Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.4% → 91.0%

Time: 22.0s

Alternatives: 19

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-296}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 10^{-284}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t\_1, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (<= t_2 -1e-296)
     t_2
     (if (<= t_2 1e-284)
       (+ t (/ (- x t) (/ z (- y a))))
       (fma (- y z) t_1 x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if (t_2 <= -1e-296) {
		tmp = t_2;
	} else if (t_2 <= 1e-284) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = fma((y - z), t_1, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_2 <= -1e-296)
		tmp = t_2;
	elseif (t_2 <= 1e-284)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = fma(Float64(y - z), t_1, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-296], t$95$2, If[LessEqual[t$95$2, 1e-284], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1e-296

   1. Initial program 89.5%

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

   if -1e-296 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.00000000000000004e-284

   1. Initial program 3.6%

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

   3. Taylor expanded in z around inf 85.8%

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

      1. associate--l+ 85.8%

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

      2. distribute-lft-out-- 85.8%

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

      3. div-sub 85.8%

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

      4. mul-1-neg 85.8%

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

      5. unsub-neg 85.8%

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

      6. distribute-rgt-out-- 85.8%

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

      7. associate-/l* 97.2%

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

   5. Simplified 97.2%

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

   if 1.00000000000000004e-284 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 91.4%

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

      1. +-commutative 91.4%

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

      2. fma-def 91.4%

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

   3. Simplified 91.4%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-296}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-284}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-296} \lor \neg \left(t\_1 \leq 10^{-284}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-296) (not (<= t_1 1e-284)))
     t_1
     (+ t (/ (- x t) (/ z (- y a)))))))

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-296) || !(t_1 <= 1e-284)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-1d-296)) .or. (.not. (t_1 <= 1d-284))) then
        tmp = t_1
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -1e-296) || !(t_1 <= 1e-284)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -1e-296) or not (t_1 <= 1e-284):
		tmp = t_1
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	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))))
	tmp = 0.0
	if ((t_1 <= -1e-296) || !(t_1 <= 1e-284))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -1e-296) || ~((t_1 <= 1e-284)))
		tmp = t_1;
	else
		tmp = t + ((x - t) / (z / (y - a)));
	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]}, If[Or[LessEqual[t$95$1, -1e-296], N[Not[LessEqual[t$95$1, 1e-284]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1e-296 or 1.00000000000000004e-284 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.4%

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

   if -1e-296 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.00000000000000004e-284

   1. Initial program 3.6%

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

   3. Taylor expanded in z around inf 85.8%

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

      1. associate--l+ 85.8%

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

      2. distribute-lft-out-- 85.8%

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

      3. div-sub 85.8%

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

      4. mul-1-neg 85.8%

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

      5. unsub-neg 85.8%

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

      6. distribute-rgt-out-- 85.8%

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

      7. associate-/l* 97.2%

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

   5. Simplified 97.2%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-296} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-284}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -8200000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-238}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-78}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-27}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+37}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= z -8200000.0)
     t_1
     (if (<= z -2.9e-238)
       (+ x (/ t (/ a y)))
       (if (<= z 6.8e-302)
         (* x (- 1.0 (/ y a)))
         (if (<= z 1.5e-78)
           (+ x (/ (* y t) a))
           (if (<= z 1.6e-27)
             (/ (- y) (/ z (- t x)))
             (if (<= z 6.8e+37) (+ x (* t (/ y a))) t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -8200000.0) {
		tmp = t_1;
	} else if (z <= -2.9e-238) {
		tmp = x + (t / (a / y));
	} else if (z <= 6.8e-302) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.5e-78) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.6e-27) {
		tmp = -y / (z / (t - x));
	} else if (z <= 6.8e+37) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (z <= (-8200000.0d0)) then
        tmp = t_1
    else if (z <= (-2.9d-238)) then
        tmp = x + (t / (a / y))
    else if (z <= 6.8d-302) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.5d-78) then
        tmp = x + ((y * t) / a)
    else if (z <= 1.6d-27) then
        tmp = -y / (z / (t - x))
    else if (z <= 6.8d+37) then
        tmp = x + (t * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -8200000.0) {
		tmp = t_1;
	} else if (z <= -2.9e-238) {
		tmp = x + (t / (a / y));
	} else if (z <= 6.8e-302) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.5e-78) {
		tmp = x + ((y * t) / a);
	} else if (z <= 1.6e-27) {
		tmp = -y / (z / (t - x));
	} else if (z <= 6.8e+37) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -8200000.0:
		tmp = t_1
	elif z <= -2.9e-238:
		tmp = x + (t / (a / y))
	elif z <= 6.8e-302:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.5e-78:
		tmp = x + ((y * t) / a)
	elif z <= 1.6e-27:
		tmp = -y / (z / (t - x))
	elif z <= 6.8e+37:
		tmp = x + (t * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -8200000.0)
		tmp = t_1;
	elseif (z <= -2.9e-238)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (z <= 6.8e-302)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.5e-78)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 1.6e-27)
		tmp = Float64(Float64(-y) / Float64(z / Float64(t - x)));
	elseif (z <= 6.8e+37)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -8200000.0)
		tmp = t_1;
	elseif (z <= -2.9e-238)
		tmp = x + (t / (a / y));
	elseif (z <= 6.8e-302)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.5e-78)
		tmp = x + ((y * t) / a);
	elseif (z <= 1.6e-27)
		tmp = -y / (z / (t - x));
	elseif (z <= 6.8e+37)
		tmp = x + (t * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8200000.0], t$95$1, If[LessEqual[z, -2.9e-238], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-302], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-78], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-27], N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+37], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -8.2e6 or 6.80000000000000011e37 < z

   1. Initial program 64.2%

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

   3. Taylor expanded in t around inf 63.1%

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

   4. Taylor expanded in a around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. unsub-neg 56.1%

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

   6. Simplified 56.1%

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

   if -8.2e6 < z < -2.8999999999999998e-238

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0 67.6%

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

      1. associate-/l* 75.9%

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

      2. associate-/r/ 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in t around inf 62.6%

