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

Percentage Accurate: 68.4% → 88.8%

Time: 19.9s

Alternatives: 22

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+142}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{z - y}{z - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+142)
   (+ t (* (- t x) (/ (- a y) z)))
   (if (<= z 2.8e+159)
     (fma (- t x) (/ (- z y) (- z a)) x)
     (+ t (/ (- t x) (/ z (- a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+142) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else if (z <= 2.8e+159) {
		tmp = fma((t - x), ((z - y) / (z - a)), x);
	} else {
		tmp = t + ((t - x) / (z / (a - y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+142)
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	elseif (z <= 2.8e+159)
		tmp = fma(Float64(t - x), Float64(Float64(z - y) / Float64(z - a)), x);
	else
		tmp = Float64(t + Float64(Float64(t - x) / Float64(z / Float64(a - y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+142], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+159], N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t + N[(N[(t - x), $MachinePrecision] / N[(z / N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0000000000000001e142

   1. Initial program 25.5%

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

      1. associate-/l* 63.5%

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

   3. Simplified 63.5%

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

      1. clear-num 63.2%

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

      2. un-div-inv 63.3%

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

   6. Applied egg-rr 63.3%

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

   7. Taylor expanded in z around inf 71.3%

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

      1. associate--l+ 71.3%

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

      2. associate-*r/ 71.3%

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

      3. associate-*r/ 71.3%

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

      4. mul-1-neg 71.3%

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

      5. div-sub 71.3%

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

      6. mul-1-neg 71.3%

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

      7. distribute-lft-out-- 71.3%

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

      8. associate-*r/ 71.3%

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

      9. mul-1-neg 71.3%

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

      10. unsub-neg 71.3%

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

      11. distribute-rgt-out-- 74.0%

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

      12. *-lft-identity 74.0%

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

      13. times-frac 92.1%

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

   9. Simplified 92.1%

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

   if -2.0000000000000001e142 < z < 2.8000000000000001e159

   1. Initial program 85.7%

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

      1. +-commutative 85.7%

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

      2. *-commutative 85.7%

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

      3. associate-/l* 94.2%

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

      4. fma-define 94.2%

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

   3. Simplified 94.2%

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

   if 2.8000000000000001e159 < z

   1. Initial program 17.6%

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

      1. associate-/l* 51.4%

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

   3. Simplified 51.4%

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

      1. clear-num 51.1%

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

      2. un-div-inv 51.5%

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

   6. Applied egg-rr 51.5%

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

   7. Taylor expanded in z around inf 53.9%

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

      1. associate--l+ 53.9%

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

      2. associate-*r/ 53.9%

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

      3. associate-*r/ 53.9%

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

      4. mul-1-neg 53.9%

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

      5. div-sub 53.9%

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

      6. mul-1-neg 53.9%

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

      7. distribute-lft-out-- 53.9%

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

      8. associate-*r/ 53.9%

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

      9. mul-1-neg 53.9%

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

      10. unsub-neg 53.9%

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

      11. distribute-rgt-out-- 53.9%

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

      12. *-lft-identity 53.9%

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

      13. times-frac 92.3%

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

   9. Simplified 92.3%

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

       1. clear-num 92.4%

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

       2. un-div-inv 92.4%

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

   11. Applied egg-rr 92.4%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+142}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+159}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{z - y}{z - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 68.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z - a}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+127}:\\ \;\;\;\;x + z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-94}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+27}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) (- z a)))) (t_2 (+ x (* y (/ (- t x) a)))))
   (if (<= a -3.4e+127)
     (+ x (* z (/ t (- z a))))
     (if (<= a -3.8e+60)
       (* y (/ (- x t) (- z a)))
       (if (<= a -2.4e-13)
         t_2
         (if (<= a -2.1e-85)
           t_1
           (if (<= a 1.25e-94)
             (+ t (* (/ y z) (- x t)))
             (if (<= a 5e+16)
               t_1
               (if (<= a 1.15e+27) (/ (* x (- y a)) z) t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / (z - a));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -3.4e+127) {
		tmp = x + (z * (t / (z - a)));
	} else if (a <= -3.8e+60) {
		tmp = y * ((x - t) / (z - a));
	} else if (a <= -2.4e-13) {
		tmp = t_2;
	} else if (a <= -2.1e-85) {
		tmp = t_1;
	} else if (a <= 1.25e-94) {
		tmp = t + ((y / z) * (x - t));
	} else if (a <= 5e+16) {
		tmp = t_1;
	} else if (a <= 1.15e+27) {
		tmp = (x * (y - a)) / z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((z - y) / (z - a))
    t_2 = x + (y * ((t - x) / a))
    if (a <= (-3.4d+127)) then
        tmp = x + (z * (t / (z - a)))
    else if (a <= (-3.8d+60)) then
        tmp = y * ((x - t) / (z - a))
    else if (a <= (-2.4d-13)) then
        tmp = t_2
    else if (a <= (-2.1d-85)) then
        tmp = t_1
    else if (a <= 1.25d-94) then
        tmp = t + ((y / z) * (x - t))
    else if (a <= 5d+16) then
        tmp = t_1
    else if (a <= 1.15d+27) then
        tmp = (x * (y - a)) / z
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / (z - a));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -3.4e+127) {
		tmp = x + (z * (t / (z - a)));
	} else if (a <= -3.8e+60) {
		tmp = y * ((x - t) / (z - a));
	} else if (a <= -2.4e-13) {
		tmp = t_2;
	} else if (a <= -2.1e-85) {
		tmp = t_1;
	} else if (a <= 1.25e-94) {
		tmp = t + ((y / z) * (x - t));
	} else if (a <= 5e+16) {
		tmp = t_1;
	} else if (a <= 1.15e+27) {
		tmp = (x * (y - a)) / z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / (z - a))
	t_2 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -3.4e+127:
		tmp = x + (z * (t / (z - a)))
	elif a <= -3.8e+60:
		tmp = y * ((x - t) / (z - a))
	elif a <= -2.4e-13:
		tmp = t_2
	elif a <= -2.1e-85:
		tmp = t_1
	elif a <= 1.25e-94:
		tmp = t + ((y / z) * (x - t))
	elif a <= 5e+16:
		tmp = t_1
	elif a <= 1.15e+27:
		tmp = (x * (y - a)) / z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / Float64(z - a)))
	t_2 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -3.4e+127)
		tmp = Float64(x + Float64(z * Float64(t / Float64(z - a))));
	elseif (a <= -3.8e+60)
		tmp = Float64(y * Float64(Float64(x - t) / Float64(z - a)));
	elseif (a <= -2.4e-13)
		tmp = t_2;
	elseif (a <= -2.1e-85)
		tmp = t_1;
	elseif (a <= 1.25e-94)
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	elseif (a <= 5e+16)
		tmp = t_1;
	elseif (a <= 1.15e+27)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / (z - a));
	t_2 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -3.4e+127)
		tmp = x + (z * (t / (z - a)));
	elseif (a <= -3.8e+60)
		tmp = y * ((x - t) / (z - a));
	elseif (a <= -2.4e-13)
		tmp = t_2;
	elseif (a <= -2.1e-85)
		tmp = t_1;
	elseif (a <= 1.25e-94)
		tmp = t + ((y / z) * (x - t));
	elseif (a <= 5e+16)
		tmp = t_1;
	elseif (a <= 1.15e+27)
		tmp = (x * (y - a)) / z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+127], N[(x + N[(z * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.8e+60], N[(y * N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.4e-13], t$95$2, If[LessEqual[a, -2.1e-85], t$95$1, If[LessEqual[a, 1.25e-94], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e+16], t$95$1, If[LessEqual[a, 1.15e+27], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -3.39999999999999977e127

   1. Initial program 76.8%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in y around 0 63.0%

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

      1. mul-1-neg 63.0%

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

      2. unsub-neg 63.0%

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

      3. associate-/l* 77.4%

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

   7. Simplified 77.4%

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

   8. Taylor expanded in t around inf 77.5%

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

   if -3.39999999999999977e127 < a < -3.80000000000000009e60

   1. Initial program 93.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 85.7%

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

      1. div-sub 85.7%

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

   7. Simplified 85.7%

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

   if -3.80000000000000009e60 < a < -2.3999999999999999e-13 or 1.15e27 < a

   1. Initial program 65.4%

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

      1. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in z around 0 54.1%

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

      1. associate-/l* 67.0%

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

   7. Simplified 67.0%

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

   if -2.3999999999999999e-13 < a < -2.1e-85 or 1.2499999999999999e-94 < a < 5e16

   1. Initial program 73.6%

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

      1. associate-/l* 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in x around 0 63.9%

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

      1. associate-/l* 79.2%

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

   7. Simplified 79.2%

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

   if -2.1e-85 < a < 1.2499999999999999e-94

   1. Initial program 63.2%

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

      1. +-commutative 63.2%

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

      2. associate-/l* 73.9%

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

      3. fma-define 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in a around 0 65.1%

