Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.1% → 90.9%

Time: 20.8s

Alternatives: 20

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: 80.1% 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: 90.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t_1\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-302}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 10^{-259}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t_1, x\right)\\ \end{array} \end{array} \]

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-302)
     t_2
     (if (<= t_2 1e-259)
       (+ t (* (/ (- t x) z) (- a y)))
       (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-302) {
		tmp = t_2;
	} else if (t_2 <= 1e-259) {
		tmp = t + (((t - x) / z) * (a - y));
	} 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-302)
		tmp = t_2;
	elseif (t_2 <= 1e-259)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	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-302], t$95$2, If[LessEqual[t$95$2, 1e-259], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $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)))) < -9.9999999999999996e-303

   1. Initial program 90.5%

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

   if -9.9999999999999996e-303 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.0000000000000001e-259

   1. Initial program 6.2%

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

   2. Taylor expanded in z around inf 83.5%

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

      1. associate--l+ 83.5%

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

      2. distribute-lft-out-- 83.5%

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

      3. div-sub 83.5%

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

      4. mul-1-neg 83.5%

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

      5. unsub-neg 83.5%

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

      6. distribute-rgt-out-- 83.5%

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

      7. associate-/l* 94.3%

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

   4. Simplified 94.3%

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

      1. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   if 1.0000000000000001e-259 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 95.4%

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

      1. +-commutative 95.4%

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

      2. fma-def 95.4%

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

   3. Simplified 95.4%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-302}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-259}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]

Alternative 2: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-302} \lor \neg \left(t_1 \leq 10^{-259}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-302) (not (<= t_1 1e-259)))
     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 <= -1e-302) || !(t_1 <= 1e-259)) {
		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 <= (-1d-302)) .or. (.not. (t_1 <= 1d-259))) 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 <= -1e-302) || !(t_1 <= 1e-259)) {
		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 <= -1e-302) or not (t_1 <= 1e-259):
		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 <= -1e-302) || !(t_1 <= 1e-259))
		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 <= -1e-302) || ~((t_1 <= 1e-259)))
		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, -1e-302], N[Not[LessEqual[t$95$1, 1e-259]], $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)))) < -9.9999999999999996e-303 or 1.0000000000000001e-259 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.8%

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

   if -9.9999999999999996e-303 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.0000000000000001e-259

   1. Initial program 6.2%

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

   2. Taylor expanded in z around inf 83.5%

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

      1. associate--l+ 83.5%

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

      2. distribute-lft-out-- 83.5%

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

      3. div-sub 83.5%

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

      4. mul-1-neg 83.5%

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

      5. unsub-neg 83.5%

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

      6. distribute-rgt-out-- 83.5%

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

      7. associate-/l* 94.3%

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

   4. Simplified 94.3%

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

      1. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-302} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 10^{-259}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]

Alternative 3: 51.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -3 \cdot 10^{+127}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-128}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-224}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t (/ a y)))))
   (if (<= z -3e+127)
     t
     (if (<= z -4.2e-58)
       t_1
       (if (<= z -2.2e-128)
         (* y (/ (- t x) a))
         (if (<= z 4.4e-272)
           t_1
           (if (<= z 2.2e-224)
             (* x (- 1.0 (/ y a)))
             (if (<= z 5.4e+35) t_1 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / y));
	double tmp;
	if (z <= -3e+127) {
		tmp = t;
	} else if (z <= -4.2e-58) {
		tmp = t_1;
	} else if (z <= -2.2e-128) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.4e-272) {
		tmp = t_1;
	} else if (z <= 2.2e-224) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 5.4e+35) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t / (a / y))
    if (z <= (-3d+127)) then
        tmp = t
    else if (z <= (-4.2d-58)) then
        tmp = t_1
    else if (z <= (-2.2d-128)) then
        tmp = y * ((t - x) / a)
    else if (z <= 4.4d-272) then
        tmp = t_1
    else if (z <= 2.2d-224) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 5.4d+35) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / y));
	double tmp;
	if (z <= -3e+127) {
		tmp = t;
	} else if (z <= -4.2e-58) {
		tmp = t_1;
	} else if (z <= -2.2e-128) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.4e-272) {
		tmp = t_1;
	} else if (z <= 2.2e-224) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 5.4e+35) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / (a / y))
	tmp = 0
	if z <= -3e+127:
		tmp = t
	elif z <= -4.2e-58:
		tmp = t_1
	elif z <= -2.2e-128:
		tmp = y * ((t - x) / a)
	elif z <= 4.4e-272:
		tmp = t_1
	elif z <= 2.2e-224:
		tmp = x * (1.0 - (y / a))
	elif z <= 5.4e+35:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / Float64(a / y)))
	tmp = 0.0
	if (z <= -3e+127)
		tmp = t;
	elseif (z <= -4.2e-58)
		tmp = t_1;
	elseif (z <= -2.2e-128)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 4.4e-272)
		tmp = t_1;
	elseif (z <= 2.2e-224)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 5.4e+35)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t / (a / y));
	tmp = 0.0;
	if (z <= -3e+127)
		tmp = t;
	elseif (z <= -4.2e-58)
		tmp = t_1;
	elseif (z <= -2.2e-128)
		tmp = y * ((t - x) / a);
	elseif (z <= 4.4e-272)
		tmp = t_1;
	elseif (z <= 2.2e-224)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 5.4e+35)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+127], t, If[LessEqual[z, -4.2e-58], t$95$1, If[LessEqual[z, -2.2e-128], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e-272], t$95$1, If[LessEqual[z, 2.2e-224], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+35], t$95$1, t]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.0000000000000002e127 or 5.40000000000000005e35 < z

   1. Initial program 64.1%

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

   2. Taylor expanded in z around inf 42.2%

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

   if -3.0000000000000002e127 < z < -4.19999999999999975e-58 or -2.20000000000000009e-128 < z < 4.39999999999999976e-272 or 2.2000000000000001e-224 < z < 5.40000000000000005e35

