inf 36.6%

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

      1. associate-/l* 52.3%

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

   10. Simplified 52.3%

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

   if -2.40000000000000019e108 < a < 1.08000000000000004e55

   1. Initial program 72.2%

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

      1. associate-/l* 81.1%

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

   3. Simplified 81.1%

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

      1. clear-num 81.0%

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

      2. un-div-inv 81.3%

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

   6. Applied egg-rr 81.3%

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

   7. Taylor expanded in a around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. unsub-neg 50.3%

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

      3. associate-/l* 61.7%

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

      4. div-sub 61.7%

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

      5. *-inverses 61.7%

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

   9. Simplified 61.7%

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

   10. Taylor expanded in x around 0 48.1%

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

       1. mul-1-neg 48.1%

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

       2. sub-neg 48.1%

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

       3. metadata-eval 48.1%

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

       4. distribute-rgt-neg-in 48.1%

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

       5. +-commutative 48.1%

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

       6. distribute-neg-in 48.1%

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

       7. metadata-eval 48.1%

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

       8. sub-neg 48.1%

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

   12. Simplified 48.1%

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

Alternative 13: 82.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-154} \lor \neg \left(a \leq 8.8 \cdot 10^{-193}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8e-154) (not (<= a 8.8e-193)))
   (+ x (* (- y z) (/ (- t x) (- a z))))
   (+ t (/ (* (- y a) (- x t)) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8e-154) || !(a <= 8.8e-193)) {
		tmp = x + ((y - z) * ((t - x) / (a - 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) :: tmp
    if ((a <= (-8d-154)) .or. (.not. (a <= 8.8d-193))) then
        tmp = x + ((y - z) * ((t - x) / (a - 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 tmp;
	if ((a <= -8e-154) || !(a <= 8.8e-193)) {
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	} else {
		tmp = t + (((y - a) * (x - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8e-154) or not (a <= 8.8e-193):
		tmp = x + ((y - z) * ((t - x) / (a - z)))
	else:
		tmp = t + (((y - a) * (x - t)) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8e-154) || !(a <= 8.8e-193))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - 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)
	tmp = 0.0;
	if ((a <= -8e-154) || ~((a <= 8.8e-193)))
		tmp = x + ((y - z) * ((t - x) / (a - z)));
	else
		tmp = t + (((y - a) * (x - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8e-154], N[Not[LessEqual[a, 8.8e-193]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - 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 a < -7.9999999999999998e-154 or 8.79999999999999906e-193 < a

   1. Initial program 70.5%

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

      1. associate-/l* 86.0%

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

   3. Simplified 86.0%

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

   if -7.9999999999999998e-154 < a < 8.79999999999999906e-193

   1. Initial program 69.5%

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

      1. associate-/l* 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in z around inf 87.5%