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

      1. associate-*r/ 67.4%

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

   8. Simplified 67.4%

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

      1. clear-num 67.3%

         \[\leadsto x + t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

      2. un-div-inv 67.4%

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

   10. Applied egg-rr 67.4%

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

   if -2.8999999999999998e-238 < z < 6.8e-302

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 86.6%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in x around inf 93.0%

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

      1. mul-1-neg 93.0%

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

      2. unsub-neg 93.0%

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

   8. Simplified 93.0%

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

   if 6.8e-302 < z < 1.49999999999999994e-78

   1. Initial program 85.8%

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

   3. Taylor expanded in z around 0 81.7%

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

      1. associate-/l* 78.7%

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

      2. associate-/r/ 81.7%

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

   5. Simplified 81.7%

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

   6. Taylor expanded in t around inf 73.5%

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

   if 1.49999999999999994e-78 < z < 1.59999999999999995e-27

   1. Initial program 99.4%

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

   3. Taylor expanded in y around inf 83.3%

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

   4. Taylor expanded in y around inf 80.3%

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

      1. div-sub 80.3%

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

      2. associate-*r/ 80.6%

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

      3. associate-/l* 80.7%

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

   6. Simplified 80.7%

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

   7. Taylor expanded in a around 0 78.9%

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

      1. mul-1-neg 78.9%

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

      2. associate-/l* 78.9%

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

      3. distribute-neg-frac 78.9%

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

   9. Simplified 78.9%

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

   if 1.59999999999999995e-27 < z < 6.80000000000000011e37

   1. Initial program 82.4%

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

   3. Taylor expanded in z around 0 73.8%

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

      1. associate-/l* 73.8%

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

      2. associate-/r/ 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in t around inf 70.9%

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

      1. associate-*r/ 70.9%

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

   8. Simplified 70.9%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8200000:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-238}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-302}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-78}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-27}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+37}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot \left(t - x\right)}{a - z}\\ t_2 := t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1200000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-284}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y (- t x)) (- a z)))) (t_2 (+ t (* (- y a) (/ x z)))))
   (if (<= z -1200000000000.0)
     t_2
     (if (<= z -7.5e-157)
       t_1
       (if (<= z -1.05e-284)
         (+ x (/ y (/ a (- t x))))
         (if (<= z 9.8e+64) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * (t - x)) / (a - z));
	double t_2 = t + ((y - a) * (x / z));
	double tmp;
	if (z <= -1200000000000.0) {
		tmp = t_2;
	} else if (z <= -7.5e-157) {
		tmp = t_1;
	} else if (z <= -1.05e-284) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 9.8e+64) {
		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 + ((y * (t - x)) / (a - z))
    t_2 = t + ((y - a) * (x / z))
    if (z <= (-1200000000000.0d0)) then
        tmp = t_2
    else if (z <= (-7.5d-157)) then
        tmp = t_1
    else if (z <= (-1.05d-284)) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 9.8d+64) 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 + ((y * (t - x)) / (a - z));
	double t_2 = t + ((y - a) * (x / z));
	double tmp;
	if (z <= -1200000000000.0) {
		tmp = t_2;
	} else if (z <= -7.5e-157) {
		tmp = t_1;
	} else if (z <= -1.05e-284) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 9.8e+64) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * (t - x)) / (a - z))
	t_2 = t + ((y - a) * (x / z))
	tmp = 0
	if z <= -1200000000000.0:
		tmp = t_2
	elif z <= -7.5e-157:
		tmp = t_1
	elif z <= -1.05e-284:
		tmp = x + (y / (a / (t - x)))
	elif z <= 9.8e+64:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * Float64(t - x)) / Float64(a - z)))
	t_2 = Float64(t + Float64(Float64(y - a) * Float64(x / z)))
	tmp = 0.0
	if (z <= -1200000000000.0)
		tmp = t_2;
	elseif (z <= -7.5e-157)
		tmp = t_1;
	elseif (z <= -1.05e-284)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 9.8e+64)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * (t - x)) / (a - z));
	t_2 = t + ((y - a) * (x / z));
	tmp = 0.0;
	if (z <= -1200000000000.0)
		tmp = t_2;
	elseif (z <= -7.5e-157)
		tmp = t_1;
	elseif (z <= -1.05e-284)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 9.8e+64)
		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[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1200000000000.0], t$95$2, If[LessEqual[z, -7.5e-157], t$95$1, If[LessEqual[z, -1.05e-284], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e+64], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2e12 or 9.8000000000000005e64 < z

   1. Initial program 61.5%

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

   3. Taylor expanded in z around inf 66.3%

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

      1. associate--l+ 66.3%

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

      2. distribute-lft-out-- 66.3%

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

      3. div-sub 66.3%

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

      4. mul-1-neg 66.3%

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

      5. unsub-neg 66.3%

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

      6. distribute-rgt-out-- 66.5%

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

      7. associate-/l* 79.6%

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

   5. Simplified 79.6%

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

   6. Taylor expanded in t around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. associate-*l/ 73.8%

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

      3. distribute-rgt-neg-in 73.8%

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

   8. Simplified 73.8%

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

   if -1.2e12 < z < -7.500000000000001e-157 or -1.04999999999999996e-284 < z < 9.8000000000000005e64