   1. Initial program 90.7%

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

   2. Taylor expanded in z around 0 67.3%

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

   3. Taylor expanded in t around inf 58.0%

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

      1. associate-/l* 62.4%

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

   5. Simplified 62.4%

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

   if -4.19999999999999975e-58 < z < -2.20000000000000009e-128

   1. Initial program 95.3%

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

   2. Taylor expanded in z around 0 62.5%

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

   3. Taylor expanded in y around inf 67.9%

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

      1. div-sub 68.2%

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

   5. Simplified 68.2%

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

   if 4.39999999999999976e-272 < z < 2.2000000000000001e-224

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 99.9%

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

   3. Taylor expanded in x around inf 96.7%

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

      1. mul-1-neg 96.7%

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

      2. unsub-neg 96.7%

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

   5. Simplified 96.7%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+127}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-58}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-128}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-272}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-224}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 50.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+127}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-128}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-271}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-225}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t (/ a y)))))
   (if (<= z -1.2e+127)
     t
     (if (<= z -1.6e-61)
       t_1
       (if (<= z -2.2e-128)
         (* y (/ (- t x) a))
         (if (<= z 4.8e-271)
           (+ x (/ (* y t) a))
           (if (<= z 5e-225)
             (* x (- 1.0 (/ y a)))
             (if (<= z 2.6e+39) t_1 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / y));
	double tmp;
	if (z <= -1.2e+127) {
		tmp = t;
	} else if (z <= -1.6e-61) {
		tmp = t_1;
	} else if (z <= -2.2e-128) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.8e-271) {
		tmp = x + ((y * t) / a);
	} else if (z <= 5e-225) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.6e+39) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t / (a / y))
    if (z <= (-1.2d+127)) then
        tmp = t
    else if (z <= (-1.6d-61)) then
        tmp = t_1
    else if (z <= (-2.2d-128)) then
        tmp = y * ((t - x) / a)
    else if (z <= 4.8d-271) then
        tmp = x + ((y * t) / a)
    else if (z <= 5d-225) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 2.6d+39) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / y));
	double tmp;
	if (z <= -1.2e+127) {
		tmp = t;
	} else if (z <= -1.6e-61) {
		tmp = t_1;
	} else if (z <= -2.2e-128) {
		tmp = y * ((t - x) / a);
	} else if (z <= 4.8e-271) {
		tmp = x + ((y * t) / a);
	} else if (z <= 5e-225) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.6e+39) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / (a / y))
	tmp = 0
	if z <= -1.2e+127:
		tmp = t
	elif z <= -1.6e-61:
		tmp = t_1
	elif z <= -2.2e-128:
		tmp = y * ((t - x) / a)
	elif z <= 4.8e-271:
		tmp = x + ((y * t) / a)
	elif z <= 5e-225:
		tmp = x * (1.0 - (y / a))
	elif z <= 2.6e+39:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / Float64(a / y)))
	tmp = 0.0
	if (z <= -1.2e+127)
		tmp = t;
	elseif (z <= -1.6e-61)
		tmp = t_1;
	elseif (z <= -2.2e-128)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 4.8e-271)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 5e-225)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 2.6e+39)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t / (a / y));
	tmp = 0.0;
	if (z <= -1.2e+127)
		tmp = t;
	elseif (z <= -1.6e-61)
		tmp = t_1;
	elseif (z <= -2.2e-128)
		tmp = y * ((t - x) / a);
	elseif (z <= 4.8e-271)
		tmp = x + ((y * t) / a);
	elseif (z <= 5e-225)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 2.6e+39)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+127], t, If[LessEqual[z, -1.6e-61], t$95$1, If[LessEqual[z, -2.2e-128], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-271], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-225], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+39], t$95$1, t]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.2000000000000001e127 or 2.6e39 < z

   1. Initial program 64.1%

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

   2. Taylor expanded in z around inf 42.2%

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

   if -1.2000000000000001e127 < z < -1.6000000000000001e-61 or 5.0000000000000001e-225 < z < 2.6e39

