Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.4% → 90.7%

Time: 14.2s

Alternatives: 13

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: 79.4% 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: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-249} \lor \neg \left(t\_1 \leq 5 \cdot 10^{-242}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-249) (not (<= t_1 5e-242)))
     t_1
     (+ t (* (/ (- t x) z) (- a y))))))

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 <= -2e-249) || !(t_1 <= 5e-242)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-249)) .or. (.not. (t_1 <= 5d-242))) then
        tmp = t_1
    else
        tmp = t + (((t - x) / z) * (a - y))
    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 <= -2e-249) || !(t_1 <= 5e-242)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-249) or not (t_1 <= 5e-242):
		tmp = t_1
	else:
		tmp = t + (((t - x) / z) * (a - y))
	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 <= -2e-249) || !(t_1 <= 5e-242))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	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 <= -2e-249) || ~((t_1 <= 5e-242)))
		tmp = t_1;
	else
		tmp = t + (((t - x) / z) * (a - y));
	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, -2e-249], N[Not[LessEqual[t$95$1, 5e-242]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $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)))) < -2.00000000000000011e-249 or 4.9999999999999998e-242 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 93.1%

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

   if -2.00000000000000011e-249 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999998e-242

   1. Initial program 3.5%

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

      1. +-commutative 3.5%

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

      2. fma-define 4.0%

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

   3. Simplified 4.0%

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

   5. Taylor expanded in z around inf 76.0%

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

      1. associate--l+ 76.0%

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

      2. distribute-lft-out-- 76.0%

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

      3. div-sub 76.0%

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

      4. mul-1-neg 76.0%

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

      5. unsub-neg 76.0%

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

      6. div-sub 76.0%

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

      7. associate-/l* 82.7%

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

      8. associate-/l* 99.7%

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

      9. distribute-rgt-out-- 99.7%

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

   7. Simplified 99.7%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-249} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 5 \cdot 10^{-242}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 38.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{+156}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.38 \cdot 10^{-261}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-154}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) a))))
   (if (<= a -8.5e+156)
     x
     (if (<= a -4.6e-129)
       t_1
       (if (<= a 1.38e-261)
         t
         (if (<= a 5.7e-154) (* x (/ y z)) (if (<= a 1e+122) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (a <= -8.5e+156) {
		tmp = x;
	} else if (a <= -4.6e-129) {
		tmp = t_1;
	} else if (a <= 1.38e-261) {
		tmp = t;
	} else if (a <= 5.7e-154) {
		tmp = x * (y / z);
	} else if (a <= 1e+122) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / a)
    if (a <= (-8.5d+156)) then
        tmp = x
    else if (a <= (-4.6d-129)) then
        tmp = t_1
    else if (a <= 1.38d-261) then
        tmp = t
    else if (a <= 5.7d-154) then
        tmp = x * (y / z)
    else if (a <= 1d+122) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (a <= -8.5e+156) {
		tmp = x;
	} else if (a <= -4.6e-129) {
		tmp = t_1;
	} else if (a <= 1.38e-261) {
		tmp = t;
	} else if (a <= 5.7e-154) {
		tmp = x * (y / z);
	} else if (a <= 1e+122) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	tmp = 0
	if a <= -8.5e+156:
		tmp = x
	elif a <= -4.6e-129:
		tmp = t_1
	elif a <= 1.38e-261:
		tmp = t
	elif a <= 5.7e-154:
		tmp = x * (y / z)
	elif a <= 1e+122:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (a <= -8.5e+156)
		tmp = x;
	elseif (a <= -4.6e-129)
		tmp = t_1;
	elseif (a <= 1.38e-261)
		tmp = t;
	elseif (a <= 5.7e-154)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1e+122)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	tmp = 0.0;
	if (a <= -8.5e+156)
		tmp = x;
	elseif (a <= -4.6e-129)
		tmp = t_1;
	elseif (a <= 1.38e-261)
		tmp = t;
	elseif (a <= 5.7e-154)
		tmp = x * (y / z);
	elseif (a <= 1e+122)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.5e+156], x, If[LessEqual[a, -4.6e-129], t$95$1, If[LessEqual[a, 1.38e-261], t, If[LessEqual[a, 5.7e-154], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e+122], t$95$1, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.49999999999999948e156 or 1.00000000000000001e122 < a

