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

Percentage Accurate: 68.8% → 89.0%

Time: 30.5s

Alternatives: 28

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+193} \lor \neg \left(t \leq 4.2 \cdot 10^{+89}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4e+193) (not (<= t 4.2e+89)))
   (+ y (/ (- x y) (/ t (- z a))))
   (fma (- y x) (/ (- z t) (- a t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4e+193) || !(t <= 4.2e+89)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4e+193) || !(t <= 4.2e+89))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = fma(Float64(y - x), Float64(Float64(z - t) / Float64(a - t)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4e+193], N[Not[LessEqual[t, 4.2e+89]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.00000000000000026e193 or 4.19999999999999972e89 < t

   1. Initial program 34.6%

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

      1. associate-*l/ 57.8%

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

   3. Simplified 57.8%

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

      1. +-commutative 57.8%

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

      2. associate-/r/ 64.1%

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

      3. div-inv 64.1%

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

      4. fma-def 64.2%

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

      5. clear-num 64.2%

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

   5. Applied egg-rr 64.2%

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

   6. Taylor expanded in t around -inf 67.8%

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

      1. mul-1-neg 67.8%

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

      2. unsub-neg 67.8%

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

      3. associate-/l* 89.4%

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

   8. Simplified 89.4%

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

   if -4.00000000000000026e193 < t < 4.19999999999999972e89

   1. Initial program 82.9%

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

      1. associate-*l/ 91.5%

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

   3. Simplified 91.5%

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

      1. +-commutative 91.5%

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

      2. associate-/r/ 94.7%

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

      3. div-inv 94.8%

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

      4. fma-def 94.8%

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

      5. clear-num 94.9%

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

   5. Applied egg-rr 94.9%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+193} \lor \neg \left(t \leq 4.2 \cdot 10^{+89}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \]

Alternative 2: 56.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;a \leq -2 \cdot 10^{+214}:\\ \;\;\;\;x \cdot \left(\frac{t}{a - t} + 1\right)\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -22000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-118}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{a - t}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-263}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (* x (- 1.0 (/ z a)))))
   (if (<= a -2e+214)
     (* x (+ (/ t (- a t)) 1.0))
     (if (<= a -5.8e+83)
       t_1
       (if (<= a -22000000000000.0)
         t_2
         (if (<= a -9.2e-107)
           t_1
           (if (<= a -6.6e-118)
             (/ (* x (- z)) (- a t))
             (if (<= a -1.5e-204)
               t_1
               (if (<= a -9e-263)
                 (* (/ z t) (- x y))
                 (if (<= a 9e+122) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -2e+214) {
		tmp = x * ((t / (a - t)) + 1.0);
	} else if (a <= -5.8e+83) {
		tmp = t_1;
	} else if (a <= -22000000000000.0) {
		tmp = t_2;
	} else if (a <= -9.2e-107) {
		tmp = t_1;
	} else if (a <= -6.6e-118) {
		tmp = (x * -z) / (a - t);
	} else if (a <= -1.5e-204) {
		tmp = t_1;
	} else if (a <= -9e-263) {
		tmp = (z / t) * (x - y);
	} else if (a <= 9e+122) {
		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 * ((z - t) / (a - t))
    t_2 = x * (1.0d0 - (z / a))
    if (a <= (-2d+214)) then
        tmp = x * ((t / (a - t)) + 1.0d0)
    else if (a <= (-5.8d+83)) then
        tmp = t_1
    else if (a <= (-22000000000000.0d0)) then
        tmp = t_2
    else if (a <= (-9.2d-107)) then
        tmp = t_1
    else if (a <= (-6.6d-118)) then
        tmp = (x * -z) / (a - t)
    else if (a <= (-1.5d-204)) then
        tmp = t_1
    else if (a <= (-9d-263)) then
        tmp = (z / t) * (x - y)
    else if (a <= 9d+122) 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 * ((z - t) / (a - t));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -2e+214) {
		tmp = x * ((t / (a - t)) + 1.0);
	} else if (a <= -5.8e+83) {
		tmp = t_1;
	} else if (a <= -22000000000000.0) {
		tmp = t_2;
	} else if (a <= -9.2e-107) {
		tmp = t_1;
	} else if (a <= -6.6e-118) {
		tmp = (x * -z) / (a - t);
	} else if (a <= -1.5e-204) {
		tmp = t_1;
	} else if (a <= -9e-263) {
		tmp = (z / t) * (x - y);
	} else if (a <= 9e+122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x * (1.0 - (z / a))
	tmp = 0
	if a <= -2e+214:
		tmp = x * ((t / (a - t)) + 1.0)
	elif a <= -5.8e+83:
		tmp = t_1
	elif a <= -22000000000000.0:
		tmp = t_2
	elif a <= -9.2e-107:
		tmp = t_1
	elif a <= -6.6e-118:
		tmp = (x * -z) / (a - t)
	elif a <= -1.5e-204:
		tmp = t_1
	elif a <= -9e-263:
		tmp = (z / t) * (x - y)
	elif a <= 9e+122:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (a <= -2e+214)
		tmp = Float64(x * Float64(Float64(t / Float64(a - t)) + 1.0));
	elseif (a <= -5.8e+83)
		tmp = t_1;
	elseif (a <= -22000000000000.0)
		tmp = t_2;
	elseif (a <= -9.2e-107)
		tmp = t_1;
	elseif (a <= -6.6e-118)
		tmp = Float64(Float64(x * Float64(-z)) / Float64(a - t));
	elseif (a <= -1.5e-204)
		tmp = t_1;
	elseif (a <= -9e-263)
		tmp = Float64(Float64(z / t) * Float64(x - y));
	elseif (a <= 9e+122)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (a <= -2e+214)
		tmp = x * ((t / (a - t)) + 1.0);
	elseif (a <= -5.8e+83)
		tmp = t_1;
	elseif (a <= -22000000000000.0)
		tmp = t_2;
	elseif (a <= -9.2e-107)
		tmp = t_1;
	elseif (a <= -6.6e-118)
		tmp = (x * -z) / (a - t);
	elseif (a <= -1.5e-204)
		tmp = t_1;
	elseif (a <= -9e-263)
		tmp = (z / t) * (x - y);
	elseif (a <= 9e+122)
		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[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2e+214], N[(x * N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.8e+83], t$95$1, If[LessEqual[a, -22000000000000.0], t$95$2, If[LessEqual[a, -9.2e-107], t$95$1, If[LessEqual[a, -6.6e-118], N[(N[(x * (-z)), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.5e-204], t$95$1, If[LessEqual[a, -9e-263], N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+122], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.9999999999999999e214

   1. Initial program 59.8%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

      1. +-commutative 89.7%

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

      2. associate-/r/ 90.6%

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

      3. div-inv 90.6%

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

      4. fma-def 90.7%

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

      5. clear-num 90.7%

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

   5. Applied egg-rr 90.7%

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

   6. Taylor expanded in x around inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. unsub-neg 66.7%

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

   8. Simplified 66.7%

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

   9. Taylor expanded in z around 0 62.9%

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

   if -1.9999999999999999e214 < a < -5.79999999999999999e83 or -2.2e13 < a < -9.20000000000000014e-107 or -6.5999999999999999e-118 < a < -1.4999999999999999e-204 or -8.9999999999999994e-263 < a < 8.99999999999999995e122