   1. Initial program 89.2%

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

   2. Taylor expanded in z around 0 60.2%

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

   3. Taylor expanded in t around inf 53.6%

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

      1. associate-/l* 61.9%

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

   5. Simplified 61.9%

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

   if -1.6000000000000001e-61 < z < -2.20000000000000009e-128

   1. Initial program 95.3%

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

   2. Taylor expanded in z around 0 62.5%

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

   3. Taylor expanded in y around inf 67.9%

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

      1. div-sub 68.2%

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

   5. Simplified 68.2%

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

   if -2.20000000000000009e-128 < z < 4.8000000000000005e-271

   1. Initial program 92.8%

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

   2. Taylor expanded in z around 0 77.8%

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

   3. Taylor expanded in t around inf 64.6%

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

   if 4.8000000000000005e-271 < z < 5.0000000000000001e-225

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 99.9%

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

   3. Taylor expanded in x around inf 96.7%

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

      1. mul-1-neg 96.7%

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

      2. unsub-neg 96.7%

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

   5. Simplified 96.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{a}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+127}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-61}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-128}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-271}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-225}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 64.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -9 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-117}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-205}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 -9e-12)
     t_2
     (if (<= z -6.5e-66)
       t_1
       (if (<= z -4.5e-117)
         (* (- y z) (/ t (- a z)))
         (if (<= z -1.1e-205)
           (* (- t x) (/ y (- a z)))
           (if (<= z 4.8e-43) 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 <= -9e-12) {
		tmp = t_2;
	} else if (z <= -6.5e-66) {
		tmp = t_1;
	} else if (z <= -4.5e-117) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= -1.1e-205) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 4.8e-43) {
		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 <= (-9d-12)) then
        tmp = t_2
    else if (z <= (-6.5d-66)) then
        tmp = t_1
    else if (z <= (-4.5d-117)) then
        tmp = (y - z) * (t / (a - z))
    else if (z <= (-1.1d-205)) then
        tmp = (t - x) * (y / (a - z))
    else if (z <= 4.8d-43) 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 <= -9e-12) {
		tmp = t_2;
	} else if (z <= -6.5e-66) {
		tmp = t_1;
	} else if (z <= -4.5e-117) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= -1.1e-205) {
		tmp = (t - x) * (y / (a - z));
	} else if (z <= 4.8e-43) {
		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 <= -9e-12:
		tmp = t_2
	elif z <= -6.5e-66:
		tmp = t_1
	elif z <= -4.5e-117:
		tmp = (y - z) * (t / (a - z))
	elif z <= -1.1e-205:
		tmp = (t - x) * (y / (a - z))
	elif z <= 4.8e-43:
		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 <= -9e-12)
		tmp = t_2;
	elseif (z <= -6.5e-66)
		tmp = t_1;
	elseif (z <= -4.5e-117)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (z <= -1.1e-205)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (z <= 4.8e-43)
		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 <= -9e-12)
		tmp = t_2;
	elseif (z <= -6.5e-66)
		tmp = t_1;
	elseif (z <= -4.5e-117)
		tmp = (y - z) * (t / (a - z));
	elseif (z <= -1.1e-205)
		tmp = (t - x) * (y / (a - z));
	elseif (z <= 4.8e-43)
		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, -9e-12], t$95$2, If[LessEqual[z, -6.5e-66], t$95$1, If[LessEqual[z, -4.5e-117], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e-205], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-43], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.99999999999999962e-12 or 4.8000000000000004e-43 < z

   1. Initial program 71.3%

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

      1. clear-num 69.9%

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

      2. un-div-inv 69.9%

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

   3. Applied egg-rr 69.9%

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

   4. Taylor expanded in t around inf 60.0%

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

      1. div-sub 60.0%

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

   6. Simplified 60.0%

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

   if -8.99999999999999962e-12 < z < -6.50000000000000024e-66 or -1.10000000000000005e-205 < z < 4.8000000000000004e-43

   1. Initial program 92.4%

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

   2. Taylor expanded in z around 0 84.0%

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

      1. associate-/l* 86.0%

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

      2. associate-/r/ 87.0%

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

   4. Simplified 87.0%

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

   if -6.50000000000000024e-66 < z < -4.49999999999999969e-117

   1. Initial program 91.5%

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

   2. Taylor expanded in x around 0 99.6%

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

      1. associate-/l* 85.4%

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

      2. associate-/r/ 99.3%

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

   4. Simplified 99.3%

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

   if -4.49999999999999969e-117 < z < -1.10000000000000005e-205

   1. Initial program 84.9%

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

   2. Taylor expanded in y around inf 55.2%

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

      1. div-sub 55.2%

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

      2. associate-*r/ 50.5%

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

      3. associate-/l* 55.3%

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

      4. associate-/r/ 60.0%

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

   4. Simplified 60.0%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-12}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-66}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-117}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-205}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-43}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]

Alternative 6: 56.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - x}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -5.7 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-63}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t x) (- a z)))) (t_2 (+ x (/ t (/ a y)))))
   (if (<= a -5.7e+41)
     t_2
     (if (<= a -3.7e-234)
       t_1
       (if (<= a 1.06e-63)
         (* t (/ (- y z) (- a z)))
         (if (<= a 1.6e+151) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = x + (t / (a / y));
	double tmp;
	if (a <= -5.7e+41) {
		tmp = t_2;
	} else if (a <= -3.7e-234) {
		tmp = t_1;
	} else if (a <= 1.06e-63) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 1.6e+151) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - x) / (a - z))
    t_2 = x + (t / (a / y))
    if (a <= (-5.7d+41)) then
        tmp = t_2
    else if (a <= (-3.7d-234)) then
        tmp = t_1
    else if (a <= 1.06d-63) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 1.6d+151) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / (a - z));
	double t_2 = x + (t / (a / y));
	double tmp;
	if (a <= -5.7e+41) {
		tmp = t_2;
	} else if (a <= -3.7e-234) {
		tmp = t_1;
	} else if (a <= 1.06e-63) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 1.6e+151) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / (a - z))
	t_2 = x + (t / (a / y))
	tmp = 0
	if a <= -5.7e+41:
		tmp = t_2
	elif a <= -3.7e-234:
		tmp = t_1
	elif a <= 1.06e-63:
		tmp = t * ((y - z) / (a - z))
	elif a <= 1.6e+151:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / Float64(a - z)))
	t_2 = Float64(x + Float64(t / Float64(a / y)))
	tmp = 0.0
	if (a <= -5.7e+41)
		tmp = t_2;
	elseif (a <= -3.7e-234)
		tmp = t_1;
	elseif (a <= 1.06e-63)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 1.6e+151)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / (a - z));
	t_2 = x + (t / (a / y));
	tmp = 0.0;
	if (a <= -5.7e+41)
		tmp = t_2;
	elseif (a <= -3.7e-234)
		tmp = t_1;
	elseif (a <= 1.06e-63)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 1.6e+151)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.7e+41], t$95$2, If[LessEqual[a, -3.7e-234], t$95$1, If[LessEqual[a, 1.06e-63], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e+151], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.70000000000000021e41 or 1.59999999999999997e151 < a

   1. Initial program 92.2%

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

   2. Taylor expanded in z around 0 65.4%

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

   3. Taylor expanded in t around inf 65.8%

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

      1. associate-/l* 69.9%

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

   5. Simplified 69.9%

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

   if -5.70000000000000021e41 < a < -3.70000000000000012e-234 or 1.06000000000000004e-63 < a < 1.59999999999999997e151