   1. Initial program 89.0%

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

      1. +-commutative 89.0%

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

      2. fma-define 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in a around inf 59.2%

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

   if -8.49999999999999948e156 < a < -4.5999999999999999e-129 or 5.6999999999999998e-154 < a < 1.00000000000000001e122

   1. Initial program 84.9%

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

   3. Taylor expanded in z around 0 56.0%

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

   4. Taylor expanded in y around inf 46.9%

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

      1. div-sub 46.9%

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

   6. Simplified 46.9%

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

   if -4.5999999999999999e-129 < a < 1.38e-261

   1. Initial program 73.7%

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

      1. clear-num 73.8%

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

      2. un-div-inv 74.8%

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

   4. Applied egg-rr 74.8%

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

   5. Taylor expanded in z around inf 44.1%

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

   if 1.38e-261 < a < 5.6999999999999998e-154

   1. Initial program 77.0%

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

      1. +-commutative 77.0%

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

      2. fma-define 77.5%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in t around 0 40.5%

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

      1. mul-1-neg 40.5%

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

      2. *-rgt-identity 40.5%

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

      3. associate-/l* 40.5%

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

      4. distribute-rgt-neg-in 40.5%

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

      5. mul-1-neg 40.5%

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

      6. distribute-lft-in 40.5%

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

      7. mul-1-neg 40.5%

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

      8. unsub-neg 40.5%

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

   7. Simplified 40.5%

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

   8. Taylor expanded in a around 0 49.6%

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

Alternative 3: 34.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-262}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.8e-36)
   x
   (if (<= a 7.2e-262)
     t
     (if (<= a 7.5e-24) (* x (/ y z)) (if (<= a 2.2e+121) (* y (/ t a)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.8e-36) {
		tmp = x;
	} else if (a <= 7.2e-262) {
		tmp = t;
	} else if (a <= 7.5e-24) {
		tmp = x * (y / z);
	} else if (a <= 2.2e+121) {
		tmp = y * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.8d-36)) then
        tmp = x
    else if (a <= 7.2d-262) then
        tmp = t
    else if (a <= 7.5d-24) then
        tmp = x * (y / z)
    else if (a <= 2.2d+121) then
        tmp = y * (t / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.8e-36) {
		tmp = x;
	} else if (a <= 7.2e-262) {
		tmp = t;
	} else if (a <= 7.5e-24) {
		tmp = x * (y / z);
	} else if (a <= 2.2e+121) {
		tmp = y * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.8e-36:
		tmp = x
	elif a <= 7.2e-262:
		tmp = t
	elif a <= 7.5e-24:
		tmp = x * (y / z)
	elif a <= 2.2e+121:
		tmp = y * (t / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.8e-36)
		tmp = x;
	elseif (a <= 7.2e-262)
		tmp = t;
	elseif (a <= 7.5e-24)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 2.2e+121)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.8e-36)
		tmp = x;
	elseif (a <= 7.2e-262)
		tmp = t;
	elseif (a <= 7.5e-24)
		tmp = x * (y / z);
	elseif (a <= 2.2e+121)
		tmp = y * (t / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.8e-36], x, If[LessEqual[a, 7.2e-262], t, If[LessEqual[a, 7.5e-24], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e+121], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.80000000000000016e-36 or 2.20000000000000001e121 < a

   1. Initial program 88.0%

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

      1. +-commutative 88.0%

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

      2. fma-define 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in a around inf 49.2%

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

   if -1.80000000000000016e-36 < a < 7.1999999999999995e-262

   1. Initial program 71.7%

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

      1. clear-num 71.6%

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

      2. un-div-inv 73.9%

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

   4. Applied egg-rr 73.9%

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

   5. Taylor expanded in z around inf 38.1%

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

   if 7.1999999999999995e-262 < a < 7.50000000000000007e-24

   1. Initial program 80.4%

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

      1. +-commutative 80.4%

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

      2. fma-define 80.6%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in t around 0 46.4%