   1. Initial program 67.6%

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

      1. associate-*l/ 82.1%

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

   3. Simplified 82.1%

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

      1. +-commutative 82.1%

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

      2. associate-/r/ 84.8%

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

      3. div-inv 84.8%

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

      4. fma-def 84.8%

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

      5. clear-num 84.9%

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

   5. Applied egg-rr 84.9%

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

   6. Taylor expanded in y around inf 69.3%

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

      1. div-sub 69.3%

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

   8. Simplified 69.3%

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

   if -5.79999999999999999e83 < a < -2.2e13 or 8.99999999999999995e122 < a

   1. Initial program 78.3%

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

      1. associate-*l/ 87.3%

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

   3. Simplified 87.3%

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

      1. +-commutative 87.3%

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

      2. associate-/r/ 94.0%

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

      3. div-inv 94.0%

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

      4. fma-def 94.2%

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

      5. clear-num 94.2%

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

   5. Applied egg-rr 94.2%

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

   6. Taylor expanded in x around inf 77.0%

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

      1. mul-1-neg 77.0%

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

      2. unsub-neg 77.0%

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

   8. Simplified 77.0%

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

   9. Taylor expanded in t around 0 72.7%

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

   if -9.20000000000000014e-107 < a < -6.5999999999999999e-118

   1. Initial program 61.5%

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

      1. associate-*l/ 42.8%

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

   3. Simplified 42.8%

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

   4. Taylor expanded in z around -inf 88.7%

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

   5. Taylor expanded in y around 0 88.7%

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

      1. associate-*r/ 88.7%

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

      2. associate-*r* 88.7%

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

      3. neg-mul-1 88.7%

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

   7. Simplified 88.7%

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

   if -1.4999999999999999e-204 < a < -8.9999999999999994e-263

   1. Initial program 68.4%

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

      1. associate-*l/ 58.3%

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

   3. Simplified 58.3%

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

   4. Taylor expanded in z around -inf 86.1%

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

   5. Taylor expanded in a around 0 79.1%

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

      1. associate-*r/ 79.1%

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

      2. associate-*r* 79.1%

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

      3. mul-1-neg 79.1%

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

   7. Simplified 79.1%

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

   8. Taylor expanded in z around 0 79.1%

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

      1. mul-1-neg 79.1%

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

      2. *-commutative 79.1%

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

      3. associate-*r/ 92.6%

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

      4. distribute-rgt-neg-in 92.6%

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

      5. distribute-neg-frac 92.6%

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

   10. Simplified 92.6%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+214}:\\ \;\;\;\;x \cdot \left(\frac{t}{a - t} + 1\right)\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -22000000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-107}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-118}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{a - t}\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-204}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-263}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 3: 42.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -10000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-144}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-204}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -1.18 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+66}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= a -3.8e+165)
     t_1
     (if (<= a -1.6e+95)
       (* y (/ (- z t) a))
       (if (<= a -10000000000.0)
         t_1
         (if (<= a -3.2e-144)
           (/ (* (- y x) z) a)
           (if (<= a -1.9e-204)
             y
             (if (<= a -1.18e-291)
               (* x (/ (- z) (- a t)))
               (if (<= a 3.6e+66) y t_1)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -3.8e+165) {
		tmp = t_1;
	} else if (a <= -1.6e+95) {
		tmp = y * ((z - t) / a);
	} else if (a <= -10000000000.0) {
		tmp = t_1;
	} else if (a <= -3.2e-144) {
		tmp = ((y - x) * z) / a;
	} else if (a <= -1.9e-204) {
		tmp = y;
	} else if (a <= -1.18e-291) {
		tmp = x * (-z / (a - t));
	} else if (a <= 3.6e+66) {
		tmp = y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (a <= (-3.8d+165)) then
        tmp = t_1
    else if (a <= (-1.6d+95)) then
        tmp = y * ((z - t) / a)
    else if (a <= (-10000000000.0d0)) then
        tmp = t_1
    else if (a <= (-3.2d-144)) then
        tmp = ((y - x) * z) / a
    else if (a <= (-1.9d-204)) then
        tmp = y
    else if (a <= (-1.18d-291)) then
        tmp = x * (-z / (a - t))
    else if (a <= 3.6d+66) then
        tmp = y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -3.8e+165) {
		tmp = t_1;
	} else if (a <= -1.6e+95) {
		tmp = y * ((z - t) / a);
	} else if (a <= -10000000000.0) {
		tmp = t_1;
	} else if (a <= -3.2e-144) {
		tmp = ((y - x) * z) / a;
	} else if (a <= -1.9e-204) {
		tmp = y;
	} else if (a <= -1.18e-291) {
		tmp = x * (-z / (a - t));
	} else if (a <= 3.6e+66) {
		tmp = y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if a <= -3.8e+165:
		tmp = t_1
	elif a <= -1.6e+95:
		tmp = y * ((z - t) / a)
	elif a <= -10000000000.0:
		tmp = t_1
	elif a <= -3.2e-144:
		tmp = ((y - x) * z) / a
	elif a <= -1.9e-204:
		tmp = y
	elif a <= -1.18e-291:
		tmp = x * (-z / (a - t))
	elif a <= 3.6e+66:
		tmp = y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (a <= -3.8e+165)
		tmp = t_1;
	elseif (a <= -1.6e+95)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (a <= -10000000000.0)
		tmp = t_1;
	elseif (a <= -3.2e-144)
		tmp = Float64(Float64(Float64(y - x) * z) / a);
	elseif (a <= -1.9e-204)
		tmp = y;
	elseif (a <= -1.18e-291)
		tmp = Float64(x * Float64(Float64(-z) / Float64(a - t)));
	elseif (a <= 3.6e+66)
		tmp = y;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (a <= -3.8e+165)
		tmp = t_1;
	elseif (a <= -1.6e+95)
		tmp = y * ((z - t) / a);
	elseif (a <= -10000000000.0)
		tmp = t_1;
	elseif (a <= -3.2e-144)
		tmp = ((y - x) * z) / a;
	elseif (a <= -1.9e-204)
		tmp = y;
	elseif (a <= -1.18e-291)
		tmp = x * (-z / (a - t));
	elseif (a <= 3.6e+66)
		tmp = y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.8e+165], t$95$1, If[LessEqual[a, -1.6e+95], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -10000000000.0], t$95$1, If[LessEqual[a, -3.2e-144], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -1.9e-204], y, If[LessEqual[a, -1.18e-291], N[(x * N[((-z) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e+66], y, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.7999999999999999e165 or -1.6e95 < a < -1e10 or 3.6e66 < a

   1. Initial program 70.8%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

      1. +-commutative 89.7%

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

      2. associate-/r/ 94.0%

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

      3. div-inv 94.0%

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

      4. fma-def 94.1%

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

      5. clear-num 94.1%

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

   5. Applied egg-rr 94.1%

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

   6. Taylor expanded in x around inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

   8. Simplified 67.2%

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

   9. Taylor expanded in t around 0 62.1%

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

   if -3.7999999999999999e165 < a < -1.6e95

   1. Initial program 73.0%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/r/ 99.6%

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

      3. div-inv 99.8%

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

      4. fma-def 99.8%

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

      5. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 79.2%

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

      1. div-sub 79.2%

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

   8. Simplified 79.2%

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

   9. Taylor expanded in a around inf 65.0%

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

   if -1e10 < a < -3.19999999999999973e-144

   1. Initial program 74.6%

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

      1. associate-*l/ 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in z around -inf 70.7%

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

   5. Taylor expanded in a around inf 49.0%

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

   if -3.19999999999999973e-144 < a < -1.89999999999999991e-204 or -1.18e-291 < a < 3.6e66

   1. Initial program 64.6%

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

      1. associate-*l/ 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in t around inf 54.1%

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

   if -1.89999999999999991e-204 < a < -1.18e-291

   1. Initial program 67.8%

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

      1. associate-*l/ 64.7%

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

   3. Simplified 64.7%

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

      1. +-commutative 64.7%

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

      2. associate-/r/ 66.9%

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

      3. div-inv 66.9%

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

      4. fma-def 66.8%

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

      5. clear-num 66.8%

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

   5. Applied egg-rr 66.8%

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

   6. Taylor expanded in x around inf 39.5%

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

      1. mul-1-neg 39.5%

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

      2. unsub-neg 39.5%

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

   8. Simplified 39.5%

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

   9. Taylor expanded in z around inf 67.9%

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

       1. associate-*r/ 67.9%

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

       2. neg-mul-1 67.9%

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

   11. Simplified 67.9%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+165}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -10000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-144}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-204}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -1.18 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+66}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 4: 48.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t}\\ t_2 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -20000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-144}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-263}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) t))) (t_2 (* x (- 1.0 (/ z a)))))
   (if (<= a -3.5e+165)
     t_2
     (if (<= a -1.8e+95)
       (* y (/ (- z t) a))
       (if (<= a -20000000000000.0)
         t_2
         (if (<= a -3.2e-144)
           (/ (* (- y x) z) a)
           (if (<= a -6e-205)
             t_1
             (if (<= a -1.8e-263)
               (* x (/ (- z) (- a t)))
               (if (<= a 5.6e+122) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -3.5e+165) {
		tmp = t_2;
	} else if (a <= -1.8e+95) {
		tmp = y * ((z - t) / a);
	} else if (a <= -20000000000000.0) {
		tmp = t_2;
	} else if (a <= -3.2e-144) {
		tmp = ((y - x) * z) / a;
	} else if (a <= -6e-205) {
		tmp = t_1;
	} else if (a <= -1.8e-263) {
		tmp = x * (-z / (a - t));
	} else if (a <= 5.6e+122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - z) / t)
    t_2 = x * (1.0d0 - (z / a))
    if (a <= (-3.5d+165)) then
        tmp = t_2
    else if (a <= (-1.8d+95)) then
        tmp = y * ((z - t) / a)
    else if (a <= (-20000000000000.0d0)) then
        tmp = t_2
    else if (a <= (-3.2d-144)) then
        tmp = ((y - x) * z) / a
    else if (a <= (-6d-205)) then
        tmp = t_1
    else if (a <= (-1.8d-263)) then
        tmp = x * (-z / (a - t))
    else if (a <= 5.6d+122) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -3.5e+165) {
		tmp = t_2;
	} else if (a <= -1.8e+95) {
		tmp = y * ((z - t) / a);
	} else if (a <= -20000000000000.0) {
		tmp = t_2;
	} else if (a <= -3.2e-144) {
		tmp = ((y - x) * z) / a;
	} else if (a <= -6e-205) {
		tmp = t_1;
	} else if (a <= -1.8e-263) {
		tmp = x * (-z / (a - t));
	} else if (a <= 5.6e+122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / t)
	t_2 = x * (1.0 - (z / a))
	tmp = 0
	if a <= -3.5e+165:
		tmp = t_2
	elif a <= -1.8e+95:
		tmp = y * ((z - t) / a)
	elif a <= -20000000000000.0:
		tmp = t_2
	elif a <= -3.2e-144:
		tmp = ((y - x) * z) / a
	elif a <= -6e-205:
		tmp = t_1
	elif a <= -1.8e-263:
		tmp = x * (-z / (a - t))
	elif a <= 5.6e+122:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / t))
	t_2 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (a <= -3.5e+165)
		tmp = t_2;
	elseif (a <= -1.8e+95)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (a <= -20000000000000.0)
		tmp = t_2;
	elseif (a <= -3.2e-144)
		tmp = Float64(Float64(Float64(y - x) * z) / a);
	elseif (a <= -6e-205)
		tmp = t_1;
	elseif (a <= -1.8e-263)
		tmp = Float64(x * Float64(Float64(-z) / Float64(a - t)));
	elseif (a <= 5.6e+122)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / t);
	t_2 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (a <= -3.5e+165)
		tmp = t_2;
	elseif (a <= -1.8e+95)
		tmp = y * ((z - t) / a);
	elseif (a <= -20000000000000.0)
		tmp = t_2;
	elseif (a <= -3.2e-144)
		tmp = ((y - x) * z) / a;
	elseif (a <= -6e-205)
		tmp = t_1;
	elseif (a <= -1.8e-263)
		tmp = x * (-z / (a - t));
	elseif (a <= 5.6e+122)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e+165], t$95$2, If[LessEqual[a, -1.8e+95], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -20000000000000.0], t$95$2, If[LessEqual[a, -3.2e-144], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -6e-205], t$95$1, If[LessEqual[a, -1.8e-263], N[(x * N[((-z) / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.6e+122], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.49999999999999996e165 or -1.79999999999999989e95 < a < -2e13 or 5.5999999999999999e122 < a