   1. Initial program 72.5%

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

      1. clear-num 72.5%

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

      2. un-div-inv 72.4%

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

   3. Applied egg-rr 72.4%

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

   4. Taylor expanded in y around inf 59.9%

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

      1. div-sub 59.9%

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

   6. Simplified 59.9%

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

   if -3.70000000000000012e-234 < a < 1.06000000000000004e-63

   1. Initial program 76.2%

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

      1. clear-num 75.0%

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

      2. un-div-inv 75.1%

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

   3. Applied egg-rr 75.1%

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

   4. Taylor expanded in t around inf 68.3%

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

      1. div-sub 68.2%

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

   6. Simplified 68.2%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-234}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-63}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 7: 57.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -4 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-235}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-64}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+150}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ t (/ a y)))))
   (if (<= a -4e+44)
     t_1
     (if (<= a -2.95e-235)
       (* (- t x) (/ y (- a z)))
       (if (<= a 7.8e-64)
         (* t (/ (- y z) (- a z)))
         (if (<= a 3.1e+150) (* y (/ (- t x) (- a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / y));
	double tmp;
	if (a <= -4e+44) {
		tmp = t_1;
	} else if (a <= -2.95e-235) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 7.8e-64) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 3.1e+150) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t / (a / y))
    if (a <= (-4d+44)) then
        tmp = t_1
    else if (a <= (-2.95d-235)) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 7.8d-64) then
        tmp = t * ((y - z) / (a - z))
    else if (a <= 3.1d+150) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t / (a / y));
	double tmp;
	if (a <= -4e+44) {
		tmp = t_1;
	} else if (a <= -2.95e-235) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 7.8e-64) {
		tmp = t * ((y - z) / (a - z));
	} else if (a <= 3.1e+150) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t / (a / y))
	tmp = 0
	if a <= -4e+44:
		tmp = t_1
	elif a <= -2.95e-235:
		tmp = (t - x) * (y / (a - z))
	elif a <= 7.8e-64:
		tmp = t * ((y - z) / (a - z))
	elif a <= 3.1e+150:
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t / Float64(a / y)))
	tmp = 0.0
	if (a <= -4e+44)
		tmp = t_1;
	elseif (a <= -2.95e-235)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 7.8e-64)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (a <= 3.1e+150)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t / (a / y));
	tmp = 0.0;
	if (a <= -4e+44)
		tmp = t_1;
	elseif (a <= -2.95e-235)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 7.8e-64)
		tmp = t * ((y - z) / (a - z));
	elseif (a <= 3.1e+150)
		tmp = y * ((t - x) / (a - z));
	else
		tmp = t_1;
	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]}, If[LessEqual[a, -4e+44], t$95$1, If[LessEqual[a, -2.95e-235], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.8e-64], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.1e+150], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.0000000000000004e44 or 3.10000000000000014e150 < a

   1. Initial program 92.2%

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

   2. Taylor expanded in z around 0 65.4%

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

   3. Taylor expanded in t around inf 65.8%

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

      1. associate-/l* 69.9%

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

   5. Simplified 69.9%

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

   if -4.0000000000000004e44 < a < -2.9500000000000002e-235

   1. Initial program 72.7%

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

   2. Taylor expanded in y around inf 63.5%

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

      1. div-sub 63.5%

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

      2. associate-*r/ 61.2%

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

      3. associate-/l* 63.3%

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

      4. associate-/r/ 69.9%

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

   4. Simplified 69.9%

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

   if -2.9500000000000002e-235 < a < 7.7999999999999994e-64

   1. Initial program 76.2%

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

      1. clear-num 75.0%

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

      2. un-div-inv 75.1%

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

   3. Applied egg-rr 75.1%

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

   4. Taylor expanded in t around inf 68.3%

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

      1. div-sub 68.2%

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

   6. Simplified 68.2%

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

   if 7.7999999999999994e-64 < a < 3.10000000000000014e150

   1. Initial program 72.3%

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

      1. clear-num 72.6%

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

      2. un-div-inv 72.2%

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

   3. Applied egg-rr 72.2%

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

   4. Taylor expanded in y around inf 56.4%

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

      1. div-sub 56.4%

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

   6. Simplified 56.4%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+44}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{-235}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-64}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+150}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 8: 29.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-39}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -7.7 \cdot 10^{-72}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-134}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+159}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.8e+38)
   (/ x (/ z y))
   (if (<= y -2.05e-39)
     t
     (if (<= y -7.7e-72)
       (/ (* y t) a)
       (if (<= y -2.7e-134) t (if (<= y 2.4e+159) x (/ (- t) (/ z y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.8e+38) {
		tmp = x / (z / y);
	} else if (y <= -2.05e-39) {
		tmp = t;
	} else if (y <= -7.7e-72) {
		tmp = (y * t) / a;
	} else if (y <= -2.7e-134) {
		tmp = t;
	} else if (y <= 2.4e+159) {
		tmp = x;
	} else {
		tmp = -t / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-3.8d+38)) then
        tmp = x / (z / y)
    else if (y <= (-2.05d-39)) then
        tmp = t
    else if (y <= (-7.7d-72)) then
        tmp = (y * t) / a
    else if (y <= (-2.7d-134)) then
        tmp = t
    else if (y <= 2.4d+159) then
        tmp = x
    else
        tmp = -t / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.8e+38) {
		tmp = x / (z / y);
	} else if (y <= -2.05e-39) {
		tmp = t;
	} else if (y <= -7.7e-72) {
		tmp = (y * t) / a;
	} else if (y <= -2.7e-134) {
		tmp = t;
	} else if (y <= 2.4e+159) {
		tmp = x;
	} else {
		tmp = -t / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.8e+38:
		tmp = x / (z / y)
	elif y <= -2.05e-39:
		tmp = t
	elif y <= -7.7e-72:
		tmp = (y * t) / a
	elif y <= -2.7e-134:
		tmp = t
	elif y <= 2.4e+159:
		tmp = x
	else:
		tmp = -t / (z / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.8e+38)
		tmp = Float64(x / Float64(z / y));
	elseif (y <= -2.05e-39)
		tmp = t;
	elseif (y <= -7.7e-72)
		tmp = Float64(Float64(y * t) / a);
	elseif (y <= -2.7e-134)
		tmp = t;
	elseif (y <= 2.4e+159)
		tmp = x;
	else
		tmp = Float64(Float64(-t) / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.8e+38)
		tmp = x / (z / y);
	elseif (y <= -2.05e-39)
		tmp = t;
	elseif (y <= -7.7e-72)
		tmp = (y * t) / a;
	elseif (y <= -2.7e-134)
		tmp = t;
	elseif (y <= 2.4e+159)
		tmp = x;
	else
		tmp = -t / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.8e+38], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.05e-39], t, If[LessEqual[y, -7.7e-72], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -2.7e-134], t, If[LessEqual[y, 2.4e+159], x, N[((-t) / N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.7999999999999998e38