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

      1. mul-1-neg 65.1%

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

      2. distribute-neg-frac2 65.1%

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

   7. Simplified 65.1%

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

   8. Taylor expanded in y around 0 83.5%

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

      1. mul-1-neg 83.5%

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

      2. div-sub 84.7%

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

      3. associate-/l* 79.6%

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

      4. unsub-neg 79.6%

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

      5. *-commutative 79.6%

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

      6. *-lft-identity 79.6%

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

      7. times-frac 89.0%

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

      8. /-rgt-identity 89.0%

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

   10. Simplified 89.0%

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

   if 5e16 < a < 1.15e27

   1. Initial program 67.8%

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

      1. associate-/l* 67.7%

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

   3. Simplified 67.7%

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

      1. clear-num 67.7%

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

      2. un-div-inv 67.7%

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

   6. Applied egg-rr 67.7%

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

   7. Taylor expanded in z around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. associate-*r/ 100.0%

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

      4. mul-1-neg 100.0%

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

      5. div-sub 100.0%

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

      6. mul-1-neg 100.0%

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

      7. distribute-lft-out-- 100.0%

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

      8. associate-*r/ 100.0%

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

      9. mul-1-neg 100.0%

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

      10. unsub-neg 100.0%

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

      11. distribute-rgt-out-- 100.0%

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

      12. *-lft-identity 100.0%

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

      13. times-frac 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in t around 0 100.0%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+127}:\\ \;\;\;\;x + z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-13}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-85}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-94}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+27}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z - a}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -2.15 \cdot 10^{+127}:\\ \;\;\;\;x + z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{+60}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z - a}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{-94}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+25}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) (- z a)))) (t_2 (+ x (* y (/ (- t x) a)))))
   (if (<= a -2.15e+127)
     (+ x (* z (/ t (- z a))))
     (if (<= a -4.4e+60)
       (/ (* y (- x t)) (- z a))
       (if (<= a -2.7e-13)
         t_2
         (if (<= a -4.7e-86)
           t_1
           (if (<= a 1.04e-94)
             (+ t (* (/ y z) (- x t)))
             (if (<= a 5e+16)
               t_1
               (if (<= a 3.05e+25) (/ (* x (- y a)) z) t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / (z - a));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -2.15e+127) {
		tmp = x + (z * (t / (z - a)));
	} else if (a <= -4.4e+60) {
		tmp = (y * (x - t)) / (z - a);
	} else if (a <= -2.7e-13) {
		tmp = t_2;
	} else if (a <= -4.7e-86) {
		tmp = t_1;
	} else if (a <= 1.04e-94) {
		tmp = t + ((y / z) * (x - t));
	} else if (a <= 5e+16) {
		tmp = t_1;
	} else if (a <= 3.05e+25) {
		tmp = (x * (y - a)) / z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((z - y) / (z - a))
    t_2 = x + (y * ((t - x) / a))
    if (a <= (-2.15d+127)) then
        tmp = x + (z * (t / (z - a)))
    else if (a <= (-4.4d+60)) then
        tmp = (y * (x - t)) / (z - a)
    else if (a <= (-2.7d-13)) then
        tmp = t_2
    else if (a <= (-4.7d-86)) then
        tmp = t_1
    else if (a <= 1.04d-94) then
        tmp = t + ((y / z) * (x - t))
    else if (a <= 5d+16) then
        tmp = t_1
    else if (a <= 3.05d+25) then
        tmp = (x * (y - a)) / z
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / (z - a));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -2.15e+127) {
		tmp = x + (z * (t / (z - a)));
	} else if (a <= -4.4e+60) {
		tmp = (y * (x - t)) / (z - a);
	} else if (a <= -2.7e-13) {
		tmp = t_2;
	} else if (a <= -4.7e-86) {
		tmp = t_1;
	} else if (a <= 1.04e-94) {
		tmp = t + ((y / z) * (x - t));
	} else if (a <= 5e+16) {
		tmp = t_1;
	} else if (a <= 3.05e+25) {
		tmp = (x * (y - a)) / z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / (z - a))
	t_2 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -2.15e+127:
		tmp = x + (z * (t / (z - a)))
	elif a <= -4.4e+60:
		tmp = (y * (x - t)) / (z - a)
	elif a <= -2.7e-13:
		tmp = t_2
	elif a <= -4.7e-86:
		tmp = t_1
	elif a <= 1.04e-94:
		tmp = t + ((y / z) * (x - t))
	elif a <= 5e+16:
		tmp = t_1
	elif a <= 3.05e+25:
		tmp = (x * (y - a)) / z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / Float64(z - a)))
	t_2 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -2.15e+127)
		tmp = Float64(x + Float64(z * Float64(t / Float64(z - a))));
	elseif (a <= -4.4e+60)
		tmp = Float64(Float64(y * Float64(x - t)) / Float64(z - a));
	elseif (a <= -2.7e-13)
		tmp = t_2;
	elseif (a <= -4.7e-86)
		tmp = t_1;
	elseif (a <= 1.04e-94)
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	elseif (a <= 5e+16)
		tmp = t_1;
	elseif (a <= 3.05e+25)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / (z - a));
	t_2 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -2.15e+127)
		tmp = x + (z * (t / (z - a)));
	elseif (a <= -4.4e+60)
		tmp = (y * (x - t)) / (z - a);
	elseif (a <= -2.7e-13)
		tmp = t_2;
	elseif (a <= -4.7e-86)
		tmp = t_1;
	elseif (a <= 1.04e-94)
		tmp = t + ((y / z) * (x - t));
	elseif (a <= 5e+16)
		tmp = t_1;
	elseif (a <= 3.05e+25)
		tmp = (x * (y - a)) / z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.15e+127], N[(x + N[(z * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.4e+60], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.7e-13], t$95$2, If[LessEqual[a, -4.7e-86], t$95$1, If[LessEqual[a, 1.04e-94], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e+16], t$95$1, If[LessEqual[a, 3.05e+25], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.14999999999999992e127

   1. Initial program 76.8%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in y around 0 63.0%

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

      1. mul-1-neg 63.0%

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

      2. unsub-neg 63.0%

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

      3. associate-/l* 77.4%

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

   7. Simplified 77.4%

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

   8. Taylor expanded in t around inf 77.5%

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

   if -2.14999999999999992e127 < a < -4.39999999999999992e60

   1. Initial program 93.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around -inf 85.9%

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

   if -4.39999999999999992e60 < a < -2.70000000000000011e-13 or 3.0500000000000001e25 < a

   1. Initial program 65.4%

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

      1. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in z around 0 54.1%

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

      1. associate-/l* 67.0%

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

   7. Simplified 67.0%

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

   if -2.70000000000000011e-13 < a < -4.7000000000000001e-86 or 1.04e-94 < a < 5e16

   1. Initial program 73.6%

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

      1. associate-/l* 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in x around 0 63.9%

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

      1. associate-/l* 79.2%

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

   7. Simplified 79.2%

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

   if -4.7000000000000001e-86 < a < 1.04e-94

   1. Initial program 63.2%

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

      1. +-commutative 63.2%

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

      2. associate-/l* 73.9%

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

      3. fma-define 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in a around 0 65.1%

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

      1. mul-1-neg 65.1%

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

      2. distribute-neg-frac2 65.1%

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

   7. Simplified 65.1%

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

   8. Taylor expanded in y around 0 83.5%

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

      1. mul-1-neg 83.5%

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

      2. div-sub 84.7%

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

      3. associate-/l* 79.6%

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

      4. unsub-neg 79.6%

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

      5. *-commutative 79.6%

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

      6. *-lft-identity 79.6%

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

      7. times-frac 89.0%

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

      8. /-rgt-identity 89.0%

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

   10. Simplified 89.0%

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

   if 5e16 < a < 3.0500000000000001e25

   1. Initial program 67.8%

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

      1. associate-/l* 67.7%

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

   3. Simplified 67.7%

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

      1. clear-num 67.7%

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

      2. un-div-inv 67.7%

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

   6. Applied egg-rr 67.7%

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

   7. Taylor expanded in z around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. associate-*r/ 100.0%

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

      4. mul-1-neg 100.0%

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

      5. div-sub 100.0%

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

      6. mul-1-neg 100.0%

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

      7. distribute-lft-out-- 100.0%

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

      8. associate-*r/ 100.0%

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

      9. mul-1-neg 100.0%

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

      10. unsub-neg 100.0%

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

      11. distribute-rgt-out-- 100.0%

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

      12. *-lft-identity 100.0%

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

      13. times-frac 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in t around 0 100.0%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{+127}:\\ \;\;\;\;x + z \cdot \frac{t}{z - a}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{+60}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z - a}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-13}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-86}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{-94}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+25}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-53}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x - t}}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+53} \lor \neg \left(z \leq 1.5 \cdot 10^{+108}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (- t x) (/ (- a y) z)))))
   (if (<= z -4.6e+105)
     t_1
     (if (<= z -1.8e-27)
       (* t (/ (- z y) (- z a)))
       (if (<= z 1.25e-53)
         (- x (/ y (/ a (- x t))))
         (if (or (<= z 1.05e+53) (not (<= z 1.5e+108)))
           t_1
           (+ x (* z (/ t (- z a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * ((a - y) / z));
	double tmp;
	if (z <= -4.6e+105) {
		tmp = t_1;
	} else if (z <= -1.8e-27) {
		tmp = t * ((z - y) / (z - a));
	} else if (z <= 1.25e-53) {
		tmp = x - (y / (a / (x - t)));
	} else if ((z <= 1.05e+53) || !(z <= 1.5e+108)) {
		tmp = t_1;
	} else {
		tmp = x + (z * (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((t - x) * ((a - y) / z))
    if (z <= (-4.6d+105)) then
        tmp = t_1
    else if (z <= (-1.8d-27)) then
        tmp = t * ((z - y) / (z - a))
    else if (z <= 1.25d-53) then
        tmp = x - (y / (a / (x - t)))
    else if ((z <= 1.05d+53) .or. (.not. (z <= 1.5d+108))) then
        tmp = t_1
    else
        tmp = x + (z * (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) * ((a - y) / z));
	double tmp;
	if (z <= -4.6e+105) {
		tmp = t_1;
	} else if (z <= -1.8e-27) {
		tmp = t * ((z - y) / (z - a));
	} else if (z <= 1.25e-53) {
		tmp = x - (y / (a / (x - t)));
	} else if ((z <= 1.05e+53) || !(z <= 1.5e+108)) {
		tmp = t_1;
	} else {
		tmp = x + (z * (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((t - x) * ((a - y) / z))
	tmp = 0
	if z <= -4.6e+105:
		tmp = t_1
	elif z <= -1.8e-27:
		tmp = t * ((z - y) / (z - a))
	elif z <= 1.25e-53:
		tmp = x - (y / (a / (x - t)))
	elif (z <= 1.05e+53) or not (z <= 1.5e+108):
		tmp = t_1
	else:
		tmp = x + (z * (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)))
	tmp = 0.0
	if (z <= -4.6e+105)
		tmp = t_1;
	elseif (z <= -1.8e-27)
		tmp = Float64(t * Float64(Float64(z - y) / Float64(z - a)));
	elseif (z <= 1.25e-53)
		tmp = Float64(x - Float64(y / Float64(a / Float64(x - t))));
	elseif ((z <= 1.05e+53) || !(z <= 1.5e+108))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z * Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((t - x) * ((a - y) / z));
	tmp = 0.0;
	if (z <= -4.6e+105)
		tmp = t_1;
	elseif (z <= -1.8e-27)
		tmp = t * ((z - y) / (z - a));
	elseif (z <= 1.25e-53)
		tmp = x - (y / (a / (x - t)));
	elseif ((z <= 1.05e+53) || ~((z <= 1.5e+108)))
		tmp = t_1;
	else
		tmp = x + (z * (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+105], t$95$1, If[LessEqual[z, -1.8e-27], N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e-53], N[(x - N[(y / N[(a / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.05e+53], N[Not[LessEqual[z, 1.5e+108]], $MachinePrecision]], t$95$1, N[(x + N[(z * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.5999999999999996e105 or 1.25e-53 < z < 1.0500000000000001e53 or 1.49999999999999992e108 < z