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

      1. mul-1-neg 46.4%

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

      2. *-rgt-identity 46.4%

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

      3. associate-/l* 46.5%

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

      4. distribute-rgt-neg-in 46.5%

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

      5. mul-1-neg 46.5%

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

      6. distribute-lft-in 46.6%

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

      7. mul-1-neg 46.6%

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

      8. unsub-neg 46.6%

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

   7. Simplified 46.6%

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

   8. Taylor expanded in a around 0 44.0%

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

   if 7.50000000000000007e-24 < a < 2.20000000000000001e121

   1. Initial program 95.8%

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

   3. Taylor expanded in z around 0 64.9%

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

   4. Taylor expanded in y around inf 58.4%

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

      1. div-sub 58.4%

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

   6. Simplified 58.4%

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

   7. Taylor expanded in t around inf 47.2%

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

Alternative 4: 36.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-260}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+67}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.5e-36)
   x
   (if (<= a 9.5e-260)
     t
     (if (<= a 8.4e-54) (* x (/ y z)) (if (<= a 3.8e+67) t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.5e-36) {
		tmp = x;
	} else if (a <= 9.5e-260) {
		tmp = t;
	} else if (a <= 8.4e-54) {
		tmp = x * (y / z);
	} else if (a <= 3.8e+67) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7.5d-36)) then
        tmp = x
    else if (a <= 9.5d-260) then
        tmp = t
    else if (a <= 8.4d-54) then
        tmp = x * (y / z)
    else if (a <= 3.8d+67) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.5e-36) {
		tmp = x;
	} else if (a <= 9.5e-260) {
		tmp = t;
	} else if (a <= 8.4e-54) {
		tmp = x * (y / z);
	} else if (a <= 3.8e+67) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.5e-36:
		tmp = x
	elif a <= 9.5e-260:
		tmp = t
	elif a <= 8.4e-54:
		tmp = x * (y / z)
	elif a <= 3.8e+67:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.5e-36)
		tmp = x;
	elseif (a <= 9.5e-260)
		tmp = t;
	elseif (a <= 8.4e-54)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 3.8e+67)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.5e-36)
		tmp = x;
	elseif (a <= 9.5e-260)
		tmp = t;
	elseif (a <= 8.4e-54)
		tmp = x * (y / z);
	elseif (a <= 3.8e+67)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.5e-36], x, If[LessEqual[a, 9.5e-260], t, If[LessEqual[a, 8.4e-54], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e+67], t, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.49999999999999972e-36 or 3.8000000000000002e67 < a

   1. Initial program 89.1%

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

      1. +-commutative 89.1%

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

      2. fma-define 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in a around inf 47.5%

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

   if -7.49999999999999972e-36 < a < 9.5000000000000001e-260 or 8.4e-54 < a < 3.8000000000000002e67

   1. Initial program 76.2%

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

      1. clear-num 76.2%

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

      2. un-div-inv 77.8%

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

   4. Applied egg-rr 77.8%

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

   5. Taylor expanded in z around inf 37.2%

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

   if 9.5000000000000001e-260 < a < 8.4e-54

   1. Initial program 82.2%

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

      1. +-commutative 82.2%

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

      2. fma-define 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in t around 0 46.8%

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

      1. mul-1-neg 46.8%

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

      2. *-rgt-identity 46.8%

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

      3. associate-/l* 46.9%

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

      4. distribute-rgt-neg-in 46.9%

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

      5. mul-1-neg 46.9%

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

      6. distribute-lft-in 47.0%

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

      7. mul-1-neg 47.0%

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

      8. unsub-neg 47.0%

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

   7. Simplified 47.0%

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

   8. Taylor expanded in a around 0 48.1%

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

Alternative 5: 78.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -85000000000 \lor \neg \left(z \leq 5.8 \cdot 10^{+124}\right):\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -85000000000.0) (not (<= z 5.8e+124)))
   (+ t (* (/ (- t x) z) (- a y)))
   (+ x (/ y (/ (- a z) (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -85000000000.0) || !(z <= 5.8e+124)) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + (y / ((a - z) / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-85000000000.0d0)) .or. (.not. (z <= 5.8d+124))) then
        tmp = t + (((t - x) / z) * (a - y))
    else
        tmp = x + (y / ((a - z) / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -85000000000.0) || !(z <= 5.8e+124)) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + (y / ((a - z) / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -85000000000.0) or not (z <= 5.8e+124):
		tmp = t + (((t - x) / z) * (a - y))
	else:
		tmp = x + (y / ((a - z) / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -85000000000.0) || !(z <= 5.8e+124))
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -85000000000.0) || ~((z <= 5.8e+124)))
		tmp = t + (((t - x) / z) * (a - y));
	else
		tmp = x + (y / ((a - z) / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -85000000000.0], N[Not[LessEqual[z, 5.8e+124]], $MachinePrecision]], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5e10 or 5.80000000000000043e124 < z