   1. Initial program 81.8%

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

   2. Taylor expanded in y around -inf 61.0%

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

   3. Taylor expanded in a around 0 41.0%

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

      1. associate-*r/ 41.0%

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

      2. mul-1-neg 41.0%

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

      3. distribute-rgt-neg-in 41.0%

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

   5. Simplified 41.0%

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

   6. Taylor expanded in t around 0 28.0%

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

      1. associate-/l* 35.8%

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

   8. Simplified 35.8%

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

   if -3.7999999999999998e38 < y < -2.05e-39 or -7.6999999999999997e-72 < y < -2.6999999999999998e-134

   1. Initial program 65.2%

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

   2. Taylor expanded in z around inf 48.8%

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

   if -2.05e-39 < y < -7.6999999999999997e-72

   1. Initial program 95.5%

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

   2. Taylor expanded in y around -inf 84.4%

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

   3. Taylor expanded in t around inf 84.4%

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

      1. associate-/l* 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in a around inf 60.1%

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

   7. Taylor expanded in t around 0 72.1%

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

      1. *-commutative 72.1%

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

   9. Simplified 72.1%

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

   if -2.6999999999999998e-134 < y < 2.4e159

   1. Initial program 79.4%

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

   2. Taylor expanded in a around inf 41.1%

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

   if 2.4e159 < y

   1. Initial program 92.3%

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

   2. Taylor expanded in y around -inf 70.4%

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

   3. Taylor expanded in t around inf 47.6%

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

      1. associate-/l* 63.4%

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

   5. Simplified 63.4%

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

   6. Taylor expanded in a around 0 38.4%

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

      1. mul-1-neg 38.4%

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

      2. associate-/l* 58.3%

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

      3. distribute-neg-frac 58.3%

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

   8. Simplified 58.3%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-39}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -7.7 \cdot 10^{-72}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-134}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+159}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z}{y}}\\ \end{array} \]

Alternative 9: 73.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00042 \lor \neg \left(z \leq 9 \cdot 10^{-46}\right):\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -0.00042) (not (<= z 9e-46)))
   (+ t (* (/ (- t x) z) (- a y)))
   (+ x (* (- t x) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.00042) || !(z <= 9e-46)) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-0.00042d0)) .or. (.not. (z <= 9d-46))) then
        tmp = t + (((t - x) / z) * (a - y))
    else
        tmp = x + ((t - x) * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.00042) || !(z <= 9e-46)) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -0.00042) or not (z <= 9e-46):
		tmp = t + (((t - x) / z) * (a - y))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -0.00042) || !(z <= 9e-46))
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -0.00042) || ~((z <= 9e-46)))
		tmp = t + (((t - x) / z) * (a - y));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -0.00042], N[Not[LessEqual[z, 9e-46]], $MachinePrecision]], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000002e-4 or 9.00000000000000001e-46 < z

   1. Initial program 70.4%

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

   2. Taylor expanded in z around inf 61.6%

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

      1. associate--l+ 61.6%

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

      2. distribute-lft-out-- 61.6%

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

      3. div-sub 61.7%

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

      4. mul-1-neg 61.7%

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

      5. unsub-neg 61.7%

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

      6. distribute-rgt-out-- 61.9%

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

      7. associate-/l* 75.6%

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

   4. Simplified 75.6%

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

      1. associate-/r/ 75.7%

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

   6. Applied egg-rr 75.7%

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

   if -4.2000000000000002e-4 < z < 9.00000000000000001e-46

   1. Initial program 92.1%

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

   2. Taylor expanded in z around 0 77.3%

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

      1. associate-/l* 80.3%

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

      2. associate-/r/ 80.4%

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

   4. Simplified 80.4%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00042 \lor \neg \left(z \leq 9 \cdot 10^{-46}\right):\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 10: 73.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-5}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-47}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.7e-5)
   (+ t (/ (- x t) (/ z (- y a))))
   (if (<= z 8e-47)
     (+ x (* (- t x) (/ y a)))
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e-5) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else if (z <= 8e-47) {
		tmp = x + ((t - x) * (y / a));
	} 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) :: tmp
    if (z <= (-1.7d-5)) then
        tmp = t + ((x - t) / (z / (y - a)))
    else if (z <= 8d-47) then
        tmp = x + ((t - x) * (y / a))
    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 tmp;
	if (z <= -1.7e-5) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else if (z <= 8e-47) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.7e-5:
		tmp = t + ((x - t) / (z / (y - a)))
	elif z <= 8e-47:
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.7e-5)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	elseif (z <= 8e-47)
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	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)
	tmp = 0.0;
	if (z <= -1.7e-5)
		tmp = t + ((x - t) / (z / (y - a)));
	elseif (z <= 8e-47)
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.7e-5], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-47], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7e-5