   1. Initial program 88.8%

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

   3. Taylor expanded in y around inf 82.3%

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

   if -7.500000000000001e-157 < z < -1.04999999999999996e-284

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 79.8%

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

      1. associate-/l* 96.9%

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

   5. Simplified 96.9%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1200000000000:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-157}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-284}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{+28}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.24 \cdot 10^{+225}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+241}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= a -8.8e+28)
     (+ x (* t (/ y a)))
     (if (<= a 2.2e+55)
       t_1
       (if (<= a 1.24e+225)
         (+ x (/ t (/ a y)))
         (if (<= a 4.6e+241) t_1 (- x (* x (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -8.8e+28) {
		tmp = x + (t * (y / a));
	} else if (a <= 2.2e+55) {
		tmp = t_1;
	} else if (a <= 1.24e+225) {
		tmp = x + (t / (a / y));
	} else if (a <= 4.6e+241) {
		tmp = t_1;
	} else {
		tmp = x - (x * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    if (a <= (-8.8d+28)) then
        tmp = x + (t * (y / a))
    else if (a <= 2.2d+55) then
        tmp = t_1
    else if (a <= 1.24d+225) then
        tmp = x + (t / (a / y))
    else if (a <= 4.6d+241) then
        tmp = t_1
    else
        tmp = x - (x * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (a <= -8.8e+28) {
		tmp = x + (t * (y / a));
	} else if (a <= 2.2e+55) {
		tmp = t_1;
	} else if (a <= 1.24e+225) {
		tmp = x + (t / (a / y));
	} else if (a <= 4.6e+241) {
		tmp = t_1;
	} else {
		tmp = x - (x * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if a <= -8.8e+28:
		tmp = x + (t * (y / a))
	elif a <= 2.2e+55:
		tmp = t_1
	elif a <= 1.24e+225:
		tmp = x + (t / (a / y))
	elif a <= 4.6e+241:
		tmp = t_1
	else:
		tmp = x - (x * (y / a))
	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 (a <= -8.8e+28)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (a <= 2.2e+55)
		tmp = t_1;
	elseif (a <= 1.24e+225)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (a <= 4.6e+241)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(x * Float64(y / a)));
	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 (a <= -8.8e+28)
		tmp = x + (t * (y / a));
	elseif (a <= 2.2e+55)
		tmp = t_1;
	elseif (a <= 1.24e+225)
		tmp = x + (t / (a / y));
	elseif (a <= 4.6e+241)
		tmp = t_1;
	else
		tmp = x - (x * (y / a));
	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[a, -8.8e+28], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e+55], t$95$1, If[LessEqual[a, 1.24e+225], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e+241], t$95$1, N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.79999999999999946e28

   1. Initial program 88.2%

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

   3. Taylor expanded in z around 0 67.1%

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

      1. associate-/l* 74.6%

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

      2. associate-/r/ 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in t around inf 61.0%

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

      1. associate-*r/ 66.4%

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

   8. Simplified 66.4%

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

   if -8.79999999999999946e28 < a < 2.2000000000000001e55 or 1.24e225 < a < 4.5999999999999999e241

   1. Initial program 72.6%

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

   3. Taylor expanded in t around inf 66.2%

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

   4. Taylor expanded in y around 0 53.7%

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

      1. +-commutative 53.7%

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

      2. associate-*r/ 55.5%

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

      3. associate-*r/ 55.5%

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

      4. mul-1-neg 55.5%

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

      5. distribute-rgt-neg-out 55.5%

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

      6. associate-*r/ 66.2%

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

      7. distribute-lft-out 66.2%

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

      8. distribute-frac-neg 66.2%

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

      9. sub-neg 66.2%

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

      10. div-sub 66.2%

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

   6. Simplified 66.2%

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

   if 2.2000000000000001e55 < a < 1.24e225

   1. Initial program 87.0%

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

   3. Taylor expanded in z around 0 60.8%

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

      1. associate-/l* 66.5%

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

      2. associate-/r/ 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in t around inf 60.1%

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

      1. associate-*r/ 63.2%

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

   8. Simplified 63.2%

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

      1. clear-num 63.3%

         \[\leadsto x + t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

      2. un-div-inv 63.3%

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

   10. Applied egg-rr 63.3%

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

   if 4.5999999999999999e241 < a

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 84.0%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in t around 0 78.7%

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

      1. associate-*r/ 78.7%

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

      2. mul-1-neg 78.7%

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

      3. distribute-lft-neg-out 78.7%

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

      4. associate-*r/ 94.7%

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

      5. distribute-lft-neg-out 94.7%

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

      6. distribute-rgt-neg-in 94.7%

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

      7. mul-1-neg 94.7%

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

      8. associate-*r/ 94.7%

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

      9. neg-mul-1 94.7%

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

   8. Simplified 94.7%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+28}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.24 \cdot 10^{+225}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+241}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-32}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -9.5e-80)
     t_2
     (if (<= z 2e-56)
       t_1
       (if (<= z 9.4e-32)
         (/ (- y) (/ z (- t x)))
         (if (<= z 5e+37) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -9.5e-80) {
		tmp = t_2;
	} else if (z <= 2e-56) {
		tmp = t_1;
	} else if (z <= 9.4e-32) {
		tmp = -y / (z / (t - x));
	} else if (z <= 5e+37) {
		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 + ((t - x) * (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-9.5d-80)) then
        tmp = t_2
    else if (z <= 2d-56) then
        tmp = t_1
    else if (z <= 9.4d-32) then
        tmp = -y / (z / (t - x))
    else if (z <= 5d+37) 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 + ((t - x) * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -9.5e-80) {
		tmp = t_2;
	} else if (z <= 2e-56) {
		tmp = t_1;
	} else if (z <= 9.4e-32) {
		tmp = -y / (z / (t - x));
	} else if (z <= 5e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -9.5e-80:
		tmp = t_2
	elif z <= 2e-56:
		tmp = t_1
	elif z <= 9.4e-32:
		tmp = -y / (z / (t - x))
	elif z <= 5e+37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -9.5e-80)
		tmp = t_2;
	elseif (z <= 2e-56)
		tmp = t_1;
	elseif (z <= 9.4e-32)
		tmp = Float64(Float64(-y) / Float64(z / Float64(t - x)));
	elseif (z <= 5e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -9.5e-80)
		tmp = t_2;
	elseif (z <= 2e-56)
		tmp = t_1;
	elseif (z <= 9.4e-32)
		tmp = -y / (z / (t - x));
	elseif (z <= 5e+37)
		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[(N[(t - x), $MachinePrecision] * 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[z, -9.5e-80], t$95$2, If[LessEqual[z, 2e-56], t$95$1, If[LessEqual[z, 9.4e-32], N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+37], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5000000000000003e-80 or 4.99999999999999989e37 < z

   1. Initial program 67.2%

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

   3. Taylor expanded in t around inf 61.6%

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

   4. Taylor expanded in y around 0 39.9%

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

      1. +-commutative 39.9%

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

      2. associate-*r/ 40.8%

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

      3. associate-*r/ 40.8%

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

      4. mul-1-neg 40.8%

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

      5. distribute-rgt-neg-out 40.8%

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

      6. associate-*r/ 61.6%

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

      7. distribute-lft-out 61.6%

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

      8. distribute-frac-neg 61.6%

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

      9. sub-neg 61.6%

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

      10. div-sub 61.6%

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

   6. Simplified 61.6%

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

   if -9.5000000000000003e-80 < z < 2.0000000000000001e-56 or 9.40000000000000039e-32 < z < 4.99999999999999989e37