   1. Initial program 64.1%

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

      1. +-commutative 64.1%

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

      2. fma-define 64.1%

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

   3. Simplified 64.1%

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

   5. Taylor expanded in z around inf 59.8%

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

      1. associate--l+ 59.8%

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

      2. distribute-lft-out-- 59.8%

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

      3. div-sub 59.8%

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

      4. mul-1-neg 59.8%

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

      5. unsub-neg 59.8%

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

      6. div-sub 59.8%

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

      7. associate-/l* 69.2%

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

      8. associate-/l* 76.2%

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

      9. distribute-rgt-out-- 76.2%

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

   7. Simplified 76.2%

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

   if -8.5e10 < z < 5.80000000000000043e124

   1. Initial program 94.0%

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

      1. clear-num 93.5%

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

      2. un-div-inv 94.4%

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

   4. Applied egg-rr 94.4%

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

   5. Taylor expanded in y around inf 85.2%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -85000000000 \lor \neg \left(z \leq 5.8 \cdot 10^{+124}\right):\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+157} \lor \neg \left(y \leq 19000000000\right):\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.8e+157) (not (<= y 19000000000.0)))
   (+ x (/ y (/ (- a z) (- t x))))
   (+ x (* t (/ (- y z) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.8e+157) || !(y <= 19000000000.0)) {
		tmp = x + (y / ((a - z) / (t - x)));
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-4.8d+157)) .or. (.not. (y <= 19000000000.0d0))) then
        tmp = x + (y / ((a - z) / (t - x)))
    else
        tmp = x + (t * ((y - z) / (a - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.8e+157) || !(y <= 19000000000.0)) {
		tmp = x + (y / ((a - z) / (t - x)));
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.8e+157) or not (y <= 19000000000.0):
		tmp = x + (y / ((a - z) / (t - x)))
	else:
		tmp = x + (t * ((y - z) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.8e+157) || !(y <= 19000000000.0))
		tmp = Float64(x + Float64(y / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4.8e+157) || ~((y <= 19000000000.0)))
		tmp = x + (y / ((a - z) / (t - x)));
	else
		tmp = x + (t * ((y - z) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.8e+157], N[Not[LessEqual[y, 19000000000.0]], $MachinePrecision]], N[(x + N[(y / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.7999999999999999e157 or 1.9e10 < y

   1. Initial program 90.0%

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

      1. clear-num 89.5%

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

      2. un-div-inv 89.4%

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

   4. Applied egg-rr 89.4%

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

   5. Taylor expanded in y around inf 84.6%

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

   if -4.7999999999999999e157 < y < 1.9e10

   1. Initial program 78.6%

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

   3. Taylor expanded in t around inf 62.6%

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

      1. associate-/l* 71.6%

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

   5. Simplified 71.6%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+157} \lor \neg \left(y \leq 19000000000\right):\\ \;\;\;\;x + \frac{y}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-157} \lor \neg \left(t \leq 2.95 \cdot 10^{-77}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.9e-157) (not (<= t 2.95e-77)))
   (+ x (* t (/ (- y z) (- a z))))
   (* x (+ (/ (- y z) (- z a)) 1.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.9e-157) || !(t <= 2.95e-77)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.9d-157)) .or. (.not. (t <= 2.95d-77))) then
        tmp = x + (t * ((y - z) / (a - z)))
    else
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.9e-157) || !(t <= 2.95e-77)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.9e-157) or not (t <= 2.95e-77):
		tmp = x + (t * ((y - z) / (a - z)))
	else:
		tmp = x * (((y - z) / (z - a)) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.9e-157) || !(t <= 2.95e-77))
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.9e-157) || ~((t <= 2.95e-77)))
		tmp = x + (t * ((y - z) / (a - z)));
	else
		tmp = x * (((y - z) / (z - a)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.9e-157], N[Not[LessEqual[t, 2.95e-77]], $MachinePrecision]], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.89999999999999999e-157 or 2.94999999999999982e-77 < t