   1. Initial program 73.0%

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

   2. Taylor expanded in z around inf 57.3%

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

      1. associate--l+ 57.3%

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

      2. distribute-lft-out-- 57.3%

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

      3. div-sub 57.3%

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

      4. mul-1-neg 57.3%

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

      5. unsub-neg 57.3%

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

      6. distribute-rgt-out-- 57.6%

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

      7. associate-/l* 77.7%

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

   4. Simplified 77.7%

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

   if -1.7e-5 < z < 7.9999999999999998e-47

   1. Initial program 92.1%

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

   2. Taylor expanded in z around 0 77.3%

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

      1. associate-/l* 80.3%

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

      2. associate-/r/ 80.4%

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

   4. Simplified 80.4%

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

   if 7.9999999999999998e-47 < z

   1. Initial program 68.4%

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

   2. Taylor expanded in z around inf 65.0%

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

      1. associate--l+ 65.0%

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

      2. distribute-lft-out-- 65.0%

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

      3. div-sub 65.0%

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

      4. mul-1-neg 65.0%

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

      5. unsub-neg 65.0%

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

      6. distribute-rgt-out-- 65.2%

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

      7. associate-/l* 74.1%

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

   4. Simplified 74.1%

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

      1. associate-/r/ 75.4%

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

   6. Applied egg-rr 75.4%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-5}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-47}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]

Alternative 11: 68.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-92} \lor \neg \left(a \leq 1.05 \cdot 10^{-31}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.5e-92) (not (<= a 1.05e-31)))
   (+ x (* (- t x) (/ y a)))
   (- t (/ y (/ z (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.5e-92) || !(a <= 1.05e-31)) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t - (y / (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 ((a <= (-5.5d-92)) .or. (.not. (a <= 1.05d-31))) then
        tmp = x + ((t - x) * (y / a))
    else
        tmp = t - (y / (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 ((a <= -5.5e-92) || !(a <= 1.05e-31)) {
		tmp = x + ((t - x) * (y / a));
	} else {
		tmp = t - (y / (z / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.5e-92) or not (a <= 1.05e-31):
		tmp = x + ((t - x) * (y / a))
	else:
		tmp = t - (y / (z / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.5e-92) || !(a <= 1.05e-31))
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	else
		tmp = Float64(t - Float64(y / Float64(z / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.5e-92) || ~((a <= 1.05e-31)))
		tmp = x + ((t - x) * (y / a));
	else
		tmp = t - (y / (z / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.5e-92], N[Not[LessEqual[a, 1.05e-31]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(y / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.5000000000000002e-92 or 1.04999999999999996e-31 < a

   1. Initial program 85.8%

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

   2. Taylor expanded in z around 0 60.7%

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

      1. associate-/l* 67.8%

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

      2. associate-/r/ 67.2%

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

   4. Simplified 67.2%

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

   if -5.5000000000000002e-92 < a < 1.04999999999999996e-31

   1. Initial program 74.4%

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

   2. Taylor expanded in z around inf 57.1%

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

      1. associate--l+ 57.1%

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

      2. +-commutative 57.1%

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

      3. associate--l+ 57.1%

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

   4. Simplified 56.9%

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

   5. Taylor expanded in a around 0 68.2%

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

      1. associate-/l* 72.4%

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

   7. Simplified 72.4%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-92} \lor \neg \left(a \leq 1.05 \cdot 10^{-31}\right):\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 12: 69.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{-6} \lor \neg \left(z \leq 1.8 \cdot 10^{-43}\right):\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.75e-6) (not (<= z 1.8e-43)))
   (- t (/ (- t x) (/ z y)))
   (+ x (* (- t x) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.75e-6) || !(z <= 1.8e-43)) {
		tmp = t - ((t - x) / (z / y));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.75d-6)) .or. (.not. (z <= 1.8d-43))) then
        tmp = t - ((t - x) / (z / y))
    else
        tmp = x + ((t - x) * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.75e-6) || !(z <= 1.8e-43)) {
		tmp = t - ((t - x) / (z / y));
	} else {
		tmp = x + ((t - x) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.75e-6) or not (z <= 1.8e-43):
		tmp = t - ((t - x) / (z / y))
	else:
		tmp = x + ((t - x) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.75e-6) || !(z <= 1.8e-43))
		tmp = Float64(t - Float64(Float64(t - x) / Float64(z / y)));
	else
		tmp = Float64(x + Float64(Float64(t - x) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.75e-6) || ~((z <= 1.8e-43)))
		tmp = t - ((t - x) / (z / y));
	else
		tmp = x + ((t - x) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.75e-6], N[Not[LessEqual[z, 1.8e-43]], $MachinePrecision]], N[(t - N[(N[(t - x), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7499999999999999e-6 or 1.7999999999999999e-43 < z

   1. Initial program 70.4%

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

   2. Taylor expanded in z around inf 61.6%

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

      1. associate--l+ 61.6%

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

      2. distribute-lft-out-- 61.6%

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

      3. div-sub 61.7%

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

      4. mul-1-neg 61.7%

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

      5. unsub-neg 61.7%

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

      6. distribute-rgt-out-- 61.9%

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

      7. associate-/l* 75.6%

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

   4. Simplified 75.6%

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

   5. Taylor expanded in y around inf 65.3%

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

   if -2.7499999999999999e-6 < z < 1.7999999999999999e-43

   1. Initial program 92.1%

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

   2. Taylor expanded in z around 0 77.3%

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

      1. associate-/l* 80.3%

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

      2. associate-/r/ 80.4%

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

   4. Simplified 80.4%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{-6} \lor \neg \left(z \leq 1.8 \cdot 10^{-43}\right):\\ \;\;\;\;t - \frac{t - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \end{array} \]