   1. Initial program 90.5%

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

   3. Taylor expanded in z around 0 80.2%

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

      1. associate-/l* 84.2%

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

      2. associate-/r/ 84.6%

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

   5. Simplified 84.6%

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

   if 2.0000000000000001e-56 < z < 9.40000000000000039e-32

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf 76.1%

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

   4. Taylor expanded in y around inf 85.5%

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

      1. div-sub 85.5%

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

      2. associate-*r/ 85.9%

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

      3. associate-/l* 86.4%

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

   6. Simplified 86.4%

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

   7. Taylor expanded in a around 0 83.6%

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

      1. mul-1-neg 83.6%

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

      2. associate-/l* 83.8%

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

      3. distribute-neg-frac 83.8%

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

   9. Simplified 83.8%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-80}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-56}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-32}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+37}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-28}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.05e-80)
     t_2
     (if (<= z 1.45e-55)
       t_1
       (if (<= z 7e-28)
         (/ y (/ (- a z) (- t x)))
         (if (<= z 2.15e+39) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.05e-80) {
		tmp = t_2;
	} else if (z <= 1.45e-55) {
		tmp = t_1;
	} else if (z <= 7e-28) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 2.15e+39) {
		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 + ((t - x) * (y / a))
    t_2 = t * ((y - z) / (a - z))
    if (z <= (-1.05d-80)) then
        tmp = t_2
    else if (z <= 1.45d-55) then
        tmp = t_1
    else if (z <= 7d-28) then
        tmp = y / ((a - z) / (t - x))
    else if (z <= 2.15d+39) 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 + ((t - x) * (y / a));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -1.05e-80) {
		tmp = t_2;
	} else if (z <= 1.45e-55) {
		tmp = t_1;
	} else if (z <= 7e-28) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 2.15e+39) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -1.05e-80:
		tmp = t_2
	elif z <= 1.45e-55:
		tmp = t_1
	elif z <= 7e-28:
		tmp = y / ((a - z) / (t - x))
	elif z <= 2.15e+39:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -1.05e-80)
		tmp = t_2;
	elseif (z <= 1.45e-55)
		tmp = t_1;
	elseif (z <= 7e-28)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (z <= 2.15e+39)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -1.05e-80)
		tmp = t_2;
	elseif (z <= 1.45e-55)
		tmp = t_1;
	elseif (z <= 7e-28)
		tmp = y / ((a - z) / (t - x));
	elseif (z <= 2.15e+39)
		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[(N[(t - x), $MachinePrecision] * 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[z, -1.05e-80], t$95$2, If[LessEqual[z, 1.45e-55], t$95$1, If[LessEqual[z, 7e-28], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e+39], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000001e-80 or 2.15e39 < z

   1. Initial program 67.2%

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

   3. Taylor expanded in t around inf 61.6%

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

   4. Taylor expanded in y around 0 39.9%

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

      1. +-commutative 39.9%

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

      2. associate-*r/ 40.8%

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

      3. associate-*r/ 40.8%

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

      4. mul-1-neg 40.8%

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

      5. distribute-rgt-neg-out 40.8%

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

      6. associate-*r/ 61.6%

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

      7. distribute-lft-out 61.6%

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

      8. distribute-frac-neg 61.6%

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

      9. sub-neg 61.6%

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

      10. div-sub 61.6%

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

   6. Simplified 61.6%

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

   if -1.05000000000000001e-80 < z < 1.45e-55 or 6.9999999999999999e-28 < z < 2.15e39

   1. Initial program 90.5%

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

   3. Taylor expanded in z around 0 80.2%

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

      1. associate-/l* 84.2%

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

      2. associate-/r/ 84.6%

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

   5. Simplified 84.6%

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

   if 1.45e-55 < z < 6.9999999999999999e-28

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf 76.1%

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

   4. Taylor expanded in y around inf 85.5%

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

      1. div-sub 85.5%

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

      2. associate-*r/ 85.9%

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

      3. associate-/l* 86.4%

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

   6. Simplified 86.4%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-80}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-28}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+39}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+90}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+160}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -1.1e-79)
     t_1
     (if (<= z 1.6e-55)
       (+ x (* (- t x) (/ y a)))
       (if (<= z 5.8e+90)
         (/ y (/ (- a z) (- t x)))
         (if (<= z 8.8e+160) (+ t (/ 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) / (a - z));
	double tmp;
	if (z <= -1.1e-79) {
		tmp = t_1;
	} else if (z <= 1.6e-55) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 5.8e+90) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 8.8e+160) {
		tmp = t + (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) / (a - z))
    if (z <= (-1.1d-79)) then
        tmp = t_1
    else if (z <= 1.6d-55) then
        tmp = x + ((t - x) * (y / a))
    else if (z <= 5.8d+90) then
        tmp = y / ((a - z) / (t - x))
    else if (z <= 8.8d+160) then
        tmp = t + (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) / (a - z));
	double tmp;
	if (z <= -1.1e-79) {
		tmp = t_1;
	} else if (z <= 1.6e-55) {
		tmp = x + ((t - x) * (y / a));
	} else if (z <= 5.8e+90) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 8.8e+160) {
		tmp = t + (a / (z / (t - x)));
	} 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 <= -1.1e-79:
		tmp = t_1
	elif z <= 1.6e-55:
		tmp = x + ((t - x) * (y / a))
	elif z <= 5.8e+90:
		tmp = y / ((a - z) / (t - x))
	elif z <= 8.8e+160:
		tmp = t + (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(a - z)))
	tmp = 0.0
	if (z <= -1.1e-79)
		tmp = t_1;
	elseif (z <= 1.6e-55)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	elseif (z <= 5.8e+90)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (z <= 8.8e+160)
		tmp = Float64(t + Float64(a / Float64(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) / (a - z));
	tmp = 0.0;
	if (z <= -1.1e-79)
		tmp = t_1;
	elseif (z <= 1.6e-55)
		tmp = x + ((t - x) * (y / a));
	elseif (z <= 5.8e+90)
		tmp = y / ((a - z) / (t - x));
	elseif (z <= 8.8e+160)
		tmp = t + (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[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e-79], t$95$1, If[LessEqual[z, 1.6e-55], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+90], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e+160], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.0999999999999999e-79 or 8.79999999999999968e160 < z