   1. Initial program 70.7%

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

      1. associate-*l/ 88.2%

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

   3. Simplified 88.2%

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

      1. +-commutative 88.2%

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

      2. associate-/r/ 93.1%

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

      3. div-inv 93.1%

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

      4. fma-def 93.2%

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

      5. clear-num 93.3%

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

   5. Applied egg-rr 93.3%

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

   6. Taylor expanded in x around inf 70.0%

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

      1. mul-1-neg 70.0%

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

      2. unsub-neg 70.0%

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

   8. Simplified 70.0%

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

   9. Taylor expanded in t around 0 65.3%

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

   if -3.49999999999999996e165 < a < -1.79999999999999989e95

   1. Initial program 73.0%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/r/ 99.6%

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

      3. div-inv 99.8%

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

      4. fma-def 99.8%

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

      5. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 79.2%

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

      1. div-sub 79.2%

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

   8. Simplified 79.2%

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

   9. Taylor expanded in a around inf 65.0%

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

   if -2e13 < a < -3.19999999999999973e-144

   1. Initial program 74.6%

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

      1. associate-*l/ 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in z around -inf 70.7%

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

   5. Taylor expanded in a around inf 49.0%

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

   if -3.19999999999999973e-144 < a < -6e-205 or -1.8e-263 < a < 5.5999999999999999e122

   1. Initial program 65.3%

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

      1. associate-*l/ 78.5%

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

   3. Simplified 78.5%

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

      1. +-commutative 78.5%

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

      2. associate-/r/ 81.4%

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

      3. div-inv 81.4%

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

      4. fma-def 81.4%

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

      5. clear-num 81.4%

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

   5. Applied egg-rr 81.4%

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

   6. Taylor expanded in y around inf 67.9%

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

      1. div-sub 67.9%

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

   8. Simplified 67.9%

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

   9. Taylor expanded in a around 0 60.5%

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

       1. associate-*r/ 60.5%

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

       2. neg-mul-1 60.5%

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

   11. Simplified 60.5%

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

   if -6e-205 < a < -1.8e-263

   1. Initial program 70.4%

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

      1. associate-*l/ 61.0%

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

   3. Simplified 61.0%

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

      1. +-commutative 61.0%

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

      2. associate-/r/ 70.1%

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

      3. div-inv 70.1%

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

      4. fma-def 70.2%

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

      5. clear-num 70.2%

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

   5. Applied egg-rr 70.2%

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

   6. Taylor expanded in x around inf 44.6%

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

      1. mul-1-neg 44.6%

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

      2. unsub-neg 44.6%

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

   8. Simplified 44.6%

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

   9. Taylor expanded in z around inf 73.9%

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

       1. associate-*r/ 73.9%

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

       2. neg-mul-1 73.9%

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

   11. Simplified 73.9%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+165}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -20000000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-144}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-205}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-263}:\\ \;\;\;\;x \cdot \frac{-z}{a - t}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 5: 48.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t - z}{t}\\ t_2 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -75000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-144}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-292}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t z) t))) (t_2 (* x (- 1.0 (/ z a)))))
   (if (<= a -3.5e+165)
     t_2
     (if (<= a -9.5e+94)
       (* y (/ (- z t) a))
       (if (<= a -75000000000.0)
         t_2
         (if (<= a -6.2e-144)
           (/ (* (- y x) z) a)
           (if (<= a -1e-204)
             t_1
             (if (<= a -6.8e-292)
               (* (/ z t) (- x y))
               (if (<= a 9e+122) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -3.5e+165) {
		tmp = t_2;
	} else if (a <= -9.5e+94) {
		tmp = y * ((z - t) / a);
	} else if (a <= -75000000000.0) {
		tmp = t_2;
	} else if (a <= -6.2e-144) {
		tmp = ((y - x) * z) / a;
	} else if (a <= -1e-204) {
		tmp = t_1;
	} else if (a <= -6.8e-292) {
		tmp = (z / t) * (x - y);
	} else if (a <= 9e+122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((t - z) / t)
    t_2 = x * (1.0d0 - (z / a))
    if (a <= (-3.5d+165)) then
        tmp = t_2
    else if (a <= (-9.5d+94)) then
        tmp = y * ((z - t) / a)
    else if (a <= (-75000000000.0d0)) then
        tmp = t_2
    else if (a <= (-6.2d-144)) then
        tmp = ((y - x) * z) / a
    else if (a <= (-1d-204)) then
        tmp = t_1
    else if (a <= (-6.8d-292)) then
        tmp = (z / t) * (x - y)
    else if (a <= 9d+122) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - z) / t);
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -3.5e+165) {
		tmp = t_2;
	} else if (a <= -9.5e+94) {
		tmp = y * ((z - t) / a);
	} else if (a <= -75000000000.0) {
		tmp = t_2;
	} else if (a <= -6.2e-144) {
		tmp = ((y - x) * z) / a;
	} else if (a <= -1e-204) {
		tmp = t_1;
	} else if (a <= -6.8e-292) {
		tmp = (z / t) * (x - y);
	} else if (a <= 9e+122) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - z) / t)
	t_2 = x * (1.0 - (z / a))
	tmp = 0
	if a <= -3.5e+165:
		tmp = t_2
	elif a <= -9.5e+94:
		tmp = y * ((z - t) / a)
	elif a <= -75000000000.0:
		tmp = t_2
	elif a <= -6.2e-144:
		tmp = ((y - x) * z) / a
	elif a <= -1e-204:
		tmp = t_1
	elif a <= -6.8e-292:
		tmp = (z / t) * (x - y)
	elif a <= 9e+122:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - z) / t))
	t_2 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (a <= -3.5e+165)
		tmp = t_2;
	elseif (a <= -9.5e+94)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (a <= -75000000000.0)
		tmp = t_2;
	elseif (a <= -6.2e-144)
		tmp = Float64(Float64(Float64(y - x) * z) / a);
	elseif (a <= -1e-204)
		tmp = t_1;
	elseif (a <= -6.8e-292)
		tmp = Float64(Float64(z / t) * Float64(x - y));
	elseif (a <= 9e+122)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - z) / t);
	t_2 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (a <= -3.5e+165)
		tmp = t_2;
	elseif (a <= -9.5e+94)
		tmp = y * ((z - t) / a);
	elseif (a <= -75000000000.0)
		tmp = t_2;
	elseif (a <= -6.2e-144)
		tmp = ((y - x) * z) / a;
	elseif (a <= -1e-204)
		tmp = t_1;
	elseif (a <= -6.8e-292)
		tmp = (z / t) * (x - y);
	elseif (a <= 9e+122)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e+165], t$95$2, If[LessEqual[a, -9.5e+94], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -75000000000.0], t$95$2, If[LessEqual[a, -6.2e-144], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -1e-204], t$95$1, If[LessEqual[a, -6.8e-292], N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+122], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.49999999999999996e165 or -9.4999999999999998e94 < a < -7.5e10 or 8.99999999999999995e122 < a

   1. Initial program 70.7%

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

      1. associate-*l/ 88.2%

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

   3. Simplified 88.2%

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

      1. +-commutative 88.2%

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

      2. associate-/r/ 93.1%

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

      3. div-inv 93.1%

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

      4. fma-def 93.2%

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

      5. clear-num 93.3%

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

   5. Applied egg-rr 93.3%

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

   6. Taylor expanded in x around inf 70.0%

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

      1. mul-1-neg 70.0%

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

      2. unsub-neg 70.0%

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

   8. Simplified 70.0%

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

   9. Taylor expanded in t around 0 65.3%

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

   if -3.49999999999999996e165 < a < -9.4999999999999998e94

   1. Initial program 73.0%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/r/ 99.6%

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

      3. div-inv 99.8%

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

      4. fma-def 99.8%

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

      5. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 79.2%

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

      1. div-sub 79.2%

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

   8. Simplified 79.2%

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

   9. Taylor expanded in a around inf 65.0%

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

   if -7.5e10 < a < -6.2000000000000001e-144

   1. Initial program 74.6%

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

      1. associate-*l/ 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in z around -inf 70.7%

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

   5. Taylor expanded in a around inf 49.0%

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

   if -6.2000000000000001e-144 < a < -1e-204 or -6.80000000000000035e-292 < a < 8.99999999999999995e122