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

      1. associate--l+ 87.5%

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

      2. associate-*r/ 87.5%

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

      3. associate-*r/ 87.5%

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

      4. mul-1-neg 87.5%

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

      5. div-sub 87.5%

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

      6. mul-1-neg 87.5%

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

      7. distribute-lft-out-- 87.5%

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

      8. associate-*r/ 87.5%

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

      9. mul-1-neg 87.5%

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

      10. unsub-neg 87.5%

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

      11. distribute-rgt-out-- 87.5%

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

   7. Simplified 87.5%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-154} \lor \neg \left(a \leq 8.8 \cdot 10^{-193}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-7}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-265}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-44}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.6e-7)
   t
   (if (<= z -2.9e-265)
     x
     (if (<= z 2.15e-44) (* t (/ y a)) (if (<= z 5.4e+56) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.6e-7) {
		tmp = t;
	} else if (z <= -2.9e-265) {
		tmp = x;
	} else if (z <= 2.15e-44) {
		tmp = t * (y / a);
	} else if (z <= 5.4e+56) {
		tmp = x;
	} 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) :: tmp
    if (z <= (-8.6d-7)) then
        tmp = t
    else if (z <= (-2.9d-265)) then
        tmp = x
    else if (z <= 2.15d-44) then
        tmp = t * (y / a)
    else if (z <= 5.4d+56) then
        tmp = x
    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 tmp;
	if (z <= -8.6e-7) {
		tmp = t;
	} else if (z <= -2.9e-265) {
		tmp = x;
	} else if (z <= 2.15e-44) {
		tmp = t * (y / a);
	} else if (z <= 5.4e+56) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.6e-7:
		tmp = t
	elif z <= -2.9e-265:
		tmp = x
	elif z <= 2.15e-44:
		tmp = t * (y / a)
	elif z <= 5.4e+56:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.6e-7)
		tmp = t;
	elseif (z <= -2.9e-265)
		tmp = x;
	elseif (z <= 2.15e-44)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 5.4e+56)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.6e-7)
		tmp = t;
	elseif (z <= -2.9e-265)
		tmp = x;
	elseif (z <= 2.15e-44)
		tmp = t * (y / a);
	elseif (z <= 5.4e+56)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.6e-7], t, If[LessEqual[z, -2.9e-265], x, If[LessEqual[z, 2.15e-44], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+56], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.6000000000000002e-7 or 5.40000000000000019e56 < z

   1. Initial program 45.1%

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

      1. associate-/l* 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in z around inf 42.8%

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

   if -8.6000000000000002e-7 < z < -2.89999999999999975e-265 or 2.15000000000000007e-44 < z < 5.40000000000000019e56

   1. Initial program 87.6%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in a around inf 37.4%

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

   if -2.89999999999999975e-265 < z < 2.15000000000000007e-44

   1. Initial program 87.5%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in x around 0 44.1%

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

      1. associate-/l* 48.6%

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

   7. Simplified 48.6%

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

   8. Taylor expanded in z around 0 30.7%

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

      1. associate-/l* 35.1%

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

   10. Simplified 35.1%

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

Alternative 15: 70.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-17} \lor \neg \left(t \leq 8.5 \cdot 10^{-104}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.1e-17) (not (<= t 8.5e-104)))
   (+ x (* (- y z) (/ t (- a z))))
   (* x (+ (/ (- y z) (- z a)) 1.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.1e-17) || !(t <= 8.5e-104)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.1d-17)) .or. (.not. (t <= 8.5d-104))) then
        tmp = x + ((y - z) * (t / (a - z)))
    else
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.1e-17) || !(t <= 8.5e-104)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.1e-17) or not (t <= 8.5e-104):
		tmp = x + ((y - z) * (t / (a - z)))
	else:
		tmp = x * (((y - z) / (z - a)) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.1e-17) || !(t <= 8.5e-104))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.1e-17) || ~((t <= 8.5e-104)))
		tmp = x + ((y - z) * (t / (a - z)));
	else
		tmp = x * (((y - z) / (z - a)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.1e-17], N[Not[LessEqual[t, 8.5e-104]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1e-17 or 8.50000000000000007e-104 < t

   1. Initial program 67.4%

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

      1. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in t around inf 77.3%

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

   if -1.1e-17 < t < 8.50000000000000007e-104

   1. Initial program 75.0%

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

      1. associate-/l* 74.2%

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

   3. Simplified 74.2%

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

   5. Taylor expanded in x around inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. unsub-neg 73.4%

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

   7. Simplified 73.4%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-17} \lor \neg \left(t \leq 8.5 \cdot 10^{-104}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-54}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-66}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.15e-54)
   (+ x (/ (- y z) (/ (- a z) t)))
   (if (<= a 1.95e-66)
     (+ t (/ (* (- y a) (- x t)) z))
     (+ x (* (- y z) (/ t (- a z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.15e-54) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else if (a <= 1.95e-66) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else {
		tmp = x + ((y - z) * (t / (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 <= (-1.15d-54)) then
        tmp = x + ((y - z) / ((a - z) / t))
    else if (a <= 1.95d-66) then
        tmp = t + (((y - a) * (x - t)) / z)
    else
        tmp = x + ((y - z) * (t / (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 <= -1.15e-54) {
		tmp = x + ((y - z) / ((a - z) / t));
	} else if (a <= 1.95e-66) {
		tmp = t + (((y - a) * (x - t)) / z);
	} else {
		tmp = x + ((y - z) * (t / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.15e-54:
		tmp = x + ((y - z) / ((a - z) / t))
	elif a <= 1.95e-66:
		tmp = t + (((y - a) * (x - t)) / z)
	else:
		tmp = x + ((y - z) * (t / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.15e-54)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	elseif (a <= 1.95e-66)
		tmp = Float64(t + Float64(Float64(Float64(y - a) * Float64(x - t)) / z));
	else
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.15e-54)
		tmp = x + ((y - z) / ((a - z) / t));
	elseif (a <= 1.95e-66)
		tmp = t + (((y - a) * (x - t)) / z);
	else
		tmp = x + ((y - z) * (t / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.15e-54], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.95e-66], N[(t + N[(N[(N[(y - a), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.1499999999999999e-54