   1. Initial program 68.0%

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

   3. Taylor expanded in t around inf 64.9%

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

   4. Taylor expanded in y around 0 42.7%

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

      1. +-commutative 42.7%

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

      2. associate-*r/ 43.7%

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

      3. associate-*r/ 43.7%

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

      4. mul-1-neg 43.7%

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

      5. distribute-rgt-neg-out 43.7%

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

      6. associate-*r/ 64.9%

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

      7. distribute-lft-out 64.9%

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

      8. distribute-frac-neg 64.9%

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

      9. sub-neg 64.9%

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

      10. div-sub 64.9%

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

   6. Simplified 64.9%

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

   if -1.0999999999999999e-79 < z < 1.6000000000000001e-55

   1. Initial program 91.3%

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

   3. Taylor expanded in z around 0 80.8%

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

      1. associate-/l* 85.3%

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

      2. associate-/r/ 85.7%

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

   5. Simplified 85.7%

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

   if 1.6000000000000001e-55 < z < 5.8000000000000003e90

   1. Initial program 84.0%

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

   3. Taylor expanded in y around inf 66.6%

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

   4. Taylor expanded in y around inf 58.7%

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

      1. div-sub 58.7%

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

      2. associate-*r/ 58.7%

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

      3. associate-/l* 58.9%

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

   6. Simplified 58.9%

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

   if 5.8000000000000003e90 < z < 8.79999999999999968e160

   1. Initial program 48.6%

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

   3. Taylor expanded in z around inf 78.9%

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

      1. associate--l+ 78.9%

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

      2. distribute-lft-out-- 78.9%

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

      3. div-sub 78.9%

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

      4. mul-1-neg 78.9%

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

      5. unsub-neg 78.9%

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

      6. distribute-rgt-out-- 78.9%

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

      7. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around 0 57.3%

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

      1. mul-1-neg 57.3%

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

      2. associate-/l* 68.6%

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

   8. Simplified 68.6%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-79}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+90}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+160}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{-38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-28}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))) (t_2 (+ t (* (- y a) (/ x z)))))
   (if (<= z -1.35e-38)
     t_2
     (if (<= z 1.7e-55)
       t_1
       (if (<= z 1.25e-28)
         (/ y (/ (- a z) (- t x)))
         (if (<= z 2.3e+37) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t + ((y - a) * (x / z));
	double tmp;
	if (z <= -1.35e-38) {
		tmp = t_2;
	} else if (z <= 1.7e-55) {
		tmp = t_1;
	} else if (z <= 1.25e-28) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 2.3e+37) {
		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 + ((t - x) * (y / a))
    t_2 = t + ((y - a) * (x / z))
    if (z <= (-1.35d-38)) then
        tmp = t_2
    else if (z <= 1.7d-55) then
        tmp = t_1
    else if (z <= 1.25d-28) then
        tmp = y / ((a - z) / (t - x))
    else if (z <= 2.3d+37) 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 + ((t - x) * (y / a));
	double t_2 = t + ((y - a) * (x / z));
	double tmp;
	if (z <= -1.35e-38) {
		tmp = t_2;
	} else if (z <= 1.7e-55) {
		tmp = t_1;
	} else if (z <= 1.25e-28) {
		tmp = y / ((a - z) / (t - x));
	} else if (z <= 2.3e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	t_2 = t + ((y - a) * (x / z))
	tmp = 0
	if z <= -1.35e-38:
		tmp = t_2
	elif z <= 1.7e-55:
		tmp = t_1
	elif z <= 1.25e-28:
		tmp = y / ((a - z) / (t - x))
	elif z <= 2.3e+37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	t_2 = Float64(t + Float64(Float64(y - a) * Float64(x / z)))
	tmp = 0.0
	if (z <= -1.35e-38)
		tmp = t_2;
	elseif (z <= 1.7e-55)
		tmp = t_1;
	elseif (z <= 1.25e-28)
		tmp = Float64(y / Float64(Float64(a - z) / Float64(t - x)));
	elseif (z <= 2.3e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	t_2 = t + ((y - a) * (x / z));
	tmp = 0.0;
	if (z <= -1.35e-38)
		tmp = t_2;
	elseif (z <= 1.7e-55)
		tmp = t_1;
	elseif (z <= 1.25e-28)
		tmp = y / ((a - z) / (t - x));
	elseif (z <= 2.3e+37)
		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[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e-38], t$95$2, If[LessEqual[z, 1.7e-55], t$95$1, If[LessEqual[z, 1.25e-28], N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+37], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35000000000000003e-38 or 2.30000000000000002e37 < z

   1. Initial program 65.3%

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

   3. Taylor expanded in z around inf 67.3%

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

      1. associate--l+ 67.3%

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

      2. distribute-lft-out-- 67.3%

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

      3. div-sub 67.3%

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

      4. mul-1-neg 67.3%

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

      5. unsub-neg 67.3%

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

      6. distribute-rgt-out-- 67.4%

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

      7. associate-/l* 78.6%

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

   5. Simplified 78.6%

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

   6. Taylor expanded in t around 0 64.6%

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

      1. mul-1-neg 64.6%

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

      2. associate-*l/ 69.6%

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

      3. distribute-rgt-neg-in 69.6%

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

   8. Simplified 69.6%

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

   if -1.35000000000000003e-38 < z < 1.69999999999999986e-55 or 1.25e-28 < z < 2.30000000000000002e37