   1. Initial program 65.5%

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

      1. associate-*l/ 78.7%

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

   3. Simplified 78.7%

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

      1. +-commutative 78.7%

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

      2. associate-/r/ 82.8%

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

      3. div-inv 82.8%

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

      4. fma-def 82.8%

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

      5. clear-num 82.8%

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

   5. Applied egg-rr 82.8%

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

   6. Taylor expanded in y around inf 68.8%

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

      1. div-sub 68.8%

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

   8. Simplified 68.8%

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

   9. Taylor expanded in a around 0 60.9%

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

       1. associate-*r/ 60.9%

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

       2. neg-mul-1 60.9%

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

   11. Simplified 60.9%

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

   if -1e-204 < a < -6.80000000000000035e-292

   1. Initial program 67.8%

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

      1. associate-*l/ 64.7%

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

   3. Simplified 64.7%

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

   4. Taylor expanded in z around -inf 86.0%

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

   5. Taylor expanded in a around 0 76.7%

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

      1. associate-*r/ 76.7%

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

      2. associate-*r* 76.7%

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

      3. mul-1-neg 76.7%

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

   7. Simplified 76.7%

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

   8. Taylor expanded in z around 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. *-commutative 76.7%

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

      3. associate-*r/ 81.5%

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

      4. distribute-rgt-neg-in 81.5%

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

      5. distribute-neg-frac 81.5%

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

   10. Simplified 81.5%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+165}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -75000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-144}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-204}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-292}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 6: 47.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -16500000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-146}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-204}:\\ \;\;\;\;\frac{-t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-291}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= a -4.5e+165)
     t_1
     (if (<= a -1.8e+95)
       (* y (/ (- z t) a))
       (if (<= a -16500000000000.0)
         t_1
         (if (<= a -3.9e-146)
           (/ (* (- y x) z) a)
           (if (<= a -2.3e-204)
             (/ (- t) (/ (- a t) y))
             (if (<= a -1.55e-291)
               (* (/ z t) (- x y))
               (if (<= a 5.6e+122) (* y (/ (- t z) t)) t_1)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -4.5e+165) {
		tmp = t_1;
	} else if (a <= -1.8e+95) {
		tmp = y * ((z - t) / a);
	} else if (a <= -16500000000000.0) {
		tmp = t_1;
	} else if (a <= -3.9e-146) {
		tmp = ((y - x) * z) / a;
	} else if (a <= -2.3e-204) {
		tmp = -t / ((a - t) / y);
	} else if (a <= -1.55e-291) {
		tmp = (z / t) * (x - y);
	} else if (a <= 5.6e+122) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (a <= (-4.5d+165)) then
        tmp = t_1
    else if (a <= (-1.8d+95)) then
        tmp = y * ((z - t) / a)
    else if (a <= (-16500000000000.0d0)) then
        tmp = t_1
    else if (a <= (-3.9d-146)) then
        tmp = ((y - x) * z) / a
    else if (a <= (-2.3d-204)) then
        tmp = -t / ((a - t) / y)
    else if (a <= (-1.55d-291)) then
        tmp = (z / t) * (x - y)
    else if (a <= 5.6d+122) then
        tmp = y * ((t - z) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -4.5e+165) {
		tmp = t_1;
	} else if (a <= -1.8e+95) {
		tmp = y * ((z - t) / a);
	} else if (a <= -16500000000000.0) {
		tmp = t_1;
	} else if (a <= -3.9e-146) {
		tmp = ((y - x) * z) / a;
	} else if (a <= -2.3e-204) {
		tmp = -t / ((a - t) / y);
	} else if (a <= -1.55e-291) {
		tmp = (z / t) * (x - y);
	} else if (a <= 5.6e+122) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if a <= -4.5e+165:
		tmp = t_1
	elif a <= -1.8e+95:
		tmp = y * ((z - t) / a)
	elif a <= -16500000000000.0:
		tmp = t_1
	elif a <= -3.9e-146:
		tmp = ((y - x) * z) / a
	elif a <= -2.3e-204:
		tmp = -t / ((a - t) / y)
	elif a <= -1.55e-291:
		tmp = (z / t) * (x - y)
	elif a <= 5.6e+122:
		tmp = y * ((t - z) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (a <= -4.5e+165)
		tmp = t_1;
	elseif (a <= -1.8e+95)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (a <= -16500000000000.0)
		tmp = t_1;
	elseif (a <= -3.9e-146)
		tmp = Float64(Float64(Float64(y - x) * z) / a);
	elseif (a <= -2.3e-204)
		tmp = Float64(Float64(-t) / Float64(Float64(a - t) / y));
	elseif (a <= -1.55e-291)
		tmp = Float64(Float64(z / t) * Float64(x - y));
	elseif (a <= 5.6e+122)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (a <= -4.5e+165)
		tmp = t_1;
	elseif (a <= -1.8e+95)
		tmp = y * ((z - t) / a);
	elseif (a <= -16500000000000.0)
		tmp = t_1;
	elseif (a <= -3.9e-146)
		tmp = ((y - x) * z) / a;
	elseif (a <= -2.3e-204)
		tmp = -t / ((a - t) / y);
	elseif (a <= -1.55e-291)
		tmp = (z / t) * (x - y);
	elseif (a <= 5.6e+122)
		tmp = y * ((t - z) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e+165], t$95$1, If[LessEqual[a, -1.8e+95], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -16500000000000.0], t$95$1, If[LessEqual[a, -3.9e-146], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -2.3e-204], N[((-t) / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.55e-291], N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.6e+122], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -4.4999999999999996e165 or -1.79999999999999989e95 < a < -1.65e13 or 5.5999999999999999e122 < a

   1. Initial program 70.7%

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

      1. associate-*l/ 88.2%

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

   3. Simplified 88.2%

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

      1. +-commutative 88.2%

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

      2. associate-/r/ 93.1%

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

      3. div-inv 93.1%

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

      4. fma-def 93.2%

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

      5. clear-num 93.3%

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

   5. Applied egg-rr 93.3%

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

   6. Taylor expanded in x around inf 70.0%

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

      1. mul-1-neg 70.0%

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

      2. unsub-neg 70.0%

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

   8. Simplified 70.0%

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

   9. Taylor expanded in t around 0 65.3%

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

   if -4.4999999999999996e165 < a < -1.79999999999999989e95

   1. Initial program 73.0%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/r/ 99.6%

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

      3. div-inv 99.8%

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

      4. fma-def 99.8%

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

      5. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 79.2%

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

      1. div-sub 79.2%

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

   8. Simplified 79.2%

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

   9. Taylor expanded in a around inf 65.0%

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

   if -1.65e13 < a < -3.90000000000000002e-146

   1. Initial program 74.6%

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

      1. associate-*l/ 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in z around -inf 70.7%