   1. Initial program 40.0%

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

      1. associate-/l* 68.6%

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

   3. Simplified 68.6%

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

      1. clear-num 68.3%

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

      2. un-div-inv 68.5%

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

   6. Applied egg-rr 68.5%

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

   7. Taylor expanded in z around inf 63.9%

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

      1. associate--l+ 63.9%

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

      2. associate-*r/ 63.9%

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

      3. associate-*r/ 63.9%

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

      4. mul-1-neg 63.9%

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

      5. div-sub 63.9%

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

      6. mul-1-neg 63.9%

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

      7. distribute-lft-out-- 63.9%

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

      8. associate-*r/ 63.9%

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

      9. mul-1-neg 63.9%

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

      10. unsub-neg 63.9%

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

      11. distribute-rgt-out-- 65.1%

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

      12. *-lft-identity 65.1%

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

      13. times-frac 83.4%

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

   9. Simplified 83.4%

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

   if -4.5999999999999996e105 < z < -1.7999999999999999e-27

   1. Initial program 78.8%

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

      1. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in x around 0 70.6%

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

      1. associate-/l* 77.3%

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

   7. Simplified 77.3%

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

   if -1.7999999999999999e-27 < z < 1.25e-53

   1. Initial program 92.9%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in z around 0 77.1%

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

      1. associate-/l* 78.7%

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

   7. Simplified 78.7%

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

      1. clear-num 78.7%

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

      2. un-div-inv 79.5%

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

   9. Applied egg-rr 79.5%

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

   if 1.0500000000000001e53 < z < 1.49999999999999992e108

   1. Initial program 91.1%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. unsub-neg 71.2%

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

      3. associate-/l* 81.0%

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

   7. Simplified 81.0%

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

   8. Taylor expanded in t around inf 81.3%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+105}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-53}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x - t}}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+53} \lor \neg \left(z \leq 1.5 \cdot 10^{+108}\right):\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{t - x}{\frac{z}{a - y}}\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-53}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x - t}}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+53} \lor \neg \left(z \leq 1.25 \cdot 10^{+108}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (/ (- t x) (/ z (- a y))))))
   (if (<= z -1.02e+84)
     t_1
     (if (<= z -6.8e-26)
       (* t (/ (- z y) (- z a)))
       (if (<= z 7e-53)
         (- x (/ y (/ a (- x t))))
         (if (or (<= z 1.05e+53) (not (<= z 1.25e+108)))
           t_1
           (+ x (* z (/ t (- z a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) / (z / (a - y)));
	double tmp;
	if (z <= -1.02e+84) {
		tmp = t_1;
	} else if (z <= -6.8e-26) {
		tmp = t * ((z - y) / (z - a));
	} else if (z <= 7e-53) {
		tmp = x - (y / (a / (x - t)));
	} else if ((z <= 1.05e+53) || !(z <= 1.25e+108)) {
		tmp = t_1;
	} else {
		tmp = x + (z * (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((t - x) / (z / (a - y)))
    if (z <= (-1.02d+84)) then
        tmp = t_1
    else if (z <= (-6.8d-26)) then
        tmp = t * ((z - y) / (z - a))
    else if (z <= 7d-53) then
        tmp = x - (y / (a / (x - t)))
    else if ((z <= 1.05d+53) .or. (.not. (z <= 1.25d+108))) then
        tmp = t_1
    else
        tmp = x + (z * (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + ((t - x) / (z / (a - y)));
	double tmp;
	if (z <= -1.02e+84) {
		tmp = t_1;
	} else if (z <= -6.8e-26) {
		tmp = t * ((z - y) / (z - a));
	} else if (z <= 7e-53) {
		tmp = x - (y / (a / (x - t)));
	} else if ((z <= 1.05e+53) || !(z <= 1.25e+108)) {
		tmp = t_1;
	} else {
		tmp = x + (z * (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + ((t - x) / (z / (a - y)))
	tmp = 0
	if z <= -1.02e+84:
		tmp = t_1
	elif z <= -6.8e-26:
		tmp = t * ((z - y) / (z - a))
	elif z <= 7e-53:
		tmp = x - (y / (a / (x - t)))
	elif (z <= 1.05e+53) or not (z <= 1.25e+108):
		tmp = t_1
	else:
		tmp = x + (z * (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(t - x) / Float64(z / Float64(a - y))))
	tmp = 0.0
	if (z <= -1.02e+84)
		tmp = t_1;
	elseif (z <= -6.8e-26)
		tmp = Float64(t * Float64(Float64(z - y) / Float64(z - a)));
	elseif (z <= 7e-53)
		tmp = Float64(x - Float64(y / Float64(a / Float64(x - t))));
	elseif ((z <= 1.05e+53) || !(z <= 1.25e+108))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z * Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + ((t - x) / (z / (a - y)));
	tmp = 0.0;
	if (z <= -1.02e+84)
		tmp = t_1;
	elseif (z <= -6.8e-26)
		tmp = t * ((z - y) / (z - a));
	elseif (z <= 7e-53)
		tmp = x - (y / (a / (x - t)));
	elseif ((z <= 1.05e+53) || ~((z <= 1.25e+108)))
		tmp = t_1;
	else
		tmp = x + (z * (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(t - x), $MachinePrecision] / N[(z / N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.02e+84], t$95$1, If[LessEqual[z, -6.8e-26], N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e-53], N[(x - N[(y / N[(a / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.05e+53], N[Not[LessEqual[z, 1.25e+108]], $MachinePrecision]], t$95$1, N[(x + N[(z * N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.0199999999999999e84 or 6.99999999999999987e-53 < z < 1.0500000000000001e53 or 1.24999999999999998e108 < z

   1. Initial program 42.9%

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

      1. associate-/l* 70.5%

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

   3. Simplified 70.5%

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

      1. clear-num 70.2%

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

      2. un-div-inv 70.4%

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

   6. Applied egg-rr 70.4%

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

   7. Taylor expanded in z around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. associate-*r/ 62.8%

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

      3. associate-*r/ 62.8%

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

      4. mul-1-neg 62.8%

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

      5. div-sub 62.8%

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

      6. mul-1-neg 62.8%

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

      7. distribute-lft-out-- 62.8%

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

      8. associate-*r/ 62.8%

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

      9. mul-1-neg 62.8%

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

      10. unsub-neg 62.8%

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

      11. distribute-rgt-out-- 63.8%

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

      12. *-lft-identity 63.8%

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

      13. times-frac 81.8%

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

   9. Simplified 81.8%

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

       1. clear-num 81.8%

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

       2. un-div-inv 81.9%

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

   11. Applied egg-rr 81.9%

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

   if -1.0199999999999999e84 < z < -6.80000000000000026e-26

   1. Initial program 75.7%

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

      1. associate-/l* 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in x around 0 75.4%