   1. Initial program 91.1%

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

   3. Taylor expanded in z around 0 78.2%

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

      1. associate-/l* 82.1%

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

      2. associate-/r/ 82.4%

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

   5. Simplified 82.4%

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

   if 1.69999999999999986e-55 < z < 1.25e-28

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf 76.1%

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

   4. Taylor expanded in y around inf 85.5%

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

      1. div-sub 85.5%

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

      2. associate-*r/ 85.9%

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

      3. associate-/l* 86.4%

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

   6. Simplified 86.4%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-38}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-55}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-28}:\\ \;\;\;\;\frac{y}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+37}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -320000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))) (t_2 (* t (- 1.0 (/ y z)))))
   (if (<= z -320000.0)
     t_2
     (if (<= z -2.15e-238)
       t_1
       (if (<= z 3.7e-298)
         (* x (- 1.0 (/ y a)))
         (if (<= z 1.9e+39) t_1 t_2))))))

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 tmp;
	if (z <= -320000.0) {
		tmp = t_2;
	} else if (z <= -2.15e-238) {
		tmp = t_1;
	} else if (z <= 3.7e-298) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.9e+39) {
		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 + (t * (y / a))
    t_2 = t * (1.0d0 - (y / z))
    if (z <= (-320000.0d0)) then
        tmp = t_2
    else if (z <= (-2.15d-238)) then
        tmp = t_1
    else if (z <= 3.7d-298) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.9d+39) 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 + (t * (y / a));
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -320000.0) {
		tmp = t_2;
	} else if (z <= -2.15e-238) {
		tmp = t_1;
	} else if (z <= 3.7e-298) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.9e+39) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	t_2 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -320000.0:
		tmp = t_2
	elif z <= -2.15e-238:
		tmp = t_1
	elif z <= 3.7e-298:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.9e+39:
		tmp = t_1
	else:
		tmp = t_2
	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)))
	tmp = 0.0
	if (z <= -320000.0)
		tmp = t_2;
	elseif (z <= -2.15e-238)
		tmp = t_1;
	elseif (z <= 3.7e-298)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.9e+39)
		tmp = t_1;
	else
		tmp = t_2;
	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));
	tmp = 0.0;
	if (z <= -320000.0)
		tmp = t_2;
	elseif (z <= -2.15e-238)
		tmp = t_1;
	elseif (z <= 3.7e-298)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.9e+39)
		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[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -320000.0], t$95$2, If[LessEqual[z, -2.15e-238], t$95$1, If[LessEqual[z, 3.7e-298], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+39], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2e5 or 1.8999999999999999e39 < z

   1. Initial program 64.2%

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

   3. Taylor expanded in t around inf 63.1%

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

   4. Taylor expanded in a around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. unsub-neg 56.1%

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

   6. Simplified 56.1%

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

   if -3.2e5 < z < -2.14999999999999984e-238 or 3.6999999999999998e-298 < z < 1.8999999999999999e39

   1. Initial program 89.7%

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

   3. Taylor expanded in z around 0 71.2%

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

      1. associate-/l* 73.5%

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

      2. associate-/r/ 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in t around inf 64.8%

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

      1. associate-*r/ 66.8%

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

   8. Simplified 66.8%

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

   if -2.14999999999999984e-238 < z < 3.6999999999999998e-298

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 86.6%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in x around inf 93.0%

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

      1. mul-1-neg 93.0%

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

      2. unsub-neg 93.0%

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

   8. Simplified 93.0%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -320000:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-238}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+39}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ t_2 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -9200000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t (/ a y)))) (t_2 (* t (- 1.0 (/ y z)))))
   (if (<= z -9200000.0)
     t_2
     (if (<= z -3.6e-238)
       t_1
       (if (<= z 8.5e-296)
         (* x (- 1.0 (/ y a)))
         (if (<= z 1.95e+37) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / y));
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -9200000.0) {
		tmp = t_2;
	} else if (z <= -3.6e-238) {
		tmp = t_1;
	} else if (z <= 8.5e-296) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.95e+37) {
		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 + (t / (a / y))
    t_2 = t * (1.0d0 - (y / z))
    if (z <= (-9200000.0d0)) then
        tmp = t_2
    else if (z <= (-3.6d-238)) then
        tmp = t_1
    else if (z <= 8.5d-296) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 1.95d+37) 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 + (t / (a / y));
	double t_2 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -9200000.0) {
		tmp = t_2;
	} else if (z <= -3.6e-238) {
		tmp = t_1;
	} else if (z <= 8.5e-296) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 1.95e+37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / (a / y))
	t_2 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -9200000.0:
		tmp = t_2
	elif z <= -3.6e-238:
		tmp = t_1
	elif z <= 8.5e-296:
		tmp = x * (1.0 - (y / a))
	elif z <= 1.95e+37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / Float64(a / y)))
	t_2 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -9200000.0)
		tmp = t_2;
	elseif (z <= -3.6e-238)
		tmp = t_1;
	elseif (z <= 8.5e-296)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 1.95e+37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t / (a / y));
	t_2 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -9200000.0)
		tmp = t_2;
	elseif (z <= -3.6e-238)
		tmp = t_1;
	elseif (z <= 8.5e-296)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 1.95e+37)
		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[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9200000.0], t$95$2, If[LessEqual[z, -3.6e-238], t$95$1, If[LessEqual[z, 8.5e-296], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+37], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.2e6 or 1.9499999999999999e37 < z

   1. Initial program 64.2%

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

   3. Taylor expanded in t around inf 63.1%

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

   4. Taylor expanded in a around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. unsub-neg 56.1%

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

   6. Simplified 56.1%

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

   if -9.2e6 < z < -3.6000000000000001e-238 or 8.50000000000000018e-296 < z < 1.9499999999999999e37

   1. Initial program 89.7%

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

   3. Taylor expanded in z around 0 71.2%

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

      1. associate-/l* 73.5%

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

      2. associate-/r/ 74.6%

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

   5. Simplified 74.6%

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

   6. Taylor expanded in t around inf 64.8%

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

      1. associate-*r/ 66.8%

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

   8. Simplified 66.8%

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

      1. clear-num 66.8%

         \[\leadsto x + t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

      2. un-div-inv 66.8%

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

   10. Applied egg-rr 66.8%

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

   if -3.6000000000000001e-238 < z < 8.50000000000000018e-296

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 86.6%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in x around inf 93.0%