Alternative 13: 58.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.8e-56)
   (* x (- 1.0 (/ y a)))
   (if (<= x 4.5e+148) (* t (/ (- y z) (- a z))) (/ (- x) (/ (- a z) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.8e-56) {
		tmp = x * (1.0 - (y / a));
	} else if (x <= 4.5e+148) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = -x / ((a - z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-6.8d-56)) then
        tmp = x * (1.0d0 - (y / a))
    else if (x <= 4.5d+148) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = -x / ((a - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.8e-56) {
		tmp = x * (1.0 - (y / a));
	} else if (x <= 4.5e+148) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = -x / ((a - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.8e-56:
		tmp = x * (1.0 - (y / a))
	elif x <= 4.5e+148:
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = -x / ((a - z) / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.8e-56)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (x <= 4.5e+148)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(Float64(-x) / Float64(Float64(a - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6.8e-56)
		tmp = x * (1.0 - (y / a));
	elseif (x <= 4.5e+148)
		tmp = t * ((y - z) / (a - z));
	else
		tmp = -x / ((a - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.8e-56], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+148], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-x) / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.79999999999999964e-56

   1. Initial program 75.7%

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

   2. Taylor expanded in z around 0 53.1%

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

   3. Taylor expanded in x around inf 53.2%

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

      1. mul-1-neg 53.2%

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

      2. unsub-neg 53.2%

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

   5. Simplified 53.2%

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

   if -6.79999999999999964e-56 < x < 4.49999999999999994e148

   1. Initial program 87.4%

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

      1. clear-num 86.1%

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

      2. un-div-inv 86.3%

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

   3. Applied egg-rr 86.3%

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

   4. Taylor expanded in t around inf 68.2%

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

      1. div-sub 68.2%

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

   6. Simplified 68.2%

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

   if 4.49999999999999994e148 < x

   1. Initial program 61.2%

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

   2. Taylor expanded in y around -inf 52.1%

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

   3. Taylor expanded in t around 0 52.1%

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

      1. mul-1-neg 52.1%

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

      2. associate-/l* 61.6%

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

      3. distribute-neg-frac 61.6%

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

   5. Simplified 61.6%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{a - z}{y}}\\ \end{array} \]

Alternative 14: 37.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+128}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-224}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-164}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.2e+128)
   t
   (if (<= z 1.45e-224)
     x
     (if (<= z 1.4e-164) (* y (/ t a)) (if (<= z 6.9e-43) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e+128) {
		tmp = t;
	} else if (z <= 1.45e-224) {
		tmp = x;
	} else if (z <= 1.4e-164) {
		tmp = y * (t / a);
	} else if (z <= 6.9e-43) {
		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 <= (-2.2d+128)) then
        tmp = t
    else if (z <= 1.45d-224) then
        tmp = x
    else if (z <= 1.4d-164) then
        tmp = y * (t / a)
    else if (z <= 6.9d-43) 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 <= -2.2e+128) {
		tmp = t;
	} else if (z <= 1.45e-224) {
		tmp = x;
	} else if (z <= 1.4e-164) {
		tmp = y * (t / a);
	} else if (z <= 6.9e-43) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.2e+128:
		tmp = t
	elif z <= 1.45e-224:
		tmp = x
	elif z <= 1.4e-164:
		tmp = y * (t / a)
	elif z <= 6.9e-43:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.2e+128)
		tmp = t;
	elseif (z <= 1.45e-224)
		tmp = x;
	elseif (z <= 1.4e-164)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 6.9e-43)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.2e+128)
		tmp = t;
	elseif (z <= 1.45e-224)
		tmp = x;
	elseif (z <= 1.4e-164)
		tmp = y * (t / a);
	elseif (z <= 6.9e-43)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.2e+128], t, If[LessEqual[z, 1.45e-224], x, If[LessEqual[z, 1.4e-164], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.9e-43], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.20000000000000017e128 or 6.89999999999999964e-43 < z

   1. Initial program 67.9%

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

   2. Taylor expanded in z around inf 40.7%

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

   if -2.20000000000000017e128 < z < 1.45e-224 or 1.4000000000000001e-164 < z < 6.89999999999999964e-43

   1. Initial program 91.2%

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

   2. Taylor expanded in a around inf 36.0%

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

   if 1.45e-224 < z < 1.4000000000000001e-164

   1. Initial program 89.4%

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

   2. Taylor expanded in y around -inf 89.1%

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

   3. Taylor expanded in t around inf 59.0%

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

      1. associate-/l* 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in a around inf 68.0%

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

      1. associate-/r/ 58.9%

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

   8. Applied egg-rr 58.9%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+128}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-224}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-164}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 37.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+128}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-224}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-165}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+128)
   t
   (if (<= z 9e-224)
     x
     (if (<= z 6.2e-165) (/ t (/ a y)) (if (<= z 4.2e-43) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+128) {
		tmp = t;
	} else if (z <= 9e-224) {
		tmp = x;
	} else if (z <= 6.2e-165) {
		tmp = t / (a / y);
	} else if (z <= 4.2e-43) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.5d+128)) then
        tmp = t
    else if (z <= 9d-224) then
        tmp = x
    else if (z <= 6.2d-165) then
        tmp = t / (a / y)
    else if (z <= 4.2d-43) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+128) {
		tmp = t;
	} else if (z <= 9e-224) {
		tmp = x;
	} else if (z <= 6.2e-165) {
		tmp = t / (a / y);
	} else if (z <= 4.2e-43) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e+128:
		tmp = t
	elif z <= 9e-224:
		tmp = x
	elif z <= 6.2e-165:
		tmp = t / (a / y)
	elif z <= 4.2e-43:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+128)
		tmp = t;
	elseif (z <= 9e-224)
		tmp = x;
	elseif (z <= 6.2e-165)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= 4.2e-43)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.5e+128)
		tmp = t;
	elseif (z <= 9e-224)
		tmp = x;
	elseif (z <= 6.2e-165)
		tmp = t / (a / y);
	elseif (z <= 4.2e-43)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+128], t, If[LessEqual[z, 9e-224], x, If[LessEqual[z, 6.2e-165], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-43], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.50000000000000045e128 or 4.2000000000000001e-43 < z