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

      1. associate-/l* 84.7%

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

   7. Simplified 84.7%

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

   if -6.80000000000000026e-26 < z < 6.99999999999999987e-53

   1. Initial program 92.9%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in z around 0 77.1%

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

      1. associate-/l* 78.7%

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

   7. Simplified 78.7%

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

      1. clear-num 78.7%

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

      2. un-div-inv 79.5%

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

   9. Applied egg-rr 79.5%

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

   if 1.0500000000000001e53 < z < 1.24999999999999998e108

   1. Initial program 91.1%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. unsub-neg 71.2%

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

      3. associate-/l* 81.0%

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

   7. Simplified 81.0%

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

   8. Taylor expanded in t around inf 81.3%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+84}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-53}:\\ \;\;\;\;x - \frac{y}{\frac{a}{x - t}}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+53} \lor \neg \left(z \leq 1.25 \cdot 10^{+108}\right):\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z - a}\\ t_2 := x + y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{-94}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+25}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) (- z a)))) (t_2 (+ x (* y (/ (- t x) a)))))
   (if (<= a -6.5e-11)
     t_2
     (if (<= a -5.1e-85)
       t_1
       (if (<= a 6.1e-94)
         (+ t (* (/ y z) (- x t)))
         (if (<= a 5e+16)
           t_1
           (if (<= a 3.05e+25) (/ (* x (- y a)) z) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / (z - a));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -6.5e-11) {
		tmp = t_2;
	} else if (a <= -5.1e-85) {
		tmp = t_1;
	} else if (a <= 6.1e-94) {
		tmp = t + ((y / z) * (x - t));
	} else if (a <= 5e+16) {
		tmp = t_1;
	} else if (a <= 3.05e+25) {
		tmp = (x * (y - a)) / z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((z - y) / (z - a))
    t_2 = x + (y * ((t - x) / a))
    if (a <= (-6.5d-11)) then
        tmp = t_2
    else if (a <= (-5.1d-85)) then
        tmp = t_1
    else if (a <= 6.1d-94) then
        tmp = t + ((y / z) * (x - t))
    else if (a <= 5d+16) then
        tmp = t_1
    else if (a <= 3.05d+25) then
        tmp = (x * (y - a)) / z
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / (z - a));
	double t_2 = x + (y * ((t - x) / a));
	double tmp;
	if (a <= -6.5e-11) {
		tmp = t_2;
	} else if (a <= -5.1e-85) {
		tmp = t_1;
	} else if (a <= 6.1e-94) {
		tmp = t + ((y / z) * (x - t));
	} else if (a <= 5e+16) {
		tmp = t_1;
	} else if (a <= 3.05e+25) {
		tmp = (x * (y - a)) / z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / (z - a))
	t_2 = x + (y * ((t - x) / a))
	tmp = 0
	if a <= -6.5e-11:
		tmp = t_2
	elif a <= -5.1e-85:
		tmp = t_1
	elif a <= 6.1e-94:
		tmp = t + ((y / z) * (x - t))
	elif a <= 5e+16:
		tmp = t_1
	elif a <= 3.05e+25:
		tmp = (x * (y - a)) / z
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / Float64(z - a)))
	t_2 = Float64(x + Float64(y * Float64(Float64(t - x) / a)))
	tmp = 0.0
	if (a <= -6.5e-11)
		tmp = t_2;
	elseif (a <= -5.1e-85)
		tmp = t_1;
	elseif (a <= 6.1e-94)
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	elseif (a <= 5e+16)
		tmp = t_1;
	elseif (a <= 3.05e+25)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / (z - a));
	t_2 = x + (y * ((t - x) / a));
	tmp = 0.0;
	if (a <= -6.5e-11)
		tmp = t_2;
	elseif (a <= -5.1e-85)
		tmp = t_1;
	elseif (a <= 6.1e-94)
		tmp = t + ((y / z) * (x - t));
	elseif (a <= 5e+16)
		tmp = t_1;
	elseif (a <= 3.05e+25)
		tmp = (x * (y - a)) / z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e-11], t$95$2, If[LessEqual[a, -5.1e-85], t$95$1, If[LessEqual[a, 6.1e-94], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e+16], t$95$1, If[LessEqual[a, 3.05e+25], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.49999999999999953e-11 or 3.0500000000000001e25 < a

   1. Initial program 72.2%

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

      1. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in z around 0 59.4%

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

      1. associate-/l* 68.7%

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

   7. Simplified 68.7%

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

   if -6.49999999999999953e-11 < a < -5.1000000000000002e-85 or 6.09999999999999992e-94 < a < 5e16

   1. Initial program 73.6%

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

      1. associate-/l* 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in x around 0 63.9%

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

      1. associate-/l* 79.2%

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

   7. Simplified 79.2%

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

   if -5.1000000000000002e-85 < a < 6.09999999999999992e-94

   1. Initial program 63.2%

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

      1. +-commutative 63.2%

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

      2. associate-/l* 73.9%

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

      3. fma-define 73.9%

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

   3. Simplified 73.9%

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

   5. Taylor expanded in a around 0 65.1%

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

      1. mul-1-neg 65.1%

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

      2. distribute-neg-frac2 65.1%

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

   7. Simplified 65.1%

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

   8. Taylor expanded in y around 0 83.5%

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

      1. mul-1-neg 83.5%

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

      2. div-sub 84.7%

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

      3. associate-/l* 79.6%

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

      4. unsub-neg 79.6%

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

      5. *-commutative 79.6%

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

      6. *-lft-identity 79.6%

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

      7. times-frac 89.0%

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

      8. /-rgt-identity 89.0%

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

   10. Simplified 89.0%

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

   if 5e16 < a < 3.0500000000000001e25

   1. Initial program 67.8%

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

      1. associate-/l* 67.7%

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

   3. Simplified 67.7%

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

      1. clear-num 67.7%

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

      2. un-div-inv 67.7%

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

   6. Applied egg-rr 67.7%

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

   7. Taylor expanded in z around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. associate-*r/ 100.0%

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

      4. mul-1-neg 100.0%

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

      5. div-sub 100.0%

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

      6. mul-1-neg 100.0%

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

      7. distribute-lft-out-- 100.0%

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

      8. associate-*r/ 100.0%

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

      9. mul-1-neg 100.0%

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

      10. unsub-neg 100.0%

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

      11. distribute-rgt-out-- 100.0%

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

      12. *-lft-identity 100.0%

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

      13. times-frac 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in t around 0 100.0%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-11}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-85}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{-94}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{+25}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{x - t}{z - a}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+142}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-225}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+161}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- x t) (- z a))))))
   (if (<= z -3.2e+142)
     (+ t (* (- t x) (/ (- a y) z)))
     (if (<= z -2.25e-144)
       t_1
       (if (<= z 8.2e-225)
         (+ x (/ (* (- y z) (- x t)) (- z a)))
         (if (<= z 8.2e+161) 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) * ((x - t) / (z - a)));
	double tmp;
	if (z <= -3.2e+142) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else if (z <= -2.25e-144) {
		tmp = t_1;
	} else if (z <= 8.2e-225) {
		tmp = x + (((y - z) * (x - t)) / (z - a));
	} else if (z <= 8.2e+161) {
		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) * ((x - t) / (z - a)))
    if (z <= (-3.2d+142)) then
        tmp = t + ((t - x) * ((a - y) / z))
    else if (z <= (-2.25d-144)) then
        tmp = t_1
    else if (z <= 8.2d-225) then
        tmp = x + (((y - z) * (x - t)) / (z - a))
    else if (z <= 8.2d+161) 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) * ((x - t) / (z - a)));
	double tmp;
	if (z <= -3.2e+142) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else if (z <= -2.25e-144) {
		tmp = t_1;
	} else if (z <= 8.2e-225) {
		tmp = x + (((y - z) * (x - t)) / (z - a));
	} else if (z <= 8.2e+161) {
		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) * ((x - t) / (z - a)))
	tmp = 0
	if z <= -3.2e+142:
		tmp = t + ((t - x) * ((a - y) / z))
	elif z <= -2.25e-144:
		tmp = t_1
	elif z <= 8.2e-225:
		tmp = x + (((y - z) * (x - t)) / (z - a))
	elif z <= 8.2e+161:
		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(x - t) / Float64(z - a))))
	tmp = 0.0
	if (z <= -3.2e+142)
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	elseif (z <= -2.25e-144)
		tmp = t_1;
	elseif (z <= 8.2e-225)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(z - a)));
	elseif (z <= 8.2e+161)
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(t - x) / Float64(z / Float64(a - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((x - t) / (z - a)));
	tmp = 0.0;
	if (z <= -3.2e+142)
		tmp = t + ((t - x) * ((a - y) / z));
	elseif (z <= -2.25e-144)
		tmp = t_1;
	elseif (z <= 8.2e-225)
		tmp = x + (((y - z) * (x - t)) / (z - a));
	elseif (z <= 8.2e+161)
		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[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+142], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.25e-144], t$95$1, If[LessEqual[z, 8.2e-225], N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+161], t$95$1, N[(t + N[(N[(t - x), $MachinePrecision] / N[(z / N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.20000000000000005e142

   1. Initial program 25.5%

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

      1. associate-/l* 63.5%

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

   3. Simplified 63.5%

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

      1. clear-num 63.2%

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

      2. un-div-inv 63.3%

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

   6. Applied egg-rr 63.3%

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

   7. Taylor expanded in z around inf 71.3%

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

      1. associate--l+ 71.3%

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

      2. associate-*r/ 71.3%

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

      3. associate-*r/ 71.3%

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

      4. mul-1-neg 71.3%

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

      5. div-sub 71.3%

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

      6. mul-1-neg 71.3%

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

      7. distribute-lft-out-- 71.3%

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

      8. associate-*r/ 71.3%

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

      9. mul-1-neg 71.3%

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

      10. unsub-neg 71.3%

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

      11. distribute-rgt-out-- 74.0%

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

      12. *-lft-identity 74.0%

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

      13. times-frac 92.1%

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

   9. Simplified 92.1%

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

   if -3.20000000000000005e142 < z < -2.2499999999999999e-144 or 8.20000000000000044e-225 < z < 8.2000000000000002e161

   1. Initial program 80.0%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   if -2.2499999999999999e-144 < z < 8.20000000000000044e-225