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

   5. Taylor expanded in a around inf 49.0%

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

   if -3.90000000000000002e-146 < a < -2.2999999999999999e-204

   1. Initial program 65.6%

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

      1. associate-*l/ 78.8%

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

   3. Simplified 78.8%

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

   4. Taylor expanded in x around 0 58.7%

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

   5. Taylor expanded in z around 0 45.1%

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

      1. mul-1-neg 45.1%

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

      2. associate-/l* 65.3%

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

      3. distribute-neg-frac 65.3%

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

   7. Simplified 65.3%

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

   if -2.2999999999999999e-204 < a < -1.55000000000000006e-291

   1. Initial program 67.8%

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

      1. associate-*l/ 64.7%

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

   3. Simplified 64.7%

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

   4. Taylor expanded in z around -inf 86.0%

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

   5. Taylor expanded in a around 0 76.7%

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

      1. associate-*r/ 76.7%

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

      2. associate-*r* 76.7%

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

      3. mul-1-neg 76.7%

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

   7. Simplified 76.7%

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

   8. Taylor expanded in z around 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. *-commutative 76.7%

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

      3. associate-*r/ 81.5%

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

      4. distribute-rgt-neg-in 81.5%

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

      5. distribute-neg-frac 81.5%

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

   10. Simplified 81.5%

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

   if -1.55000000000000006e-291 < a < 5.5999999999999999e122

   1. Initial program 65.5%

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

      1. associate-*l/ 78.7%

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

   3. Simplified 78.7%

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

      1. +-commutative 78.7%

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

      2. associate-/r/ 83.4%

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

      3. div-inv 83.4%

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

      4. fma-def 83.4%

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

      5. clear-num 83.4%

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

   5. Applied egg-rr 83.4%

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

   6. Taylor expanded in y around inf 68.2%

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

      1. div-sub 68.2%

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

   8. Simplified 68.2%

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

   9. Taylor expanded in a around 0 60.2%

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

       1. associate-*r/ 60.2%

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

       2. neg-mul-1 60.2%

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

   11. Simplified 60.2%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+165}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -16500000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -3.9 \cdot 10^{-146}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-204}:\\ \;\;\;\;\frac{-t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-291}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 7: 46.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;a \leq -4.25 \cdot 10^{+167}:\\ \;\;\;\;x \cdot \left(\frac{t}{a - t} + 1\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -4200000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-145}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-204}:\\ \;\;\;\;\frac{-t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-292}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= a -4.25e+167)
     (* x (+ (/ t (- a t)) 1.0))
     (if (<= a -5e+94)
       (* y (/ (- z t) a))
       (if (<= a -4200000000000.0)
         t_1
         (if (<= a -8.2e-145)
           (/ (* (- y x) z) a)
           (if (<= a -5.1e-204)
             (/ (- t) (/ (- a t) y))
             (if (<= a -7.2e-292)
               (* (/ z t) (- x y))
               (if (<= a 5.6e+122) (* y (/ (- t z) t)) t_1)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -4.25e+167) {
		tmp = x * ((t / (a - t)) + 1.0);
	} else if (a <= -5e+94) {
		tmp = y * ((z - t) / a);
	} else if (a <= -4200000000000.0) {
		tmp = t_1;
	} else if (a <= -8.2e-145) {
		tmp = ((y - x) * z) / a;
	} else if (a <= -5.1e-204) {
		tmp = -t / ((a - t) / y);
	} else if (a <= -7.2e-292) {
		tmp = (z / t) * (x - y);
	} else if (a <= 5.6e+122) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (a <= (-4.25d+167)) then
        tmp = x * ((t / (a - t)) + 1.0d0)
    else if (a <= (-5d+94)) then
        tmp = y * ((z - t) / a)
    else if (a <= (-4200000000000.0d0)) then
        tmp = t_1
    else if (a <= (-8.2d-145)) then
        tmp = ((y - x) * z) / a
    else if (a <= (-5.1d-204)) then
        tmp = -t / ((a - t) / y)
    else if (a <= (-7.2d-292)) then
        tmp = (z / t) * (x - y)
    else if (a <= 5.6d+122) then
        tmp = y * ((t - z) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -4.25e+167) {
		tmp = x * ((t / (a - t)) + 1.0);
	} else if (a <= -5e+94) {
		tmp = y * ((z - t) / a);
	} else if (a <= -4200000000000.0) {
		tmp = t_1;
	} else if (a <= -8.2e-145) {
		tmp = ((y - x) * z) / a;
	} else if (a <= -5.1e-204) {
		tmp = -t / ((a - t) / y);
	} else if (a <= -7.2e-292) {
		tmp = (z / t) * (x - y);
	} else if (a <= 5.6e+122) {
		tmp = y * ((t - z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if a <= -4.25e+167:
		tmp = x * ((t / (a - t)) + 1.0)
	elif a <= -5e+94:
		tmp = y * ((z - t) / a)
	elif a <= -4200000000000.0:
		tmp = t_1
	elif a <= -8.2e-145:
		tmp = ((y - x) * z) / a
	elif a <= -5.1e-204:
		tmp = -t / ((a - t) / y)
	elif a <= -7.2e-292:
		tmp = (z / t) * (x - y)
	elif a <= 5.6e+122:
		tmp = y * ((t - z) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (a <= -4.25e+167)
		tmp = Float64(x * Float64(Float64(t / Float64(a - t)) + 1.0));
	elseif (a <= -5e+94)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (a <= -4200000000000.0)
		tmp = t_1;
	elseif (a <= -8.2e-145)
		tmp = Float64(Float64(Float64(y - x) * z) / a);
	elseif (a <= -5.1e-204)
		tmp = Float64(Float64(-t) / Float64(Float64(a - t) / y));
	elseif (a <= -7.2e-292)
		tmp = Float64(Float64(z / t) * Float64(x - y));
	elseif (a <= 5.6e+122)
		tmp = Float64(y * Float64(Float64(t - z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (a <= -4.25e+167)
		tmp = x * ((t / (a - t)) + 1.0);
	elseif (a <= -5e+94)
		tmp = y * ((z - t) / a);
	elseif (a <= -4200000000000.0)
		tmp = t_1;
	elseif (a <= -8.2e-145)
		tmp = ((y - x) * z) / a;
	elseif (a <= -5.1e-204)
		tmp = -t / ((a - t) / y);
	elseif (a <= -7.2e-292)
		tmp = (z / t) * (x - y);
	elseif (a <= 5.6e+122)
		tmp = y * ((t - z) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.25e+167], N[(x * N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5e+94], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4200000000000.0], t$95$1, If[LessEqual[a, -8.2e-145], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -5.1e-204], N[((-t) / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.2e-292], N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.6e+122], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -4.25000000000000003e167

   1. Initial program 59.5%

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

      1. associate-*l/ 89.5%

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

   3. Simplified 89.5%

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

      1. +-commutative 89.5%

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

      2. associate-/r/ 91.4%

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

      3. div-inv 91.4%

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

      4. fma-def 91.4%

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

      5. clear-num 91.5%

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

   5. Applied egg-rr 91.5%

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

   6. Taylor expanded in x around inf 59.7%

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

      1. mul-1-neg 59.7%

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

      2. unsub-neg 59.7%

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

   8. Simplified 59.7%

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

   9. Taylor expanded in z around 0 56.9%

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

   if -4.25000000000000003e167 < a < -5.0000000000000001e94

   1. Initial program 73.0%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/r/ 99.6%

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

      3. div-inv 99.8%

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

      4. fma-def 99.8%

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

      5. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 79.2%

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

      1. div-sub 79.2%

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

   8. Simplified 79.2%

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

   9. Taylor expanded in a around inf 65.0%

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

   if -5.0000000000000001e94 < a < -4.2e12 or 5.5999999999999999e122 < a

   1. Initial program 77.0%

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

      1. associate-*l/ 87.5%

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

   3. Simplified 87.5%

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

      1. +-commutative 87.5%

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

      2. associate-/r/ 94.1%

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

      3. div-inv 94.1%

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

      4. fma-def 94.3%

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

      5. clear-num 94.3%

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

   5. Applied egg-rr 94.3%

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

   6. Taylor expanded in x around inf 75.7%

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

      1. mul-1-neg 75.7%

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

      2. unsub-neg 75.7%

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

   8. Simplified 75.7%

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

   9. Taylor expanded in t around 0 71.4%

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

   if -4.2e12 < a < -8.1999999999999995e-145

   1. Initial program 74.6%

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

      1. associate-*l/ 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in z around -inf 70.7%