   1. Initial program 67.1%

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

      1. associate-/l* 85.0%

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

   3. Simplified 85.0%

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

      1. clear-num 85.0%

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

      2. un-div-inv 85.1%

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

   6. Applied egg-rr 85.1%

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

   7. Taylor expanded in t around inf 75.0%

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

   if -1.1499999999999999e-54 < a < 1.94999999999999991e-66

   1. Initial program 76.7%

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

      1. associate-/l* 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in z around inf 80.4%

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

      1. associate--l+ 80.4%

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

      2. associate-*r/ 80.4%

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

      3. associate-*r/ 80.4%

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

      4. mul-1-neg 80.4%

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

      5. div-sub 81.3%

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

      6. mul-1-neg 81.3%

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

      7. distribute-lft-out-- 81.3%

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

      8. associate-*r/ 81.3%

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

      9. mul-1-neg 81.3%

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

      10. unsub-neg 81.3%

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

      11. distribute-rgt-out-- 81.3%

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

   7. Simplified 81.3%

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

   if 1.94999999999999991e-66 < a

   1. Initial program 65.0%

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

      1. associate-/l* 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in t around inf 74.0%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-54}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-66}:\\ \;\;\;\;t + \frac{\left(y - a\right) \cdot \left(x - t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 70.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-17}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.9e-17)
   (+ x (* (- y z) (/ t (- a z))))
   (if (<= t 4.4e-104)
     (* x (+ (/ (- y z) (- z a)) 1.0))
     (+ x (/ (- y z) (/ (- a z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e-17) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (t <= 4.4e-104) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else {
		tmp = x + ((y - z) / ((a - z) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.9d-17)) then
        tmp = x + ((y - z) * (t / (a - z)))
    else if (t <= 4.4d-104) then
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    else
        tmp = x + ((y - z) / ((a - z) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.9e-17) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (t <= 4.4e-104) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else {
		tmp = x + ((y - z) / ((a - z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.9e-17:
		tmp = x + ((y - z) * (t / (a - z)))
	elif t <= 4.4e-104:
		tmp = x * (((y - z) / (z - a)) + 1.0)
	else:
		tmp = x + ((y - z) / ((a - z) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.9e-17)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	elseif (t <= 4.4e-104)
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	else
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.9e-17)
		tmp = x + ((y - z) * (t / (a - z)));
	elseif (t <= 4.4e-104)
		tmp = x * (((y - z) / (z - a)) + 1.0);
	else
		tmp = x + ((y - z) / ((a - z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.9e-17], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e-104], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9000000000000001e-17