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

      1. mul-1-neg 93.0%

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

      2. unsub-neg 93.0%

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

   8. Simplified 93.0%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9200000:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-238}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-9}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.2e+28)
   x
   (if (<= a 1.4e-9)
     (* t (- 1.0 (/ y z)))
     (if (<= a 9.5e+72) (* t (/ (- y z) a)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.2e+28) {
		tmp = x;
	} else if (a <= 1.4e-9) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 9.5e+72) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-8.2d+28)) then
        tmp = x
    else if (a <= 1.4d-9) then
        tmp = t * (1.0d0 - (y / z))
    else if (a <= 9.5d+72) then
        tmp = t * ((y - z) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.2e+28) {
		tmp = x;
	} else if (a <= 1.4e-9) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= 9.5e+72) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.2e+28:
		tmp = x
	elif a <= 1.4e-9:
		tmp = t * (1.0 - (y / z))
	elif a <= 9.5e+72:
		tmp = t * ((y - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.2e+28)
		tmp = x;
	elseif (a <= 1.4e-9)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (a <= 9.5e+72)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.2e+28)
		tmp = x;
	elseif (a <= 1.4e-9)
		tmp = t * (1.0 - (y / z));
	elseif (a <= 9.5e+72)
		tmp = t * ((y - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.2e+28], x, If[LessEqual[a, 1.4e-9], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e+72], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.19999999999999961e28 or 9.50000000000000054e72 < a

   1. Initial program 92.1%

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

   3. Taylor expanded in a around inf 55.1%

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

   if -8.19999999999999961e28 < a < 1.39999999999999992e-9

   1. Initial program 70.0%

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

   3. Taylor expanded in t around inf 66.8%

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

   4. Taylor expanded in a around 0 56.6%

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

      1. mul-1-neg 56.6%

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

      2. unsub-neg 56.6%

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

   6. Simplified 56.6%

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

   if 1.39999999999999992e-9 < a < 9.50000000000000054e72

   1. Initial program 76.4%

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

   3. Taylor expanded in t around inf 45.5%

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

   4. Taylor expanded in y around 0 41.3%

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

      1. +-commutative 41.3%

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

      2. associate-*r/ 41.3%

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

      3. associate-*r/ 41.3%

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

      4. mul-1-neg 41.3%

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

      5. distribute-rgt-neg-out 41.3%

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

      6. associate-*r/ 45.5%

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

      7. distribute-lft-out 45.5%

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

      8. distribute-frac-neg 45.5%

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

      9. sub-neg 45.5%

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

      10. div-sub 45.5%

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

   6. Simplified 45.5%

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

   7. Taylor expanded in a around inf 33.8%

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

      1. associate-*r/ 33.8%

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

   9. Simplified 33.8%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-9}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 77.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-39} \lor \neg \left(z \leq 2.8 \cdot 10^{+37}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.7e-39) (not (<= z 2.8e+37)))
   (+ t (/ (- x t) (/ z (- y a))))
   (+ x (/ (* y (- t x)) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.7e-39) || !(z <= 2.8e+37)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((y * (t - x)) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.7d-39)) .or. (.not. (z <= 2.8d+37))) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = x + ((y * (t - x)) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.7e-39) || !(z <= 2.8e+37)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + ((y * (t - x)) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.7e-39) or not (z <= 2.8e+37):
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = x + ((y * (t - x)) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.7e-39) || !(z <= 2.8e+37))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.7e-39) || ~((z <= 2.8e+37)))
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = x + ((y * (t - x)) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.7e-39], N[Not[LessEqual[z, 2.8e+37]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.70000000000000015e-39 or 2.7999999999999998e37 < z

   1. Initial program 65.3%

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

   3. Taylor expanded in z around inf 67.3%

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

      1. associate--l+ 67.3%

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

      2. distribute-lft-out-- 67.3%

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

      3. div-sub 67.3%

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

      4. mul-1-neg 67.3%

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

      5. unsub-neg 67.3%

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

      6. distribute-rgt-out-- 67.4%

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

      7. associate-/l* 78.6%

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

   5. Simplified 78.6%

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

   if -3.70000000000000015e-39 < z < 2.7999999999999998e37

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf 84.4%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-39} \lor \neg \left(z \leq 2.8 \cdot 10^{+37}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-40} \lor \neg \left(z \leq 1.9 \cdot 10^{+37}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.2e-40) (not (<= z 1.9e+37)))
   (* t (- 1.0 (/ y z)))
   (* x (- 1.0 (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.2e-40) || !(z <= 1.9e+37)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.2d-40)) .or. (.not. (z <= 1.9d+37))) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.2e-40) || !(z <= 1.9e+37)) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.2e-40) or not (z <= 1.9e+37):
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.2e-40) || !(z <= 1.9e+37))
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.2e-40) || ~((z <= 1.9e+37)))
		tmp = t * (1.0 - (y / z));
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.2e-40], N[Not[LessEqual[z, 1.9e+37]], $MachinePrecision]], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.2e-40 or 1.89999999999999995e37 < z

   1. Initial program 65.3%

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

   3. Taylor expanded in t around inf 61.9%

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

   4. Taylor expanded in a around 0 55.4%

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

      1. mul-1-neg 55.4%

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

      2. unsub-neg 55.4%

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

   6. Simplified 55.4%

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

   if -9.2e-40 < z < 1.89999999999999995e37

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0 75.0%

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

      1. associate-/l* 78.6%

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

      2. associate-/r/ 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in x around inf 54.9%

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

      1. mul-1-neg 54.9%

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

      2. unsub-neg 54.9%

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

   8. Simplified 54.9%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-40} \lor \neg \left(z \leq 1.9 \cdot 10^{+37}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6e+28) x (if (<= a 6.4e+72) (* t (- 1.0 (/ y z))) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6e+28) {
		tmp = x;
	} else if (a <= 6.4e+72) {
		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 <= (-6d+28)) then
        tmp = x
    else if (a <= 6.4d+72) 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 <= -6e+28) {
		tmp = x;
	} else if (a <= 6.4e+72) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6e+28:
		tmp = x
	elif a <= 6.4e+72:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6e+28)
		tmp = x;
	elseif (a <= 6.4e+72)
		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 <= -6e+28)
		tmp = x;
	elseif (a <= 6.4e+72)
		tmp = t * (1.0 - (y / z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6e+28], x, If[LessEqual[a, 6.4e+72], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -6.0000000000000002e28 or 6.4000000000000003e72 < a