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

   5. Taylor expanded in a around inf 49.0%

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

   if -8.1999999999999995e-145 < a < -5.10000000000000027e-204

   1. Initial program 65.6%

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

      1. associate-*l/ 78.8%

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

   3. Simplified 78.8%

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

   4. Taylor expanded in x around 0 58.7%

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

   5. Taylor expanded in z around 0 45.1%

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

      1. mul-1-neg 45.1%

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

      2. associate-/l* 65.3%

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

      3. distribute-neg-frac 65.3%

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

   7. Simplified 65.3%

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

   if -5.10000000000000027e-204 < a < -7.2000000000000004e-292

   1. Initial program 67.8%

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

      1. associate-*l/ 64.7%

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

   3. Simplified 64.7%

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

   4. Taylor expanded in z around -inf 86.0%

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

   5. Taylor expanded in a around 0 76.7%

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

      1. associate-*r/ 76.7%

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

      2. associate-*r* 76.7%

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

      3. mul-1-neg 76.7%

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

   7. Simplified 76.7%

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

   8. Taylor expanded in z around 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. *-commutative 76.7%

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

      3. associate-*r/ 81.5%

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

      4. distribute-rgt-neg-in 81.5%

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

      5. distribute-neg-frac 81.5%

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

   10. Simplified 81.5%

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

   if -7.2000000000000004e-292 < a < 5.5999999999999999e122

   1. Initial program 65.5%

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

      1. associate-*l/ 78.7%

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

   3. Simplified 78.7%

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

      1. +-commutative 78.7%

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

      2. associate-/r/ 83.4%

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

      3. div-inv 83.4%

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

      4. fma-def 83.4%

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

      5. clear-num 83.4%

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

   5. Applied egg-rr 83.4%

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

   6. Taylor expanded in y around inf 68.2%

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

      1. div-sub 68.2%

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

   8. Simplified 68.2%

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

   9. Taylor expanded in a around 0 60.2%

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

       1. associate-*r/ 60.2%

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

       2. neg-mul-1 60.2%

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

   11. Simplified 60.2%

       \[\leadsto y \cdot \color{blue}{\frac{-\left(z - t\right)}{t}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.25 \cdot 10^{+167}:\\ \;\;\;\;x \cdot \left(\frac{t}{a - t} + 1\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -4200000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-145}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-204}:\\ \;\;\;\;\frac{-t}{\frac{a - t}{y}}\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-292}:\\ \;\;\;\;\frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+122}:\\ \;\;\;\;y \cdot \frac{t - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 8: 36.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{t}{z}}\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{+116}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -750000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-55}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-141}:\\ \;\;\;\;\frac{-x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-291}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ t z))))
   (if (<= a -3.6e+165)
     x
     (if (<= a -1.25e+116)
       (/ z (/ a y))
       (if (<= a -750000000000.0)
         x
         (if (<= a -4.2e-55)
           (/ y (/ a z))
           (if (<= a -6.6e-60)
             t_1
             (if (<= a -1.2e-141)
               (/ (- x) (/ a z))
               (if (<= a -1.95e-291) t_1 (if (<= a 5.4e+75) y x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t / z);
	double tmp;
	if (a <= -3.6e+165) {
		tmp = x;
	} else if (a <= -1.25e+116) {
		tmp = z / (a / y);
	} else if (a <= -750000000000.0) {
		tmp = x;
	} else if (a <= -4.2e-55) {
		tmp = y / (a / z);
	} else if (a <= -6.6e-60) {
		tmp = t_1;
	} else if (a <= -1.2e-141) {
		tmp = -x / (a / z);
	} else if (a <= -1.95e-291) {
		tmp = t_1;
	} else if (a <= 5.4e+75) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (t / z)
    if (a <= (-3.6d+165)) then
        tmp = x
    else if (a <= (-1.25d+116)) then
        tmp = z / (a / y)
    else if (a <= (-750000000000.0d0)) then
        tmp = x
    else if (a <= (-4.2d-55)) then
        tmp = y / (a / z)
    else if (a <= (-6.6d-60)) then
        tmp = t_1
    else if (a <= (-1.2d-141)) then
        tmp = -x / (a / z)
    else if (a <= (-1.95d-291)) then
        tmp = t_1
    else if (a <= 5.4d+75) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t / z);
	double tmp;
	if (a <= -3.6e+165) {
		tmp = x;
	} else if (a <= -1.25e+116) {
		tmp = z / (a / y);
	} else if (a <= -750000000000.0) {
		tmp = x;
	} else if (a <= -4.2e-55) {
		tmp = y / (a / z);
	} else if (a <= -6.6e-60) {
		tmp = t_1;
	} else if (a <= -1.2e-141) {
		tmp = -x / (a / z);
	} else if (a <= -1.95e-291) {
		tmp = t_1;
	} else if (a <= 5.4e+75) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t / z)
	tmp = 0
	if a <= -3.6e+165:
		tmp = x
	elif a <= -1.25e+116:
		tmp = z / (a / y)
	elif a <= -750000000000.0:
		tmp = x
	elif a <= -4.2e-55:
		tmp = y / (a / z)
	elif a <= -6.6e-60:
		tmp = t_1
	elif a <= -1.2e-141:
		tmp = -x / (a / z)
	elif a <= -1.95e-291:
		tmp = t_1
	elif a <= 5.4e+75:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t / z))
	tmp = 0.0
	if (a <= -3.6e+165)
		tmp = x;
	elseif (a <= -1.25e+116)
		tmp = Float64(z / Float64(a / y));
	elseif (a <= -750000000000.0)
		tmp = x;
	elseif (a <= -4.2e-55)
		tmp = Float64(y / Float64(a / z));
	elseif (a <= -6.6e-60)
		tmp = t_1;
	elseif (a <= -1.2e-141)
		tmp = Float64(Float64(-x) / Float64(a / z));
	elseif (a <= -1.95e-291)
		tmp = t_1;
	elseif (a <= 5.4e+75)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t / z);
	tmp = 0.0;
	if (a <= -3.6e+165)
		tmp = x;
	elseif (a <= -1.25e+116)
		tmp = z / (a / y);
	elseif (a <= -750000000000.0)
		tmp = x;
	elseif (a <= -4.2e-55)
		tmp = y / (a / z);
	elseif (a <= -6.6e-60)
		tmp = t_1;
	elseif (a <= -1.2e-141)
		tmp = -x / (a / z);
	elseif (a <= -1.95e-291)
		tmp = t_1;
	elseif (a <= 5.4e+75)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.6e+165], x, If[LessEqual[a, -1.25e+116], N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -750000000000.0], x, If[LessEqual[a, -4.2e-55], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.6e-60], t$95$1, If[LessEqual[a, -1.2e-141], N[((-x) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.95e-291], t$95$1, If[LessEqual[a, 5.4e+75], y, x]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -3.5999999999999998e165 or -1.25000000000000006e116 < a < -7.5e11 or 5.39999999999999996e75 < a

   1. Initial program 70.5%

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

      1. associate-*l/ 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in a around inf 54.0%

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

   if -3.5999999999999998e165 < a < -1.25000000000000006e116

   1. Initial program 76.3%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around -inf 43.7%

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

   5. Taylor expanded in a around inf 43.5%

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

      1. associate-/l* 59.1%

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

   7. Simplified 59.1%

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

   8. Taylor expanded in y around inf 51.1%

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

   if -7.5e11 < a < -4.2000000000000003e-55

   1. Initial program 71.0%

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

      1. associate-*l/ 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in z around -inf 64.9%

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

   5. Taylor expanded in y around inf 33.1%

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

      1. associate-/l* 47.6%

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

   7. Simplified 47.6%

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

   8. Taylor expanded in a around inf 32.2%

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

      1. associate-/l* 39.6%

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

   10. Simplified 39.6%

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

   if -4.2000000000000003e-55 < a < -6.5999999999999996e-60 or -1.2e-141 < a < -1.95000000000000008e-291

   1. Initial program 67.0%

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

      1. associate-*l/ 70.1%

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

   3. Simplified 70.1%

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

   4. Taylor expanded in z around -inf 64.4%

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

   5. Taylor expanded in a around 0 54.3%

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

      1. associate-*r/ 54.3%

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

      2. associate-*r* 54.3%

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

      3. mul-1-neg 54.3%

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

   7. Simplified 54.3%

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

   8. Taylor expanded in y around 0 41.1%

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

      1. associate-/l* 54.6%

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

   10. Simplified 54.6%

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

   if -6.5999999999999996e-60 < a < -1.2e-141

   1. Initial program 78.4%

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

      1. associate-*l/ 68.5%

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

   3. Simplified 68.5%

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

   4. Taylor expanded in z around -inf 75.7%

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

   5. Taylor expanded in a around inf 57.4%

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

      1. associate-/l* 52.4%

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

   7. Simplified 52.4%

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

   8. Taylor expanded in y around 0 40.6%

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

      1. mul-1-neg 40.6%

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

      2. associate-/l* 45.7%

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

   10. Simplified 45.7%

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

   if -1.95000000000000008e-291 < a < 5.39999999999999996e75

   1. Initial program 64.6%

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

      1. associate-*l/ 75.9%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in t around inf 51.3%

      \[\leadsto \color{blue}{y} \]
3. Recombined 6 regimes into one program.

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{+116}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -750000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-55}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-141}:\\ \;\;\;\;\frac{-x}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 48.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+99}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+154}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+228}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z a) (/ x t))))
   (if (<= t -5.2e+99)
     y
     (if (<= t 1.18e+28)
       (* x (- 1.0 (/ z a)))
       (if (<= t 5.6e+85)
         t_1
         (if (<= t 2.35e+90)
           (* y (/ z a))
           (if (<= t 3.2e+154) y (if (<= t 1.6e+228) t_1 y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - a) * (x / t);
	double tmp;
	if (t <= -5.2e+99) {
		tmp = y;
	} else if (t <= 1.18e+28) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 5.6e+85) {
		tmp = t_1;
	} else if (t <= 2.35e+90) {
		tmp = y * (z / a);
	} else if (t <= 3.2e+154) {
		tmp = y;
	} else if (t <= 1.6e+228) {
		tmp = t_1;
	} else {
		tmp = 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 = (z - a) * (x / t)
    if (t <= (-5.2d+99)) then
        tmp = y
    else if (t <= 1.18d+28) then
        tmp = x * (1.0d0 - (z / a))
    else if (t <= 5.6d+85) then
        tmp = t_1
    else if (t <= 2.35d+90) then
        tmp = y * (z / a)
    else if (t <= 3.2d+154) then
        tmp = y
    else if (t <= 1.6d+228) then
        tmp = t_1
    else
        tmp = 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 = (z - a) * (x / t);
	double tmp;
	if (t <= -5.2e+99) {
		tmp = y;
	} else if (t <= 1.18e+28) {
		tmp = x * (1.0 - (z / a));
	} else if (t <= 5.6e+85) {
		tmp = t_1;
	} else if (t <= 2.35e+90) {
		tmp = y * (z / a);
	} else if (t <= 3.2e+154) {
		tmp = y;
	} else if (t <= 1.6e+228) {
		tmp = t_1;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - a) * (x / t)
	tmp = 0
	if t <= -5.2e+99:
		tmp = y
	elif t <= 1.18e+28:
		tmp = x * (1.0 - (z / a))
	elif t <= 5.6e+85:
		tmp = t_1
	elif t <= 2.35e+90:
		tmp = y * (z / a)
	elif t <= 3.2e+154:
		tmp = y
	elif t <= 1.6e+228:
		tmp = t_1
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - a) * Float64(x / t))
	tmp = 0.0
	if (t <= -5.2e+99)
		tmp = y;
	elseif (t <= 1.18e+28)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	elseif (t <= 5.6e+85)
		tmp = t_1;
	elseif (t <= 2.35e+90)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 3.2e+154)
		tmp = y;
	elseif (t <= 1.6e+228)
		tmp = t_1;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - a) * (x / t);
	tmp = 0.0;
	if (t <= -5.2e+99)
		tmp = y;
	elseif (t <= 1.18e+28)
		tmp = x * (1.0 - (z / a));
	elseif (t <= 5.6e+85)
		tmp = t_1;
	elseif (t <= 2.35e+90)
		tmp = y * (z / a);
	elseif (t <= 3.2e+154)
		tmp = y;
	elseif (t <= 1.6e+228)
		tmp = t_1;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e+99], y, If[LessEqual[t, 1.18e+28], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e+85], t$95$1, If[LessEqual[t, 2.35e+90], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+154], y, If[LessEqual[t, 1.6e+228], t$95$1, y]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.1999999999999999e99 or 2.3500000000000001e90 < t < 3.2e154 or 1.6000000000000001e228 < t