   1. Initial program 99.4%

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

   if 8.2000000000000002e161 < z

   1. Initial program 17.6%

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

      1. associate-/l* 51.4%

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

   3. Simplified 51.4%

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

      1. clear-num 51.1%

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

      2. un-div-inv 51.5%

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

   6. Applied egg-rr 51.5%

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

   7. Taylor expanded in z around inf 53.9%

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

      1. associate--l+ 53.9%

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

      2. associate-*r/ 53.9%

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

      3. associate-*r/ 53.9%

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

      4. mul-1-neg 53.9%

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

      5. div-sub 53.9%

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

      6. mul-1-neg 53.9%

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

      7. distribute-lft-out-- 53.9%

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

      8. associate-*r/ 53.9%

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

      9. mul-1-neg 53.9%

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

      10. unsub-neg 53.9%

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

      11. distribute-rgt-out-- 53.9%

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

      12. *-lft-identity 53.9%

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

      13. times-frac 92.3%

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

   9. Simplified 92.3%

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

       1. clear-num 92.4%

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

       2. un-div-inv 92.4%

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

   11. Applied egg-rr 92.4%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+142}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-144}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-225}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+161}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{x - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+142}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-145}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-223}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+166}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.5e+142)
   (+ t (* (- t x) (/ (- a y) z)))
   (if (<= z -2.5e-145)
     (+ x (* (- y z) (/ (- x t) (- z a))))
     (if (<= z 5e-223)
       (+ x (/ (* (- y z) (- x t)) (- z a)))
       (if (<= z 9.8e+166)
         (+ x (/ (- y z) (/ (- a z) (- t x))))
         (+ t (/ (- t x) (/ z (- a y)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.5e+142) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else if (z <= -2.5e-145) {
		tmp = x + ((y - z) * ((x - t) / (z - a)));
	} else if (z <= 5e-223) {
		tmp = x + (((y - z) * (x - t)) / (z - a));
	} else if (z <= 9.8e+166) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} 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 <= (-4.5d+142)) then
        tmp = t + ((t - x) * ((a - y) / z))
    else if (z <= (-2.5d-145)) then
        tmp = x + ((y - z) * ((x - t) / (z - a)))
    else if (z <= 5d-223) then
        tmp = x + (((y - z) * (x - t)) / (z - a))
    else if (z <= 9.8d+166) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    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 <= -4.5e+142) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else if (z <= -2.5e-145) {
		tmp = x + ((y - z) * ((x - t) / (z - a)));
	} else if (z <= 5e-223) {
		tmp = x + (((y - z) * (x - t)) / (z - a));
	} else if (z <= 9.8e+166) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t + ((t - x) / (z / (a - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.5e+142:
		tmp = t + ((t - x) * ((a - y) / z))
	elif z <= -2.5e-145:
		tmp = x + ((y - z) * ((x - t) / (z - a)))
	elif z <= 5e-223:
		tmp = x + (((y - z) * (x - t)) / (z - a))
	elif z <= 9.8e+166:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t + ((t - x) / (z / (a - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.5e+142)
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	elseif (z <= -2.5e-145)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(x - t) / Float64(z - a))));
	elseif (z <= 5e-223)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * Float64(x - t)) / Float64(z - a)));
	elseif (z <= 9.8e+166)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = Float64(t + Float64(Float64(t - x) / Float64(z / Float64(a - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.5e+142)
		tmp = t + ((t - x) * ((a - y) / z));
	elseif (z <= -2.5e-145)
		tmp = x + ((y - z) * ((x - t) / (z - a)));
	elseif (z <= 5e-223)
		tmp = x + (((y - z) * (x - t)) / (z - a));
	elseif (z <= 9.8e+166)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t + ((t - x) / (z / (a - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.5e+142], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5e-145], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-223], N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.8e+166], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(t - x), $MachinePrecision] / N[(z / N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.4999999999999999e142

   1. Initial program 25.5%

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

      1. associate-/l* 63.5%

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

   3. Simplified 63.5%

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

      1. clear-num 63.2%

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

      2. un-div-inv 63.3%

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

   6. Applied egg-rr 63.3%

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

   7. Taylor expanded in z around inf 71.3%

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

      1. associate--l+ 71.3%

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

      2. associate-*r/ 71.3%

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

      3. associate-*r/ 71.3%

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

      4. mul-1-neg 71.3%

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

      5. div-sub 71.3%

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

      6. mul-1-neg 71.3%

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

      7. distribute-lft-out-- 71.3%

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

      8. associate-*r/ 71.3%

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

      9. mul-1-neg 71.3%

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

      10. unsub-neg 71.3%

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

      11. distribute-rgt-out-- 74.0%

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

      12. *-lft-identity 74.0%

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

      13. times-frac 92.1%

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

   9. Simplified 92.1%

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

   if -4.4999999999999999e142 < z < -2.4999999999999999e-145

   1. Initial program 74.5%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   if -2.4999999999999999e-145 < z < 5.00000000000000024e-223

   1. Initial program 99.4%

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

   if 5.00000000000000024e-223 < z < 9.79999999999999938e166

   1. Initial program 84.8%

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

      1. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

      1. clear-num 90.1%

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

      2. un-div-inv 91.4%

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

   6. Applied egg-rr 91.4%

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

   if 9.79999999999999938e166 < z

   1. Initial program 17.6%

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

      1. associate-/l* 51.4%

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

   3. Simplified 51.4%

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

      1. clear-num 51.1%

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

      2. un-div-inv 51.5%

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

   6. Applied egg-rr 51.5%

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

   7. Taylor expanded in z around inf 53.9%

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

      1. associate--l+ 53.9%

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

      2. associate-*r/ 53.9%

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

      3. associate-*r/ 53.9%

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

      4. mul-1-neg 53.9%

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

      5. div-sub 53.9%

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

      6. mul-1-neg 53.9%

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

      7. distribute-lft-out-- 53.9%

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

      8. associate-*r/ 53.9%

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

      9. mul-1-neg 53.9%

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

      10. unsub-neg 53.9%

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

      11. distribute-rgt-out-- 53.9%

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

      12. *-lft-identity 53.9%

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

      13. times-frac 92.3%

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

   9. Simplified 92.3%

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

       1. clear-num 92.4%

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

       2. un-div-inv 92.4%

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

   11. Applied egg-rr 92.4%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+142}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-145}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-223}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(x - t\right)}{z - a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+166}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x - t}{z - a}\\ t_2 := t \cdot \frac{z - y}{z - a}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-140}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-139}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 16500:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- x t) (- z a)))) (t_2 (* t (/ (- z y) (- z a)))))
   (if (<= t -1.45e-140)
     t_2
     (if (<= t -1.5e-200)
       t_1
       (if (<= t 4e-139) (- x (* x (/ y a))) (if (<= t 16500.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((x - t) / (z - a));
	double t_2 = t * ((z - y) / (z - a));
	double tmp;
	if (t <= -1.45e-140) {
		tmp = t_2;
	} else if (t <= -1.5e-200) {
		tmp = t_1;
	} else if (t <= 4e-139) {
		tmp = x - (x * (y / a));
	} else if (t <= 16500.0) {
		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 * ((x - t) / (z - a))
    t_2 = t * ((z - y) / (z - a))
    if (t <= (-1.45d-140)) then
        tmp = t_2
    else if (t <= (-1.5d-200)) then
        tmp = t_1
    else if (t <= 4d-139) then
        tmp = x - (x * (y / a))
    else if (t <= 16500.0d0) 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 * ((x - t) / (z - a));
	double t_2 = t * ((z - y) / (z - a));
	double tmp;
	if (t <= -1.45e-140) {
		tmp = t_2;
	} else if (t <= -1.5e-200) {
		tmp = t_1;
	} else if (t <= 4e-139) {
		tmp = x - (x * (y / a));
	} else if (t <= 16500.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((x - t) / (z - a))
	t_2 = t * ((z - y) / (z - a))
	tmp = 0
	if t <= -1.45e-140:
		tmp = t_2
	elif t <= -1.5e-200:
		tmp = t_1
	elif t <= 4e-139:
		tmp = x - (x * (y / a))
	elif t <= 16500.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(x - t) / Float64(z - a)))
	t_2 = Float64(t * Float64(Float64(z - y) / Float64(z - a)))
	tmp = 0.0
	if (t <= -1.45e-140)
		tmp = t_2;
	elseif (t <= -1.5e-200)
		tmp = t_1;
	elseif (t <= 4e-139)
		tmp = Float64(x - Float64(x * Float64(y / a)));
	elseif (t <= 16500.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((x - t) / (z - a));
	t_2 = t * ((z - y) / (z - a));
	tmp = 0.0;
	if (t <= -1.45e-140)
		tmp = t_2;
	elseif (t <= -1.5e-200)
		tmp = t_1;
	elseif (t <= 4e-139)
		tmp = x - (x * (y / a));
	elseif (t <= 16500.0)
		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[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e-140], t$95$2, If[LessEqual[t, -1.5e-200], t$95$1, If[LessEqual[t, 4e-139], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 16500.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.44999999999999999e-140 or 16500 < t

   1. Initial program 74.0%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in x around 0 60.4%

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

      1. associate-/l* 79.3%

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

   7. Simplified 79.3%

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

   if -1.44999999999999999e-140 < t < -1.49999999999999997e-200 or 4.00000000000000012e-139 < t < 16500