   1. Initial program 67.9%

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

   2. Taylor expanded in z around inf 40.7%

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

   if -8.50000000000000045e128 < z < 9.0000000000000009e-224 or 6.19999999999999992e-165 < z < 4.2000000000000001e-43

   1. Initial program 91.2%

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

   2. Taylor expanded in a around inf 36.0%

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

   if 9.0000000000000009e-224 < z < 6.19999999999999992e-165

   1. Initial program 89.4%

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

   2. Taylor expanded in y around -inf 89.1%

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

   3. Taylor expanded in t around inf 59.0%

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

      1. associate-/l* 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in a around inf 68.0%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+128}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-224}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-165}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16: 49.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-104} \lor \neg \left(a \leq 4.2 \cdot 10^{-60}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4e-104) (not (<= a 4.2e-60)))
   (+ x (/ t (/ a y)))
   (/ y (/ z (- x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4e-104) || !(a <= 4.2e-60)) {
		tmp = x + (t / (a / y));
	} else {
		tmp = y / (z / (x - 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 ((a <= (-4d-104)) .or. (.not. (a <= 4.2d-60))) then
        tmp = x + (t / (a / y))
    else
        tmp = y / (z / (x - 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 ((a <= -4e-104) || !(a <= 4.2e-60)) {
		tmp = x + (t / (a / y));
	} else {
		tmp = y / (z / (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4e-104) or not (a <= 4.2e-60):
		tmp = x + (t / (a / y))
	else:
		tmp = y / (z / (x - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4e-104) || !(a <= 4.2e-60))
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(y / Float64(z / Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4e-104) || ~((a <= 4.2e-60)))
		tmp = x + (t / (a / y));
	else
		tmp = y / (z / (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4e-104], N[Not[LessEqual[a, 4.2e-60]], $MachinePrecision]], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(z / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.99999999999999971e-104 or 4.19999999999999982e-60 < a

   1. Initial program 84.9%

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

   2. Taylor expanded in z around 0 59.3%

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

   3. Taylor expanded in t around inf 54.5%

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

      1. associate-/l* 57.1%

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

   5. Simplified 57.1%

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

   if -3.99999999999999971e-104 < a < 4.19999999999999982e-60

   1. Initial program 74.7%

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

   2. Taylor expanded in y around -inf 56.6%

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

   3. Taylor expanded in a around 0 44.1%

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

      1. associate-*r/ 44.1%

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

      2. mul-1-neg 44.1%

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

      3. distribute-rgt-neg-in 44.1%

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

   5. Simplified 44.1%

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

   6. Taylor expanded in y around 0 44.1%

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

      1. associate-/l* 47.0%

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

   8. Simplified 47.0%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-104} \lor \neg \left(a \leq 4.2 \cdot 10^{-60}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x - t}}\\ \end{array} \]

Alternative 17: 47.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+126}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+126) t (if (<= z 1.15e-42) (* x (- 1.0 (/ y a))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+126) {
		tmp = t;
	} else if (z <= 1.15e-42) {
		tmp = x * (1.0 - (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 <= (-8d+126)) then
        tmp = t
    else if (z <= 1.15d-42) then
        tmp = x * (1.0d0 - (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 <= -8e+126) {
		tmp = t;
	} else if (z <= 1.15e-42) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e+126:
		tmp = t
	elif z <= 1.15e-42:
		tmp = x * (1.0 - (y / a))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+126)
		tmp = t;
	elseif (z <= 1.15e-42)
		tmp = Float64(x * Float64(1.0 - 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 <= -8e+126)
		tmp = t;
	elseif (z <= 1.15e-42)
		tmp = x * (1.0 - (y / a));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+126], t, If[LessEqual[z, 1.15e-42], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -7.9999999999999994e126 or 1.15000000000000002e-42 < z

   1. Initial program 67.9%

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

   2. Taylor expanded in z around inf 40.7%

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

   if -7.9999999999999994e126 < z < 1.15000000000000002e-42

   1. Initial program 91.1%

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

   2. Taylor expanded in z around 0 72.2%

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

   3. Taylor expanded in x around inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. unsub-neg 53.4%

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

   5. Simplified 53.4%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+126}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18: 37.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+126}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e+126) t (if (<= z 1.15e-42) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e+126) {
		tmp = t;
	} else if (z <= 1.15e-42) {
		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 <= (-3.2d+126)) then
        tmp = t
    else if (z <= 1.15d-42) 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 <= -3.2e+126) {
		tmp = t;
	} else if (z <= 1.15e-42) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e+126:
		tmp = t
	elif z <= 1.15e-42:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e+126)
		tmp = t;
	elseif (z <= 1.15e-42)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.2e+126)
		tmp = t;
	elseif (z <= 1.15e-42)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e+126], t, If[LessEqual[z, 1.15e-42], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1999999999999998e126 or 1.15000000000000002e-42 < z

   1. Initial program 67.9%

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

   2. Taylor expanded in z around inf 40.7%

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

   if -3.1999999999999998e126 < z < 1.15000000000000002e-42

   1. Initial program 91.1%

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

   2. Taylor expanded in a around inf 34.6%

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

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+126}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 19: 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 81.0%

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

2. Taylor expanded in y around 0 33.5%

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

   1. mul-1-neg 33.5%

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

   2. unsub-neg 33.5%

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

   3. associate-/l* 42.5%

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

   4. associate-/r/ 42.8%

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

4. Simplified 42.8%

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

5. Taylor expanded in t around 0 24.0%

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

   1. mul-1-neg 24.0%

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

7. Simplified 24.0%

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

8. Taylor expanded in z around inf 2.8%

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

   1. distribute-rgt1-in 2.8%

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

   2. metadata-eval 2.8%

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

   3. mul0-lft 2.8%

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

10. Simplified 2.8%

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

11. Final simplification 2.8%

    \[\leadsto 0 \]

Alternative 20: 25.4% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.0%

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

2. Taylor expanded in z around inf 21.7%

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

3. Final simplification 21.7%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023298 
(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)))))