   1. Initial program 90.2%

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

   3. Taylor expanded in t around inf 66.5%

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

      1. associate-/l* 78.2%

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

   5. Simplified 78.2%

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

   if -3.89999999999999999e-157 < t < 2.94999999999999982e-77

   1. Initial program 67.4%

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

      1. +-commutative 67.4%

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

      2. fma-define 67.6%

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

   3. Simplified 67.6%

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

   5. Taylor expanded in t around 0 63.1%

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

      1. mul-1-neg 63.1%

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

      2. *-rgt-identity 63.1%

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

      3. associate-/l* 68.8%

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

      4. distribute-rgt-neg-in 68.8%

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

      5. mul-1-neg 68.8%

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

      6. distribute-lft-in 68.7%

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

      7. mul-1-neg 68.7%

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

      8. unsub-neg 68.7%

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

   7. Simplified 68.7%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-157} \lor \neg \left(t \leq 2.95 \cdot 10^{-77}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-36} \lor \neg \left(a \leq 4.1 \cdot 10^{+67}\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.7e-36) (not (<= a 4.1e+67)))
   (+ x (* y (/ (- t x) a)))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.7e-36) || !(a <= 4.1e+67)) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.7d-36)) .or. (.not. (a <= 4.1d+67))) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.7e-36) || !(a <= 4.1e+67)) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.7e-36) or not (a <= 4.1e+67):
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.7e-36) || !(a <= 4.1e+67))
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.7e-36) || ~((a <= 4.1e+67)))
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.7e-36], N[Not[LessEqual[a, 4.1e+67]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.7000000000000003e-36 or 4.09999999999999979e67 < a

   1. Initial program 89.1%

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

   3. Taylor expanded in z around 0 68.2%

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

      1. associate-/l* 76.0%

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

   5. Simplified 76.0%

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

   if -4.7000000000000003e-36 < a < 4.09999999999999979e67

   1. Initial program 78.0%

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

      1. clear-num 78.1%

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

      2. un-div-inv 79.1%

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

   4. Applied egg-rr 79.1%

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

   5. Taylor expanded in t around inf 66.0%

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

      1. +-commutative 66.0%

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

      2. mul-1-neg 66.0%

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

      3. unsub-neg 66.0%

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

      4. +-commutative 66.0%

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

      5. associate-/l* 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in t around inf 61.9%

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

      1. div-sub 61.9%

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

   10. Simplified 61.9%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-36} \lor \neg \left(a \leq 4.1 \cdot 10^{+67}\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-19} \lor \neg \left(x \leq 7.8 \cdot 10^{+45}\right):\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -7.2e-19) (not (<= x 7.8e+45)))
   (- x (* x (/ y a)))
   (* t (/ (- y z) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -7.2e-19) || !(x <= 7.8e+45)) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-7.2d-19)) .or. (.not. (x <= 7.8d+45))) then
        tmp = x - (x * (y / a))
    else
        tmp = t * ((y - z) / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -7.2e-19) || !(x <= 7.8e+45)) {
		tmp = x - (x * (y / a));
	} else {
		tmp = t * ((y - z) / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -7.2e-19) or not (x <= 7.8e+45):
		tmp = x - (x * (y / a))
	else:
		tmp = t * ((y - z) / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -7.2e-19) || !(x <= 7.8e+45))
		tmp = Float64(x - Float64(x * Float64(y / a)));
	else
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -7.2e-19) || ~((x <= 7.8e+45)))
		tmp = x - (x * (y / a));
	else
		tmp = t * ((y - z) / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -7.2e-19], N[Not[LessEqual[x, 7.8e+45]], $MachinePrecision]], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.2000000000000002e-19 or 7.7999999999999999e45 < x

   1. Initial program 81.7%

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

   3. Taylor expanded in t around 0 55.5%

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

      1. mul-1-neg 55.5%

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

      2. associate-/l* 65.8%

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

      3. distribute-rgt-neg-in 65.8%

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

      4. mul-1-neg 65.8%

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

      5. mul-1-neg 65.8%

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

      6. distribute-frac-neg2 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in z around 0 53.2%