   1. Initial program 61.9%

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

      1. associate-/l* 64.5%

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

   3. Simplified 64.5%

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

   5. Taylor expanded in y around inf 60.1%

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

      1. div-sub 60.1%

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

   7. Simplified 60.1%

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

   if -1.49999999999999997e-200 < t < 4.00000000000000012e-139

   1. Initial program 61.8%

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

      1. associate-/l* 73.0%

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

   3. Simplified 73.0%

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

   5. Taylor expanded in z around 0 54.4%

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

      1. associate-/l* 63.4%

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

   7. Simplified 63.4%

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

   8. Taylor expanded in t around 0 53.0%

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

      1. mul-1-neg 53.0%

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

      2. associate-/l* 64.0%

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

      3. distribute-rgt-neg-in 64.0%

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

      4. mul-1-neg 64.0%

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

      5. associate-*r/ 64.0%

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

      6. neg-mul-1 64.0%

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

   10. Simplified 64.0%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-140}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-139}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 16500:\\ \;\;\;\;y \cdot \frac{x - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -33000:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-26} \lor \neg \left(z \leq 8 \cdot 10^{+90}\right):\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7e+69)
   t
   (if (<= z -33000.0)
     (* t (/ y (- a z)))
     (if (or (<= z -1.9e-26) (not (<= z 8e+90)))
       (+ t (* a (/ t z)))
       (+ x (* t (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+69) {
		tmp = t;
	} else if (z <= -33000.0) {
		tmp = t * (y / (a - z));
	} else if ((z <= -1.9e-26) || !(z <= 8e+90)) {
		tmp = t + (a * (t / z));
	} else {
		tmp = x + (t * (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 <= (-7d+69)) then
        tmp = t
    else if (z <= (-33000.0d0)) then
        tmp = t * (y / (a - z))
    else if ((z <= (-1.9d-26)) .or. (.not. (z <= 8d+90))) then
        tmp = t + (a * (t / z))
    else
        tmp = x + (t * (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 <= -7e+69) {
		tmp = t;
	} else if (z <= -33000.0) {
		tmp = t * (y / (a - z));
	} else if ((z <= -1.9e-26) || !(z <= 8e+90)) {
		tmp = t + (a * (t / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7e+69:
		tmp = t
	elif z <= -33000.0:
		tmp = t * (y / (a - z))
	elif (z <= -1.9e-26) or not (z <= 8e+90):
		tmp = t + (a * (t / z))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7e+69)
		tmp = t;
	elseif (z <= -33000.0)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif ((z <= -1.9e-26) || !(z <= 8e+90))
		tmp = Float64(t + Float64(a * Float64(t / z)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7e+69)
		tmp = t;
	elseif (z <= -33000.0)
		tmp = t * (y / (a - z));
	elseif ((z <= -1.9e-26) || ~((z <= 8e+90)))
		tmp = t + (a * (t / z));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7e+69], t, If[LessEqual[z, -33000.0], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.9e-26], N[Not[LessEqual[z, 8e+90]], $MachinePrecision]], N[(t + N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.99999999999999974e69

   1. Initial program 33.8%

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

      1. associate-/l* 70.7%

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

   3. Simplified 70.7%

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

   5. Taylor expanded in z around inf 53.8%

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

   if -6.99999999999999974e69 < z < -33000

   1. Initial program 90.4%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in x around 0 79.5%

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

      1. associate-/l* 89.0%

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

   7. Simplified 89.0%

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

   8. Taylor expanded in y around inf 58.2%

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

      1. associate-/l* 67.6%

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

   10. Simplified 67.6%

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

   if -33000 < z < -1.90000000000000007e-26 or 7.99999999999999973e90 < z

   1. Initial program 44.3%

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

      1. associate-/l* 66.6%

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

   3. Simplified 66.6%

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

   5. Taylor expanded in x around 0 44.0%

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

      1. associate-/l* 65.5%

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

   7. Simplified 65.5%

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

   8. Taylor expanded in y around 0 36.4%

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

      1. mul-1-neg 36.4%

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

      2. associate-/l* 56.0%

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

      3. distribute-lft-neg-in 56.0%

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

   10. Simplified 56.0%

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

   11. Taylor expanded in z around inf 45.5%

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

       1. associate-/l* 49.5%

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

   13. Simplified 49.5%

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

   if -1.90000000000000007e-26 < z < 7.99999999999999973e90

   1. Initial program 90.2%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in z around 0 69.0%

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

      1. associate-/l* 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in t around inf 55.4%

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

      1. associate-/l* 56.9%

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

   10. Simplified 56.9%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -33000:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-26} \lor \neg \left(z \leq 8 \cdot 10^{+90}\right):\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4900000:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-42}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-85}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+69)
   t
   (if (<= z -4900000.0)
     (* t (/ y (- z)))
     (if (<= z -1.3e-42)
       t
       (if (<= z 2.45e-85) (* t (/ y a)) (if (<= z 6.2e+90) x t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+69) {
		tmp = t;
	} else if (z <= -4900000.0) {
		tmp = t * (y / -z);
	} else if (z <= -1.3e-42) {
		tmp = t;
	} else if (z <= 2.45e-85) {
		tmp = t * (y / a);
	} else if (z <= 6.2e+90) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.8d+69)) then
        tmp = t
    else if (z <= (-4900000.0d0)) then
        tmp = t * (y / -z)
    else if (z <= (-1.3d-42)) then
        tmp = t
    else if (z <= 2.45d-85) then
        tmp = t * (y / a)
    else if (z <= 6.2d+90) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+69) {
		tmp = t;
	} else if (z <= -4900000.0) {
		tmp = t * (y / -z);
	} else if (z <= -1.3e-42) {
		tmp = t;
	} else if (z <= 2.45e-85) {
		tmp = t * (y / a);
	} else if (z <= 6.2e+90) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+69:
		tmp = t
	elif z <= -4900000.0:
		tmp = t * (y / -z)
	elif z <= -1.3e-42:
		tmp = t
	elif z <= 2.45e-85:
		tmp = t * (y / a)
	elif z <= 6.2e+90:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+69)
		tmp = t;
	elseif (z <= -4900000.0)
		tmp = Float64(t * Float64(y / Float64(-z)));
	elseif (z <= -1.3e-42)
		tmp = t;
	elseif (z <= 2.45e-85)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 6.2e+90)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.8e+69)
		tmp = t;
	elseif (z <= -4900000.0)
		tmp = t * (y / -z);
	elseif (z <= -1.3e-42)
		tmp = t;
	elseif (z <= 2.45e-85)
		tmp = t * (y / a);
	elseif (z <= 6.2e+90)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+69], t, If[LessEqual[z, -4900000.0], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.3e-42], t, If[LessEqual[z, 2.45e-85], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+90], x, t]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8000000000000001e69 or -4.9e6 < z < -1.3e-42 or 6.19999999999999977e90 < z

   1. Initial program 42.2%

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

      1. associate-/l* 71.0%

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

   3. Simplified 71.0%

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

   5. Taylor expanded in z around inf 49.1%

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

   if -1.8000000000000001e69 < z < -4.9e6

   1. Initial program 90.4%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in x around 0 79.5%

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

      1. associate-/l* 89.0%

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

   7. Simplified 89.0%

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

   8. Taylor expanded in y around inf 58.2%

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

      1. associate-/l* 67.6%

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

   10. Simplified 67.6%

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

   11. Taylor expanded in a around 0 47.3%

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

       1. mul-1-neg 47.3%

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

       2. associate-/l* 56.7%

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

       3. distribute-lft-neg-in 56.7%

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

   13. Simplified 56.7%

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

   if -1.3e-42 < z < 2.45000000000000007e-85

   1. Initial program 92.9%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in x around 0 52.0%

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

      1. associate-/l* 53.1%

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

   7. Simplified 53.1%

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

   8. Taylor expanded in z around 0 39.3%

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

      1. associate-*r/ 40.4%

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

   10. Simplified 40.4%

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

   if 2.45000000000000007e-85 < z < 6.19999999999999977e90

   1. Initial program 83.1%

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

      1. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in a around inf 35.1%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4900000:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-42}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-85}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{z - y}{z - a}\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{-135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-199}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;t \leq 17000:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z y) (- z a)))))
   (if (<= t -2.6e-135)
     t_1
     (if (<= t -3.4e-199)
       (+ t (* (/ y z) (- x t)))
       (if (<= t 17000.0) (* x (+ (/ (- y z) (- z a)) 1.0)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / (z - a));
	double tmp;
	if (t <= -2.6e-135) {
		tmp = t_1;
	} else if (t <= -3.4e-199) {
		tmp = t + ((y / z) * (x - t));
	} else if (t <= 17000.0) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((z - y) / (z - a))
    if (t <= (-2.6d-135)) then
        tmp = t_1
    else if (t <= (-3.4d-199)) then
        tmp = t + ((y / z) * (x - t))
    else if (t <= 17000.0d0) then
        tmp = x * (((y - z) / (z - a)) + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((z - y) / (z - a));
	double tmp;
	if (t <= -2.6e-135) {
		tmp = t_1;
	} else if (t <= -3.4e-199) {
		tmp = t + ((y / z) * (x - t));
	} else if (t <= 17000.0) {
		tmp = x * (((y - z) / (z - a)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((z - y) / (z - a))
	tmp = 0
	if t <= -2.6e-135:
		tmp = t_1
	elif t <= -3.4e-199:
		tmp = t + ((y / z) * (x - t))
	elif t <= 17000.0:
		tmp = x * (((y - z) / (z - a)) + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(z - y) / Float64(z - a)))
	tmp = 0.0
	if (t <= -2.6e-135)
		tmp = t_1;
	elseif (t <= -3.4e-199)
		tmp = Float64(t + Float64(Float64(y / z) * Float64(x - t)));
	elseif (t <= 17000.0)
		tmp = Float64(x * Float64(Float64(Float64(y - z) / Float64(z - a)) + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((z - y) / (z - a));
	tmp = 0.0;
	if (t <= -2.6e-135)
		tmp = t_1;
	elseif (t <= -3.4e-199)
		tmp = t + ((y / z) * (x - t));
	elseif (t <= 17000.0)
		tmp = x * (((y - z) / (z - a)) + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e-135], t$95$1, If[LessEqual[t, -3.4e-199], N[(t + N[(N[(y / z), $MachinePrecision] * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 17000.0], N[(x * N[(N[(N[(y - z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.60000000000000004e-135 or 17000 < t

   1. Initial program 73.6%

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

      1. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

   5. Taylor expanded in x around 0 60.5%

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

      1. associate-/l* 79.6%

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

   7. Simplified 79.6%

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

   if -2.60000000000000004e-135 < t < -3.40000000000000006e-199

   1. Initial program 60.0%

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

      1. +-commutative 60.0%

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

      2. associate-/l* 43.8%

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

      3. fma-define 43.7%

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

   3. Simplified 43.7%

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

   5. Taylor expanded in a around 0 26.5%

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

      1. mul-1-neg 26.5%

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

      2. distribute-neg-frac2 26.5%

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

   7. Simplified 26.5%

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

   8. Taylor expanded in y around 0 66.0%

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

      1. mul-1-neg 66.0%

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

      2. div-sub 66.0%

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

      3. associate-/l* 60.3%

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

      4. unsub-neg 60.3%

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

      5. *-commutative 60.3%

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

      6. *-lft-identity 60.3%

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

      7. times-frac 71.4%

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

      8. /-rgt-identity 71.4%

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

   10. Simplified 71.4%

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

   if -3.40000000000000006e-199 < t < 17000

   1. Initial program 63.1%

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

      1. associate-/l* 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in x around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. unsub-neg 67.4%