   1. Initial program 92.1%

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

   3. Taylor expanded in a around inf 55.1%

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

   if -6.0000000000000002e28 < a < 6.4000000000000003e72

   1. Initial program 70.9%

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

   3. Taylor expanded in t around inf 63.8%

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

   4. Taylor expanded in a around 0 50.4%

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

      1. mul-1-neg 50.4%

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

      2. unsub-neg 50.4%

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

   6. Simplified 50.4%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 37.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-46}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2e+21)
   x
   (if (<= a -5.8e-91) (/ x (/ z y)) (if (<= a 1.15e-46) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e+21) {
		tmp = x;
	} else if (a <= -5.8e-91) {
		tmp = x / (z / y);
	} else if (a <= 1.15e-46) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2d+21)) then
        tmp = x
    else if (a <= (-5.8d-91)) then
        tmp = x / (z / y)
    else if (a <= 1.15d-46) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e+21) {
		tmp = x;
	} else if (a <= -5.8e-91) {
		tmp = x / (z / y);
	} else if (a <= 1.15e-46) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2e+21:
		tmp = x
	elif a <= -5.8e-91:
		tmp = x / (z / y)
	elif a <= 1.15e-46:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2e+21)
		tmp = x;
	elseif (a <= -5.8e-91)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 1.15e-46)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2e+21)
		tmp = x;
	elseif (a <= -5.8e-91)
		tmp = x / (z / y);
	elseif (a <= 1.15e-46)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2e+21], x, If[LessEqual[a, -5.8e-91], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e-46], t, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -2e21 or 1.15e-46 < a

   1. Initial program 88.7%

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

   3. Taylor expanded in a around inf 45.3%

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

   if -2e21 < a < -5.8000000000000001e-91

   1. Initial program 87.1%

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

   3. Taylor expanded in y around inf 69.8%

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

   4. Taylor expanded in y around inf 75.6%

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

      1. div-sub 75.6%

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

      2. associate-*r/ 72.1%

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

      3. associate-/l* 76.0%

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

   6. Simplified 76.0%

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

   7. Taylor expanded in a around 0 45.0%

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

      1. mul-1-neg 45.0%

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

      2. associate-/l* 45.0%

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

      3. distribute-neg-frac 45.0%

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

   9. Simplified 45.0%

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

   10. Taylor expanded in t around 0 38.2%

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

       1. associate-/l* 46.7%

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

   12. Simplified 46.7%

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

   if -5.8000000000000001e-91 < a < 1.15e-46

   1. Initial program 64.9%

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

   3. Taylor expanded in z around inf 42.5%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-46}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 37.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-45}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-46}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e+29)
   x
   (if (<= a -1.6e-45) (/ (- x) (/ a y)) (if (<= a 1.75e-46) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e+29) {
		tmp = x;
	} else if (a <= -1.6e-45) {
		tmp = -x / (a / y);
	} else if (a <= 1.75e-46) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.6d+29)) then
        tmp = x
    else if (a <= (-1.6d-45)) then
        tmp = -x / (a / y)
    else if (a <= 1.75d-46) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e+29) {
		tmp = x;
	} else if (a <= -1.6e-45) {
		tmp = -x / (a / y);
	} else if (a <= 1.75e-46) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e+29:
		tmp = x
	elif a <= -1.6e-45:
		tmp = -x / (a / y)
	elif a <= 1.75e-46:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e+29)
		tmp = x;
	elseif (a <= -1.6e-45)
		tmp = Float64(Float64(-x) / Float64(a / y));
	elseif (a <= 1.75e-46)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.6e+29)
		tmp = x;
	elseif (a <= -1.6e-45)
		tmp = -x / (a / y);
	elseif (a <= 1.75e-46)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e+29], x, If[LessEqual[a, -1.6e-45], N[((-x) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.75e-46], t, x]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.59999999999999993e29 or 1.7500000000000001e-46 < a

   1. Initial program 89.9%

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

   3. Taylor expanded in a around inf 46.5%

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

   if -1.59999999999999993e29 < a < -1.60000000000000004e-45

   1. Initial program 81.1%

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

   3. Taylor expanded in y around inf 71.8%

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

   4. Taylor expanded in y around inf 72.8%

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

      1. div-sub 72.8%

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

      2. associate-*r/ 68.9%

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

      3. associate-/l* 73.2%

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

   6. Simplified 73.2%

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

   7. Taylor expanded in a around inf 56.6%

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

   8. Taylor expanded in t around 0 33.7%

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

      1. mul-1-neg 33.7%

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

      2. associate-/l* 42.6%

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

      3. distribute-neg-frac 42.6%

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

   10. Simplified 42.6%

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

   if -1.60000000000000004e-45 < a < 1.7500000000000001e-46

   1. Initial program 66.0%

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

   3. Taylor expanded in z around inf 42.1%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-45}:\\ \;\;\;\;\frac{-x}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-46}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 38.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.7e+14) t (if (<= z 3.2e+90) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.7e+14) {
		tmp = t;
	} else if (z <= 3.2e+90) {
		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 <= (-2.7d+14)) then
        tmp = t
    else if (z <= 3.2d+90) 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 <= -2.7e+14) {
		tmp = t;
	} else if (z <= 3.2e+90) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.7e+14:
		tmp = t
	elif z <= 3.2e+90:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.7e+14)
		tmp = t;
	elseif (z <= 3.2e+90)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.7e+14)
		tmp = t;
	elseif (z <= 3.2e+90)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.7e+14], t, If[LessEqual[z, 3.2e+90], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e14 or 3.19999999999999998e90 < z

   1. Initial program 61.6%

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

   3. Taylor expanded in z around inf 53.6%

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

   if -2.7e14 < z < 3.19999999999999998e90

   1. Initial program 89.9%

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

   3. Taylor expanded in a around inf 34.7%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 25.0% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.2%

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

3. Taylor expanded in z around inf 25.5%

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

4. Final simplification 25.5%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))