   1. Initial program 56.6%

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

      1. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in t around inf 81.9%

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

   if -1.9000000000000001e-17 < t < 4.40000000000000023e-104

   1. Initial program 75.0%

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

      1. associate-/l* 74.2%

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

   3. Simplified 74.2%

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

   5. Taylor expanded in x around inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. unsub-neg 73.4%

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

   7. Simplified 73.4%

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

   if 4.40000000000000023e-104 < t

   1. Initial program 76.0%

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

      1. associate-/l* 84.8%

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

   3. Simplified 84.8%

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

      1. clear-num 84.8%

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

      2. un-div-inv 85.3%

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

   6. Applied egg-rr 85.3%

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

   7. Taylor expanded in t around inf 73.8%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{-17}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 35.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-48}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.6e+107)
   x
   (if (<= a -2.7e-48) t (if (<= a 1.08e+50) (* x (/ y z)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e+107) {
		tmp = x;
	} else if (a <= -2.7e-48) {
		tmp = t;
	} else if (a <= 1.08e+50) {
		tmp = x * (y / z);
	} 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+107)) then
        tmp = x
    else if (a <= (-2.7d-48)) then
        tmp = t
    else if (a <= 1.08d+50) then
        tmp = x * (y / z)
    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+107) {
		tmp = x;
	} else if (a <= -2.7e-48) {
		tmp = t;
	} else if (a <= 1.08e+50) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.6e+107:
		tmp = x
	elif a <= -2.7e-48:
		tmp = t
	elif a <= 1.08e+50:
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.6e+107)
		tmp = x;
	elseif (a <= -2.7e-48)
		tmp = t;
	elseif (a <= 1.08e+50)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.6e+107)
		tmp = x;
	elseif (a <= -2.7e-48)
		tmp = t;
	elseif (a <= 1.08e+50)
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.6e+107], x, If[LessEqual[a, -2.7e-48], t, If[LessEqual[a, 1.08e+50], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.5999999999999998e107 or 1.08000000000000004e50 < a

   1. Initial program 66.9%

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

      1. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in a around inf 48.3%

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

   if -3.5999999999999998e107 < a < -2.70000000000000011e-48

   1. Initial program 60.7%

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

      1. associate-/l* 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in z around inf 33.9%

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

   if -2.70000000000000011e-48 < a < 1.08000000000000004e50

   1. Initial program 75.2%

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

      1. associate-/l* 81.2%

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

   3. Simplified 81.2%

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

      1. clear-num 81.1%

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

      2. un-div-inv 81.4%

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

   6. Applied egg-rr 81.4%

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

   7. Taylor expanded in a around 0 56.6%

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

      1. mul-1-neg 56.6%

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

      2. unsub-neg 56.6%

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

      3. associate-/l* 67.0%

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

      4. div-sub 67.0%

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

      5. *-inverses 67.0%

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

   9. Simplified 67.0%

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

   10. Taylor expanded in x around -inf 35.8%

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

       1. associate-/l* 40.1%

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

   12. Simplified 40.1%

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

Alternative 19: 54.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+90} \lor \neg \left(a \leq 2.2 \cdot 10^{-61}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.6e+90) (not (<= a 2.2e-61)))
   (+ x (* t (/ y a)))
   (* t (- 1.0 (/ y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.6e+90) || !(a <= 2.2e-61)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.6d+90)) .or. (.not. (a <= 2.2d-61))) then
        tmp = x + (t * (y / a))
    else
        tmp = t * (1.0d0 - (y / 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 <= -3.6e+90) || !(a <= 2.2e-61)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.6e+90) or not (a <= 2.2e-61):
		tmp = x + (t * (y / a))
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.6e+90) || !(a <= 2.2e-61))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.6e+90) || ~((a <= 2.2e-61)))
		tmp = x + (t * (y / a));
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.6e+90], N[Not[LessEqual[a, 2.2e-61]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.6e90 or 2.20000000000000009e-61 < a

   1. Initial program 65.2%

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

      1. associate-/l* 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in z around 0 58.8%