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

   7. Simplified 67.4%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-135}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-199}:\\ \;\;\;\;t + \frac{y}{z} \cdot \left(x - t\right)\\ \mathbf{elif}\;t \leq 17000:\\ \;\;\;\;x \cdot \left(\frac{y - z}{z - a} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+142}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+163}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{x - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.1e+142)
   (+ t (* (- t x) (/ (- a y) z)))
   (if (<= z 2.75e+163)
     (+ x (* (- y z) (/ (- x t) (- z a))))
     (+ t (/ (- t x) (/ z (- a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+142) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else if (z <= 2.75e+163) {
		tmp = x + ((y - z) * ((x - t) / (z - 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 <= (-1.1d+142)) then
        tmp = t + ((t - x) * ((a - y) / z))
    else if (z <= 2.75d+163) then
        tmp = x + ((y - z) * ((x - t) / (z - 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 <= -1.1e+142) {
		tmp = t + ((t - x) * ((a - y) / z));
	} else if (z <= 2.75e+163) {
		tmp = x + ((y - z) * ((x - t) / (z - a)));
	} else {
		tmp = t + ((t - x) / (z / (a - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.1e+142:
		tmp = t + ((t - x) * ((a - y) / z))
	elif z <= 2.75e+163:
		tmp = x + ((y - z) * ((x - t) / (z - a)))
	else:
		tmp = t + ((t - x) / (z / (a - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.1e+142)
		tmp = Float64(t + Float64(Float64(t - x) * Float64(Float64(a - y) / z)));
	elseif (z <= 2.75e+163)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(Float64(x - t) / Float64(z - a))));
	else
		tmp = Float64(t + Float64(Float64(t - x) / Float64(z / Float64(a - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.1e+142)
		tmp = t + ((t - x) * ((a - y) / z));
	elseif (z <= 2.75e+163)
		tmp = x + ((y - z) * ((x - t) / (z - a)));
	else
		tmp = t + ((t - x) / (z / (a - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.1e+142], N[(t + N[(N[(t - x), $MachinePrecision] * N[(N[(a - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.75e+163], N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(t - x), $MachinePrecision] / N[(z / N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.09999999999999993e142

   1. Initial program 25.5%

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

      1. associate-/l* 63.5%

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

   3. Simplified 63.5%

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

      1. clear-num 63.2%

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

      2. un-div-inv 63.3%

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

   6. Applied egg-rr 63.3%

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

   7. Taylor expanded in z around inf 71.3%

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

      1. associate--l+ 71.3%

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

      2. associate-*r/ 71.3%

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

      3. associate-*r/ 71.3%

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

      4. mul-1-neg 71.3%

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

      5. div-sub 71.3%

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

      6. mul-1-neg 71.3%

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

      7. distribute-lft-out-- 71.3%

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

      8. associate-*r/ 71.3%

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

      9. mul-1-neg 71.3%

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

      10. unsub-neg 71.3%

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

      11. distribute-rgt-out-- 74.0%

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

      12. *-lft-identity 74.0%

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

      13. times-frac 92.1%

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

   9. Simplified 92.1%

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

   if -1.09999999999999993e142 < z < 2.75000000000000007e163

   1. Initial program 85.7%

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

      1. associate-/l* 89.8%

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

   3. Simplified 89.8%

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

   if 2.75000000000000007e163 < z

   1. Initial program 17.6%

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

      1. associate-/l* 51.4%

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

   3. Simplified 51.4%

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

      1. clear-num 51.1%

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

      2. un-div-inv 51.5%

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

   6. Applied egg-rr 51.5%

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

   7. Taylor expanded in z around inf 53.9%

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

      1. associate--l+ 53.9%

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

      2. associate-*r/ 53.9%

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

      3. associate-*r/ 53.9%

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

      4. mul-1-neg 53.9%

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

      5. div-sub 53.9%

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

      6. mul-1-neg 53.9%

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

      7. distribute-lft-out-- 53.9%

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

      8. associate-*r/ 53.9%

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

      9. mul-1-neg 53.9%

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

      10. unsub-neg 53.9%

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

      11. distribute-rgt-out-- 53.9%

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

      12. *-lft-identity 53.9%

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

      13. times-frac 92.3%

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

   9. Simplified 92.3%

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

       1. clear-num 92.4%

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

       2. un-div-inv 92.4%

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

   11. Applied egg-rr 92.4%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+142}:\\ \;\;\;\;t + \left(t - x\right) \cdot \frac{a - y}{z}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+163}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{x - t}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{\frac{z}{a - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-199} \lor \neg \left(t \leq 3.5 \cdot 10^{-10}\right):\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.5e-199) (not (<= t 3.5e-10)))
   (* t (/ (- z y) (- z a)))
   (- x (* x (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.5e-199) || !(t <= 3.5e-10)) {
		tmp = t * ((z - y) / (z - a));
	} else {
		tmp = x - (x * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.5d-199)) .or. (.not. (t <= 3.5d-10))) then
        tmp = t * ((z - y) / (z - a))
    else
        tmp = x - (x * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.5e-199) || !(t <= 3.5e-10)) {
		tmp = t * ((z - y) / (z - a));
	} else {
		tmp = x - (x * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.5e-199) or not (t <= 3.5e-10):
		tmp = t * ((z - y) / (z - a))
	else:
		tmp = x - (x * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.5e-199) || !(t <= 3.5e-10))
		tmp = Float64(t * Float64(Float64(z - y) / Float64(z - a)));
	else
		tmp = Float64(x - Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.5e-199) || ~((t <= 3.5e-10)))
		tmp = t * ((z - y) / (z - a));
	else
		tmp = x - (x * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.5e-199], N[Not[LessEqual[t, 3.5e-10]], $MachinePrecision]], N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.49999999999999992e-199 or 3.4999999999999998e-10 < t

   1. Initial program 72.1%

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

      1. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in x around 0 57.6%

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

      1. associate-/l* 74.5%

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

   7. Simplified 74.5%

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

   if -1.49999999999999992e-199 < t < 3.4999999999999998e-10

   1. Initial program 63.1%

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

      1. associate-/l* 74.0%

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

   3. Simplified 74.0%

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

   5. Taylor expanded in z around 0 49.9%

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

      1. associate-/l* 58.1%

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

   7. Simplified 58.1%

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

   8. Taylor expanded in t around 0 46.7%

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

      1. mul-1-neg 46.7%

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

      2. associate-/l* 56.4%

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

      3. distribute-rgt-neg-in 56.4%

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

      4. mul-1-neg 56.4%

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

      5. associate-*r/ 56.4%

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

      6. neg-mul-1 56.4%

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

   10. Simplified 56.4%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-199} \lor \neg \left(t \leq 3.5 \cdot 10^{-10}\right):\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-11} \lor \neg \left(a \leq 1.25 \cdot 10^{-12}\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.8e-11) (not (<= a 1.25e-12)))
   (+ x (* y (/ (- t x) a)))
   (* t (/ (- z y) (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.8e-11) || !(a <= 1.25e-12)) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t * ((z - y) / (z - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-5.8d-11)) .or. (.not. (a <= 1.25d-12))) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t * ((z - y) / (z - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.8e-11) || !(a <= 1.25e-12)) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t * ((z - y) / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.8e-11) or not (a <= 1.25e-12):
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t * ((z - y) / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.8e-11) || !(a <= 1.25e-12))
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = Float64(t * Float64(Float64(z - y) / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.8e-11) || ~((a <= 1.25e-12)))
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t * ((z - y) / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.8e-11], N[Not[LessEqual[a, 1.25e-12]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.8e-11 or 1.24999999999999992e-12 < a

   1. Initial program 71.4%

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

      1. associate-/l* 88.2%

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

   3. Simplified 88.2%

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

   5. Taylor expanded in z around 0 58.5%

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

      1. associate-/l* 67.2%

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

   7. Simplified 67.2%

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

   if -5.8e-11 < a < 1.24999999999999992e-12

   1. Initial program 67.4%

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

      1. associate-/l* 75.8%

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

   3. Simplified 75.8%

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

   5. Taylor expanded in x around 0 60.6%

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

      1. associate-/l* 75.3%

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

   7. Simplified 75.3%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-11} \lor \neg \left(a \leq 1.25 \cdot 10^{-12}\right):\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 55.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -58000000000000 \lor \neg \left(z \leq 6 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{t}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -58000000000000.0) (not (<= z 6e+90)))
   (/ t (- 1.0 (/ a z)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -58000000000000.0) || !(z <= 6e+90)) {
		tmp = t / (1.0 - (a / z));
	} else {
		tmp = x + (t * (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 <= (-58000000000000.0d0)) .or. (.not. (z <= 6d+90))) then
        tmp = t / (1.0d0 - (a / z))
    else
        tmp = x + (t * (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 <= -58000000000000.0) || !(z <= 6e+90)) {
		tmp = t / (1.0 - (a / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -58000000000000.0) or not (z <= 6e+90):
		tmp = t / (1.0 - (a / z))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -58000000000000.0) || !(z <= 6e+90))
		tmp = Float64(t / Float64(1.0 - Float64(a / z)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -58000000000000.0) || ~((z <= 6e+90)))
		tmp = t / (1.0 - (a / z));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -58000000000000.0], N[Not[LessEqual[z, 6e+90]], $MachinePrecision]], N[(t / N[(1.0 - N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8e13 or 5.99999999999999957e90 < z