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

      1. mul-1-neg 53.2%

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

      2. unsub-neg 53.2%

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

      3. associate-/l* 58.9%

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

   8. Simplified 58.9%

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

   if -7.2000000000000002e-19 < x < 7.7999999999999999e45

   1. Initial program 84.9%

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

      1. clear-num 83.0%

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

      2. un-div-inv 83.5%

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

   4. Applied egg-rr 83.5%

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

   5. Taylor expanded in t around inf 87.7%

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

      1. +-commutative 87.7%

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

      2. mul-1-neg 87.7%

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

      3. unsub-neg 87.7%

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

      4. +-commutative 87.7%

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

      5. associate-/l* 81.7%

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

   7. Simplified 81.7%

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

   8. Taylor expanded in t around inf 70.8%

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

      1. div-sub 70.8%

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

   10. Simplified 70.8%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-19} \lor \neg \left(x \leq 7.8 \cdot 10^{+45}\right):\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+52}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+129}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.4e+52) t (if (<= z 1.25e+129) (+ x (* t (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e+52) {
		tmp = t;
	} else if (z <= 1.25e+129) {
		tmp = x + (t * (y / a));
	} 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 <= (-4.4d+52)) then
        tmp = t
    else if (z <= 1.25d+129) then
        tmp = x + (t * (y / a))
    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 <= -4.4e+52) {
		tmp = t;
	} else if (z <= 1.25e+129) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.4e+52:
		tmp = t
	elif z <= 1.25e+129:
		tmp = x + (t * (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.4e+52)
		tmp = t;
	elseif (z <= 1.25e+129)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.4e+52)
		tmp = t;
	elseif (z <= 1.25e+129)
		tmp = x + (t * (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.4e+52], t, If[LessEqual[z, 1.25e+129], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4e52 or 1.2500000000000001e129 < z

   1. Initial program 63.5%

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

      1. clear-num 61.9%

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

      2. un-div-inv 61.7%

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

   4. Applied egg-rr 61.7%

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

   5. Taylor expanded in z around inf 46.0%

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

   if -4.4e52 < z < 1.2500000000000001e129

   1. Initial program 92.6%

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

   3. Taylor expanded in z around 0 68.4%

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

   4. Taylor expanded in t around inf 55.5%

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

      1. associate-/l* 59.0%

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

   6. Simplified 59.0%

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

Alternative 11: 36.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.1e-35) x (if (<= a 3.05e+69) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e-35) {
		tmp = x;
	} else if (a <= 3.05e+69) {
		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 <= (-1.1d-35)) then
        tmp = x
    else if (a <= 3.05d+69) 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 <= -1.1e-35) {
		tmp = x;
	} else if (a <= 3.05e+69) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.1e-35:
		tmp = x
	elif a <= 3.05e+69:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.1e-35)
		tmp = x;
	elseif (a <= 3.05e+69)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.1e-35)
		tmp = x;
	elseif (a <= 3.05e+69)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.1e-35], x, If[LessEqual[a, 3.05e+69], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.09999999999999997e-35 or 3.05e69 < a

   1. Initial program 89.1%

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

      1. +-commutative 89.1%

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

      2. fma-define 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in a around inf 47.5%

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

   if -1.09999999999999997e-35 < a < 3.05e69

   1. Initial program 78.0%

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

      1. clear-num 78.1%

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

      2. un-div-inv 79.1%

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

   4. Applied egg-rr 79.1%

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

   5. Taylor expanded in z around inf 29.6%

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

Alternative 12: 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 83.3%

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

   1. clear-num 82.4%

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

   2. un-div-inv 82.9%

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

4. Applied egg-rr 82.9%

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

5. Taylor expanded in z around inf 19.9%

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

Alternative 13: 2.8% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.3%

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

3. Taylor expanded in t around 0 42.4%

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

   1. mul-1-neg 42.4%

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

   2. associate-/l* 46.8%

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

   3. distribute-rgt-neg-in 46.8%

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

   4. mul-1-neg 46.8%

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

   5. mul-1-neg 46.8%

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

   6. distribute-frac-neg2 46.8%

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

5. Simplified 46.8%

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

6. Taylor expanded in z around inf 2.7%

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

   1. distribute-rgt1-in 2.7%

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

   2. metadata-eval 2.7%

      \[\leadsto \color{blue}{0} \cdot x \]

8. Simplified 2.7%

   \[\leadsto \color{blue}{0 \cdot x} \]

9. Taylor expanded in x around 0 2.7%

   \[\leadsto \color{blue}{0} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024170 
(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)))))