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

   6. Taylor expanded in t around inf 57.9%

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

      1. associate-/l* 62.8%

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

   8. Simplified 62.8%

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

   if -3.6e90 < a < 2.20000000000000009e-61

   1. Initial program 74.7%

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

      1. associate-/l* 79.6%

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

   3. Simplified 79.6%

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

      1. clear-num 79.5%

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

      2. un-div-inv 79.8%

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

   6. Applied egg-rr 79.8%

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

   7. Taylor expanded in a around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. unsub-neg 54.8%

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

      3. associate-/l* 64.5%

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

      4. div-sub 64.5%

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

      5. *-inverses 64.5%

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

   9. Simplified 64.5%

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

   10. Taylor expanded in x around 0 51.2%

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

       1. mul-1-neg 51.2%

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

       2. sub-neg 51.2%

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

       3. metadata-eval 51.2%

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

       4. distribute-rgt-neg-in 51.2%

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

       5. +-commutative 51.2%

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

       6. distribute-neg-in 51.2%

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

       7. metadata-eval 51.2%

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

       8. sub-neg 51.2%

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

   12. Simplified 51.2%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+90} \lor \neg \left(a \leq 2.2 \cdot 10^{-61}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 48.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+56}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e+107) x (if (<= a 6.2e+56) (* t (- 1.0 (/ y z))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+107) {
		tmp = x;
	} else if (a <= 6.2e+56) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9.5d+107)) then
        tmp = x
    else if (a <= 6.2d+56) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+107) {
		tmp = x;
	} else if (a <= 6.2e+56) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e+107:
		tmp = x
	elif a <= 6.2e+56:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e+107)
		tmp = x;
	elseif (a <= 6.2e+56)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.5e+107)
		tmp = x;
	elseif (a <= 6.2e+56)
		tmp = t * (1.0 - (y / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e+107], x, If[LessEqual[a, 6.2e+56], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -9.50000000000000019e107 or 6.20000000000000009e56 < a

   1. Initial program 66.9%

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

      1. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in a around inf 48.3%

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

   if -9.50000000000000019e107 < a < 6.20000000000000009e56

   1. Initial program 72.2%

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

      1. associate-/l* 81.1%

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

   3. Simplified 81.1%

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

      1. clear-num 81.0%

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

      2. un-div-inv 81.3%

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

   6. Applied egg-rr 81.3%

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

   7. Taylor expanded in a around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. unsub-neg 50.3%

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

      3. associate-/l* 61.7%

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

      4. div-sub 61.7%

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

      5. *-inverses 61.7%

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

   9. Simplified 61.7%

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

   10. Taylor expanded in x around 0 48.1%

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

       1. mul-1-neg 48.1%

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

       2. sub-neg 48.1%

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

       3. metadata-eval 48.1%

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

       4. distribute-rgt-neg-in 48.1%

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

       5. +-commutative 48.1%

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

       6. distribute-neg-in 48.1%

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

       7. metadata-eval 48.1%

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

       8. sub-neg 48.1%

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

   12. Simplified 48.1%

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

Alternative 21: 37.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-6}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.4e-6) t (if (<= z 8.6e+57) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e-6) {
		tmp = t;
	} else if (z <= 8.6e+57) {
		tmp = x;
	} 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) :: tmp
    if (z <= (-5.4d-6)) then
        tmp = t
    else if (z <= 8.6d+57) then
        tmp = x
    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 tmp;
	if (z <= -5.4e-6) {
		tmp = t;
	} else if (z <= 8.6e+57) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.4e-6:
		tmp = t
	elif z <= 8.6e+57:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.4e-6)
		tmp = t;
	elseif (z <= 8.6e+57)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.4e-6)
		tmp = t;
	elseif (z <= 8.6e+57)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.4e-6], t, If[LessEqual[z, 8.6e+57], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -5.39999999999999997e-6 or 8.60000000000000066e57 < z

   1. Initial program 45.1%

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

      1. associate-/l* 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in z around inf 42.8%

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

   if -5.39999999999999997e-6 < z < 8.60000000000000066e57

   1. Initial program 87.5%

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

      1. associate-/l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in a around inf 32.1%

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

Alternative 22: 24.7% 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 70.3%

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

   1. associate-/l* 83.0%

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

3. Simplified 83.0%

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

5. Taylor expanded in z around inf 21.8%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Alternative 23: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 70.3%

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

   1. associate-/l* 83.0%

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

3. Simplified 83.0%

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

5. Taylor expanded in y around 0 35.9%

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

   1. mul-1-neg 35.9%

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

   2. unsub-neg 35.9%

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

   3. associate-/l* 45.0%

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

7. Simplified 45.0%

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

8. Taylor expanded in t around 0 23.0%

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

   1. mul-1-neg 23.0%

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

   2. associate-/l* 24.3%

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

10. Simplified 24.3%

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

11. Taylor expanded in z around inf 2.7%

    \[\leadsto \color{blue}{x + -1 \cdot x} \]
12. Step-by-step derivation

    1. distribute-rgt1-in 2.7%

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

    2. metadata-eval 2.7%

       \[\leadsto \color{blue}{0} \cdot x \]

    3. mul0-lft 2.7%

       \[\leadsto \color{blue}{0} \]

13. Simplified 2.7%

    \[\leadsto \color{blue}{0} \]
14. Add Preprocessing

Developer target: 83.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024100 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

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

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