   1. Initial program 36.6%

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

      1. associate-*l/ 65.1%

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

   3. Simplified 65.1%

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

   4. Taylor expanded in t around inf 62.0%

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

   if -5.1999999999999999e99 < t < 1.18000000000000009e28

   1. Initial program 87.8%

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

      1. associate-*l/ 92.6%

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

   3. Simplified 92.6%

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

      1. +-commutative 92.6%

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

      2. associate-/r/ 96.5%

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

      3. div-inv 96.6%

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

      4. fma-def 96.6%

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

      5. clear-num 96.6%

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

   5. Applied egg-rr 96.6%

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

   6. Taylor expanded in x around inf 61.2%

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

      1. mul-1-neg 61.2%

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

      2. unsub-neg 61.2%

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

   8. Simplified 61.2%

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

   9. Taylor expanded in t around 0 52.9%

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

   if 1.18000000000000009e28 < t < 5.5999999999999998e85 or 3.2e154 < t < 1.6000000000000001e228

   1. Initial program 52.8%

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

      1. associate-*l/ 66.8%

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

   3. Simplified 66.8%

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

      1. +-commutative 66.8%

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

      2. associate-/r/ 67.2%

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

      3. div-inv 67.2%

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

      4. fma-def 67.5%

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

      5. clear-num 67.5%

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

   5. Applied egg-rr 67.5%

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

   6. Taylor expanded in t around -inf 67.7%

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

      1. mul-1-neg 67.7%

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

      2. unsub-neg 67.7%

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

      3. associate-/l* 74.8%

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

   8. Simplified 74.8%

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

   9. Taylor expanded in y around 0 53.2%

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

       1. associate-/l* 56.5%

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

       2. associate-/r/ 60.2%

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

   11. Simplified 60.2%

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

   if 5.5999999999999998e85 < t < 2.3500000000000001e90

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-/r/ 100.0%

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

      3. div-inv 100.0%

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

      4. fma-def 100.0%

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

      5. clear-num 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around inf 52.2%

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

      1. div-sub 52.2%

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

   8. Simplified 52.2%

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

   9. Taylor expanded in t around 0 52.2%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+99}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+85}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+154}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+228}:\\ \;\;\;\;\left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 10: 41.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;a \leq -1.56 \cdot 10^{+168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -22000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{-145}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+66}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= a -1.56e+168)
     t_1
     (if (<= a -1.5e+95)
       (* y (/ (- z t) a))
       (if (<= a -22000000000000.0)
         t_1
         (if (<= a -2.75e-145)
           (* (- y x) (/ z a))
           (if (<= a -1.2e-291) (/ x (/ t z)) (if (<= a 4.6e+66) y t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -1.56e+168) {
		tmp = t_1;
	} else if (a <= -1.5e+95) {
		tmp = y * ((z - t) / a);
	} else if (a <= -22000000000000.0) {
		tmp = t_1;
	} else if (a <= -2.75e-145) {
		tmp = (y - x) * (z / a);
	} else if (a <= -1.2e-291) {
		tmp = x / (t / z);
	} else if (a <= 4.6e+66) {
		tmp = y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (a <= (-1.56d+168)) then
        tmp = t_1
    else if (a <= (-1.5d+95)) then
        tmp = y * ((z - t) / a)
    else if (a <= (-22000000000000.0d0)) then
        tmp = t_1
    else if (a <= (-2.75d-145)) then
        tmp = (y - x) * (z / a)
    else if (a <= (-1.2d-291)) then
        tmp = x / (t / z)
    else if (a <= 4.6d+66) then
        tmp = y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -1.56e+168) {
		tmp = t_1;
	} else if (a <= -1.5e+95) {
		tmp = y * ((z - t) / a);
	} else if (a <= -22000000000000.0) {
		tmp = t_1;
	} else if (a <= -2.75e-145) {
		tmp = (y - x) * (z / a);
	} else if (a <= -1.2e-291) {
		tmp = x / (t / z);
	} else if (a <= 4.6e+66) {
		tmp = y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if a <= -1.56e+168:
		tmp = t_1
	elif a <= -1.5e+95:
		tmp = y * ((z - t) / a)
	elif a <= -22000000000000.0:
		tmp = t_1
	elif a <= -2.75e-145:
		tmp = (y - x) * (z / a)
	elif a <= -1.2e-291:
		tmp = x / (t / z)
	elif a <= 4.6e+66:
		tmp = y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (a <= -1.56e+168)
		tmp = t_1;
	elseif (a <= -1.5e+95)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (a <= -22000000000000.0)
		tmp = t_1;
	elseif (a <= -2.75e-145)
		tmp = Float64(Float64(y - x) * Float64(z / a));
	elseif (a <= -1.2e-291)
		tmp = Float64(x / Float64(t / z));
	elseif (a <= 4.6e+66)
		tmp = y;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (a <= -1.56e+168)
		tmp = t_1;
	elseif (a <= -1.5e+95)
		tmp = y * ((z - t) / a);
	elseif (a <= -22000000000000.0)
		tmp = t_1;
	elseif (a <= -2.75e-145)
		tmp = (y - x) * (z / a);
	elseif (a <= -1.2e-291)
		tmp = x / (t / z);
	elseif (a <= 4.6e+66)
		tmp = y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.56e+168], t$95$1, If[LessEqual[a, -1.5e+95], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -22000000000000.0], t$95$1, If[LessEqual[a, -2.75e-145], N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.2e-291], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.6e+66], y, t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.5599999999999999e168 or -1.49999999999999996e95 < a < -2.2e13 or 4.6e66 < a

   1. Initial program 70.8%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

      1. +-commutative 89.7%

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

      2. associate-/r/ 94.0%

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

      3. div-inv 94.0%

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

      4. fma-def 94.1%

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

      5. clear-num 94.1%

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

   5. Applied egg-rr 94.1%

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

   6. Taylor expanded in x around inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

   8. Simplified 67.2%

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

   9. Taylor expanded in t around 0 62.1%

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

   if -1.5599999999999999e168 < a < -1.49999999999999996e95

   1. Initial program 73.0%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/r/ 99.6%

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

      3. div-inv 99.8%

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

      4. fma-def 99.8%

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

      5. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 79.2%

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

      1. div-sub 79.2%

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

   8. Simplified 79.2%

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

   9. Taylor expanded in a around inf 65.0%

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

   if -2.2e13 < a < -2.75000000000000008e-145

   1. Initial program 74.6%

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

      1. associate-*l/ 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in z around -inf 70.7%

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

   5. Taylor expanded in a around inf 49.0%

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

      1. associate-/l* 46.3%

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

   7. Simplified 46.3%

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

      1. associate-/r/ 49.0%

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

   9. Applied egg-rr 49.0%

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

   if -2.75000000000000008e-145 < a < -1.20000000000000006e-291

   1. Initial program 66.9%

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

      1. associate-*l/ 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in z around -inf 64.2%

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

   5. Taylor expanded in a around 0 55.8%

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

      1. associate-*r/ 55.8%

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

      2. associate-*r* 55.8%

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

      3. mul-1-neg 55.8%

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

   7. Simplified 55.8%

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

   8. Taylor expanded in y around 0 41.3%

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

      1. associate-/l* 56.0%

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

   10. Simplified 56.0%

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

   if -1.20000000000000006e-291 < a < 4.6e66

   1. Initial program 64.4%

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

      1. associate-*l/ 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in t around inf 53.3%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.56 \cdot 10^{+168}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -22000000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{-145}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{+66}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 11: 41.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;a \leq -3.65 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -52000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-147}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-292}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+66}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ z a)))))
   (if (<= a -3.65e+165)
     t_1
     (if (<= a -3.1e+94)
       (* y (/ (- z t) a))
       (if (<= a -52000000000.0)
         t_1
         (if (<= a -5.2e-147)
           (/ (* (- y x) z) a)
           (if (<= a -9.6e-292) (/ x (/ t z)) (if (<= a 3.4e+66) y t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -3.65e+165) {
		tmp = t_1;
	} else if (a <= -3.1e+94) {
		tmp = y * ((z - t) / a);
	} else if (a <= -52000000000.0) {
		tmp = t_1;
	} else if (a <= -5.2e-147) {
		tmp = ((y - x) * z) / a;
	} else if (a <= -9.6e-292) {
		tmp = x / (t / z);
	} else if (a <= 3.4e+66) {
		tmp = y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (z / a))
    if (a <= (-3.65d+165)) then
        tmp = t_1
    else if (a <= (-3.1d+94)) then
        tmp = y * ((z - t) / a)
    else if (a <= (-52000000000.0d0)) then
        tmp = t_1
    else if (a <= (-5.2d-147)) then
        tmp = ((y - x) * z) / a
    else if (a <= (-9.6d-292)) then
        tmp = x / (t / z)
    else if (a <= 3.4d+66) then
        tmp = y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -3.65e+165) {
		tmp = t_1;
	} else if (a <= -3.1e+94) {
		tmp = y * ((z - t) / a);
	} else if (a <= -52000000000.0) {
		tmp = t_1;
	} else if (a <= -5.2e-147) {
		tmp = ((y - x) * z) / a;
	} else if (a <= -9.6e-292) {
		tmp = x / (t / z);
	} else if (a <= 3.4e+66) {
		tmp = y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (z / a))
	tmp = 0
	if a <= -3.65e+165:
		tmp = t_1
	elif a <= -3.1e+94:
		tmp = y * ((z - t) / a)
	elif a <= -52000000000.0:
		tmp = t_1
	elif a <= -5.2e-147:
		tmp = ((y - x) * z) / a
	elif a <= -9.6e-292:
		tmp = x / (t / z)
	elif a <= 3.4e+66:
		tmp = y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (a <= -3.65e+165)
		tmp = t_1;
	elseif (a <= -3.1e+94)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (a <= -52000000000.0)
		tmp = t_1;
	elseif (a <= -5.2e-147)
		tmp = Float64(Float64(Float64(y - x) * z) / a);
	elseif (a <= -9.6e-292)
		tmp = Float64(x / Float64(t / z));
	elseif (a <= 3.4e+66)
		tmp = y;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (a <= -3.65e+165)
		tmp = t_1;
	elseif (a <= -3.1e+94)
		tmp = y * ((z - t) / a);
	elseif (a <= -52000000000.0)
		tmp = t_1;
	elseif (a <= -5.2e-147)
		tmp = ((y - x) * z) / a;
	elseif (a <= -9.6e-292)
		tmp = x / (t / z);
	elseif (a <= 3.4e+66)
		tmp = y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.65e+165], t$95$1, If[LessEqual[a, -3.1e+94], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -52000000000.0], t$95$1, If[LessEqual[a, -5.2e-147], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, -9.6e-292], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e+66], y, t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.6500000000000001e165 or -3.09999999999999991e94 < a < -5.2e10 or 3.4000000000000003e66 < a