   1. Initial program 39.0%

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

      1. associate-/l* 68.5%

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

   3. Simplified 68.5%

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

   5. Taylor expanded in x around 0 40.5%

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

      1. associate-/l* 66.0%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in y around 0 34.1%

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

      1. mul-1-neg 34.1%

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

      2. associate-/l* 57.0%

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

      3. distribute-lft-neg-in 57.0%

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

   10. Simplified 57.0%

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

   11. Taylor expanded in t around 0 34.1%

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

       1. mul-1-neg 34.1%

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

       2. *-rgt-identity 34.1%

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

       3. times-frac 48.5%

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

       4. /-rgt-identity 48.5%

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

       5. associate-/r/ 57.0%

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

       6. div-sub 57.0%

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

       7. sub-neg 57.0%

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

       8. *-inverses 57.0%

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

       9. metadata-eval 57.0%

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

   13. Simplified 57.0%

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

   if -5.8e13 < z < 5.99999999999999957e90

   1. Initial program 89.7%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in z around 0 66.8%

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

      1. associate-/l* 69.3%

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

   7. Simplified 69.3%

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

   8. Taylor expanded in t around inf 54.1%

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

      1. associate-/l* 56.1%

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

   10. Simplified 56.1%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -58000000000000 \lor \neg \left(z \leq 6 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{t}{1 - \frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 37.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+71}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+129}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.2e+71) t (if (<= z 2.4e+129) (* t (/ y (- a z))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.2e+71) {
		tmp = t;
	} else if (z <= 2.4e+129) {
		tmp = t * (y / (a - z));
	} 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 <= (-6.2d+71)) then
        tmp = t
    else if (z <= 2.4d+129) then
        tmp = t * (y / (a - z))
    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 <= -6.2e+71) {
		tmp = t;
	} else if (z <= 2.4e+129) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.2e+71:
		tmp = t
	elif z <= 2.4e+129:
		tmp = t * (y / (a - z))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.2e+71)
		tmp = t;
	elseif (z <= 2.4e+129)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.2e+71)
		tmp = t;
	elseif (z <= 2.4e+129)
		tmp = t * (y / (a - z));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.2e+71], t, If[LessEqual[z, 2.4e+129], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -6.20000000000000036e71 or 2.3999999999999999e129 < z

   1. Initial program 31.9%

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

      1. associate-/l* 64.4%

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

   3. Simplified 64.4%

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

   5. Taylor expanded in z around inf 53.2%

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

   if -6.20000000000000036e71 < z < 2.3999999999999999e129

   1. Initial program 89.9%

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

      1. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in x around 0 51.5%

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

      1. associate-/l* 54.3%

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

   7. Simplified 54.3%

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

   8. Taylor expanded in y around inf 37.6%

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

      1. associate-/l* 40.4%

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

   10. Simplified 40.4%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+71}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+129}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 37.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+129}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e+69)
   t
   (if (<= z 2.9e+129) (* t (/ y (- a z))) (+ t (* a (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+69) {
		tmp = t;
	} else if (z <= 2.9e+129) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t + (a * (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.8d+69)) then
        tmp = t
    else if (z <= 2.9d+129) then
        tmp = t * (y / (a - z))
    else
        tmp = t + (a * (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+69) {
		tmp = t;
	} else if (z <= 2.9e+129) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t + (a * (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e+69:
		tmp = t
	elif z <= 2.9e+129:
		tmp = t * (y / (a - z))
	else:
		tmp = t + (a * (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e+69)
		tmp = t;
	elseif (z <= 2.9e+129)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = Float64(t + Float64(a * Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.8e+69)
		tmp = t;
	elseif (z <= 2.9e+129)
		tmp = t * (y / (a - z));
	else
		tmp = t + (a * (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e+69], t, If[LessEqual[z, 2.9e+129], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.79999999999999973e69

   1. Initial program 33.8%

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

      1. associate-/l* 70.7%

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

   3. Simplified 70.7%

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

   5. Taylor expanded in z around inf 53.8%

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

   if -6.79999999999999973e69 < z < 2.90000000000000003e129

   1. Initial program 89.9%

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

      1. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in x around 0 51.5%

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

      1. associate-/l* 54.3%

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

   7. Simplified 54.3%

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

   8. Taylor expanded in y around inf 37.6%

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

      1. associate-/l* 40.4%

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

   10. Simplified 40.4%

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

   if 2.90000000000000003e129 < z

   1. Initial program 29.0%

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

      1. associate-/l* 54.3%

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

   3. Simplified 54.3%

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

   5. Taylor expanded in x around 0 34.1%

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

      1. associate-/l* 60.9%

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

   7. Simplified 60.9%

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

   8. Taylor expanded in y around 0 29.5%

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

      1. mul-1-neg 29.5%

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

      2. associate-/l* 56.3%

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

      3. distribute-lft-neg-in 56.3%

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

   10. Simplified 56.3%

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

   11. Taylor expanded in z around inf 47.3%

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

       1. associate-/l* 52.7%

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

   13. Simplified 52.7%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+69}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+129}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + a \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 54.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e-16)
   (+ x (/ (* t y) a))
   (if (<= a 2.3e+14) (* t (- 1.0 (/ y z))) (+ x (* y (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e-16) {
		tmp = x + ((t * y) / a);
	} else if (a <= 2.3e+14) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.6d-16)) then
        tmp = x + ((t * y) / a)
    else if (a <= 2.3d+14) then
        tmp = t * (1.0d0 - (y / z))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e-16) {
		tmp = x + ((t * y) / a);
	} else if (a <= 2.3e+14) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e-16:
		tmp = x + ((t * y) / a)
	elif a <= 2.3e+14:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e-16)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	elseif (a <= 2.3e+14)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.6e-16)
		tmp = x + ((t * y) / a);
	elseif (a <= 2.3e+14)
		tmp = t * (1.0 - (y / z));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e-16], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+14], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.60000000000000011e-16

   1. Initial program 80.5%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around 0 66.9%

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

      1. associate-/l* 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in t around inf 59.1%

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

   if -1.60000000000000011e-16 < a < 2.3e14

   1. Initial program 66.3%

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

      1. +-commutative 66.3%

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

      2. associate-/l* 74.6%

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

      3. fma-define 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in a around 0 59.3%

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

      1. mul-1-neg 59.3%

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

      2. distribute-neg-frac2 59.3%

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

   7. Simplified 59.3%

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

   8. Taylor expanded in t around inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. associate-/l* 63.7%

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

      3. distribute-lft-neg-in 63.7%

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

      4. div-sub 63.7%

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

      5. sub-neg 63.7%

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

      6. *-inverses 63.7%

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

      7. metadata-eval 63.7%

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

   10. Simplified 63.7%

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

   if 2.3e14 < a

   1. Initial program 63.8%

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

      1. associate-/l* 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in z around 0 51.5%

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

      1. associate-/l* 65.5%

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

   7. Simplified 65.5%

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

   8. Taylor expanded in t around inf 51.9%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+14}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 36.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-44}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-86}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e-44)
   t
   (if (<= z 2.95e-86) (* t (/ y a)) (if (<= z 6e+90) x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e-44) {
		tmp = t;
	} else if (z <= 2.95e-86) {
		tmp = t * (y / a);
	} else if (z <= 6e+90) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.15d-44)) then
        tmp = t
    else if (z <= 2.95d-86) then
        tmp = t * (y / a)
    else if (z <= 6d+90) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e-44) {
		tmp = t;
	} else if (z <= 2.95e-86) {
		tmp = t * (y / a);
	} else if (z <= 6e+90) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e-44:
		tmp = t
	elif z <= 2.95e-86:
		tmp = t * (y / a)
	elif z <= 6e+90:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e-44)
		tmp = t;
	elseif (z <= 2.95e-86)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 6e+90)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.15e-44)
		tmp = t;
	elseif (z <= 2.95e-86)
		tmp = t * (y / a);
	elseif (z <= 6e+90)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e-44], t, If[LessEqual[z, 2.95e-86], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+90], x, t]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.14999999999999999e-44 or 5.99999999999999957e90 < z

   1. Initial program 45.8%

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

      1. associate-/l* 72.4%

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

   3. Simplified 72.4%

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

   5. Taylor expanded in z around inf 45.7%

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

   if -1.14999999999999999e-44 < z < 2.94999999999999999e-86

   1. Initial program 92.9%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in x around 0 52.0%

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

      1. associate-/l* 53.1%

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

   7. Simplified 53.1%

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

   8. Taylor expanded in z around 0 39.3%

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

      1. associate-*r/ 40.4%

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

   10. Simplified 40.4%

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

   if 2.94999999999999999e-86 < z < 5.99999999999999957e90

   1. Initial program 83.1%

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

      1. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in a around inf 35.1%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-44}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-86}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 38.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.8e-12) x (if (<= a 5e+16) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e-12) {
		tmp = x;
	} else if (a <= 5e+16) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.8d-12)) then
        tmp = x
    else if (a <= 5d+16) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8e-12) {
		tmp = x;
	} else if (a <= 5e+16) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.8e-12:
		tmp = x
	elif a <= 5e+16:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.8e-12)
		tmp = x;
	elseif (a <= 5e+16)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.8e-12)
		tmp = x;
	elseif (a <= 5e+16)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.8e-12], x, If[LessEqual[a, 5e+16], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.8000000000000002e-12 or 5e16 < a

   1. Initial program 72.1%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in a around inf 37.7%

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

   if -2.8000000000000002e-12 < a < 5e16

   1. Initial program 67.0%

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

      1. associate-/l* 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in z around inf 39.1%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 24.5% 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 69.3%

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

   1. associate-/l* 81.6%

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

3. Simplified 81.6%

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

5. Taylor expanded in z around inf 26.4%

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

6. Final simplification 26.4%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 83.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((y / z) * (t - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024071 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

  (+ x (/ (* (- y z) (- t x)) (- a z))))