   1. Initial program 70.8%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

      1. +-commutative 89.7%

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

      2. associate-/r/ 94.0%

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

      3. div-inv 94.0%

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

      4. fma-def 94.1%

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

      5. clear-num 94.1%

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

   5. Applied egg-rr 94.1%

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

   6. Taylor expanded in x around inf 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

   8. Simplified 67.2%

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

   9. Taylor expanded in t around 0 62.1%

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

   if -3.6500000000000001e165 < a < -3.09999999999999991e94

   1. Initial program 73.0%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/r/ 99.6%

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

      3. div-inv 99.8%

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

      4. fma-def 99.8%

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

      5. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 79.2%

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

      1. div-sub 79.2%

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

   8. Simplified 79.2%

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

   9. Taylor expanded in a around inf 65.0%

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

   if -5.2e10 < a < -5.1999999999999997e-147

   1. Initial program 74.6%

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

      1. associate-*l/ 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in z around -inf 70.7%

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

   5. Taylor expanded in a around inf 49.0%

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

   if -5.1999999999999997e-147 < a < -9.6000000000000005e-292

   1. Initial program 66.9%

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

      1. associate-*l/ 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in z around -inf 64.2%

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

   5. Taylor expanded in a around 0 55.8%

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

      1. associate-*r/ 55.8%

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

      2. associate-*r* 55.8%

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

      3. mul-1-neg 55.8%

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

   7. Simplified 55.8%

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

   8. Taylor expanded in y around 0 41.3%

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

      1. associate-/l* 56.0%

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

   10. Simplified 56.0%

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

   if -9.6000000000000005e-292 < a < 3.4000000000000003e66

   1. Initial program 64.4%

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

      1. associate-*l/ 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in t around inf 53.3%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.65 \cdot 10^{+165}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -52000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-147}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{a}\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-292}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+66}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 12: 54.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+214}:\\ \;\;\;\;x \cdot \left(\frac{t}{a - t} + 1\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -20000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-291}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (* x (- 1.0 (/ z a)))))
   (if (<= a -2.3e+214)
     (* x (+ (/ t (- a t)) 1.0))
     (if (<= a -7e+83)
       t_1
       (if (<= a -20000000000000.0)
         t_2
         (if (<= a -1.2e-291)
           (* z (/ (- y x) (- a t)))
           (if (<= a 1.12e+123) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -2.3e+214) {
		tmp = x * ((t / (a - t)) + 1.0);
	} else if (a <= -7e+83) {
		tmp = t_1;
	} else if (a <= -20000000000000.0) {
		tmp = t_2;
	} else if (a <= -1.2e-291) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 1.12e+123) {
		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 * ((z - t) / (a - t))
    t_2 = x * (1.0d0 - (z / a))
    if (a <= (-2.3d+214)) then
        tmp = x * ((t / (a - t)) + 1.0d0)
    else if (a <= (-7d+83)) then
        tmp = t_1
    else if (a <= (-20000000000000.0d0)) then
        tmp = t_2
    else if (a <= (-1.2d-291)) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 1.12d+123) 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 * ((z - t) / (a - t));
	double t_2 = x * (1.0 - (z / a));
	double tmp;
	if (a <= -2.3e+214) {
		tmp = x * ((t / (a - t)) + 1.0);
	} else if (a <= -7e+83) {
		tmp = t_1;
	} else if (a <= -20000000000000.0) {
		tmp = t_2;
	} else if (a <= -1.2e-291) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 1.12e+123) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x * (1.0 - (z / a))
	tmp = 0
	if a <= -2.3e+214:
		tmp = x * ((t / (a - t)) + 1.0)
	elif a <= -7e+83:
		tmp = t_1
	elif a <= -20000000000000.0:
		tmp = t_2
	elif a <= -1.2e-291:
		tmp = z * ((y - x) / (a - t))
	elif a <= 1.12e+123:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x * Float64(1.0 - Float64(z / a)))
	tmp = 0.0
	if (a <= -2.3e+214)
		tmp = Float64(x * Float64(Float64(t / Float64(a - t)) + 1.0));
	elseif (a <= -7e+83)
		tmp = t_1;
	elseif (a <= -20000000000000.0)
		tmp = t_2;
	elseif (a <= -1.2e-291)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 1.12e+123)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x * (1.0 - (z / a));
	tmp = 0.0;
	if (a <= -2.3e+214)
		tmp = x * ((t / (a - t)) + 1.0);
	elseif (a <= -7e+83)
		tmp = t_1;
	elseif (a <= -20000000000000.0)
		tmp = t_2;
	elseif (a <= -1.2e-291)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 1.12e+123)
		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[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e+214], N[(x * N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7e+83], t$95$1, If[LessEqual[a, -20000000000000.0], t$95$2, If[LessEqual[a, -1.2e-291], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.12e+123], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.2999999999999999e214

   1. Initial program 59.8%

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

      1. associate-*l/ 89.7%

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

   3. Simplified 89.7%

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

      1. +-commutative 89.7%

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

      2. associate-/r/ 90.6%

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

      3. div-inv 90.6%

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

      4. fma-def 90.7%

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

      5. clear-num 90.7%

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

   5. Applied egg-rr 90.7%

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

   6. Taylor expanded in x around inf 66.7%

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

      1. mul-1-neg 66.7%

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

      2. unsub-neg 66.7%

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

   8. Simplified 66.7%

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

   9. Taylor expanded in z around 0 62.9%

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

   if -2.2999999999999999e214 < a < -6.99999999999999954e83 or -1.20000000000000006e-291 < a < 1.12e123

   1. Initial program 65.4%

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

      1. associate-*l/ 82.4%

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

   3. Simplified 82.4%

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

      1. +-commutative 82.4%

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

      2. associate-/r/ 86.4%

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

      3. div-inv 86.4%

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

      4. fma-def 86.4%

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

      5. clear-num 86.5%

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

   5. Applied egg-rr 86.5%

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

   6. Taylor expanded in y around inf 69.3%

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

      1. div-sub 69.3%

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

   8. Simplified 69.3%

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

   if -6.99999999999999954e83 < a < -2e13 or 1.12e123 < a

   1. Initial program 78.3%

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

      1. associate-*l/ 87.3%

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

   3. Simplified 87.3%

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

      1. +-commutative 87.3%

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

      2. associate-/r/ 94.0%

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

      3. div-inv 94.0%

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

      4. fma-def 94.2%

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

      5. clear-num 94.2%

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

   5. Applied egg-rr 94.2%

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

   6. Taylor expanded in x around inf 77.0%

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

      1. mul-1-neg 77.0%

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

      2. unsub-neg 77.0%

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

   8. Simplified 77.0%

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

   9. Taylor expanded in t around 0 72.7%

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

   if -2e13 < a < -1.20000000000000006e-291

   1. Initial program 70.7%

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

      1. associate-*l/ 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in z around inf 70.3%

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

      1. div-sub 70.3%

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

   6. Simplified 70.3%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+214}:\\ \;\;\;\;x \cdot \left(\frac{t}{a - t} + 1\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -20000000000000:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-291}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \end{array} \]

Alternative 13: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-144}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-170}:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+34}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ y (- a t)) (- t z)))))
   (if (<= a -1.8e-17)
     t_1
     (if (<= a -6.2e-144)
       (* z (/ (- y x) (- a t)))
       (if (<= a 7e-170)
         (- y (/ (- y x) (/ t z)))
         (if (<= a 7e+34) (+ y (* (- z a) (/ x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (a <= -1.8e-17) {
		tmp = t_1;
	} else if (a <= -6.2e-144) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 7e-170) {
		tmp = y - ((y - x) / (t / z));
	} else if (a <= 7e+34) {
		tmp = y + ((z - a) * (x / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y / (a - t)) * (t - z))
    if (a <= (-1.8d-17)) then
        tmp = t_1
    else if (a <= (-6.2d-144)) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 7d-170) then
        tmp = y - ((y - x) / (t / z))
    else if (a <= 7d+34) then
        tmp = y + ((z - a) * (x / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / (a - t)) * (t - z));
	double tmp;
	if (a <= -1.8e-17) {
		tmp = t_1;
	} else if (a <= -6.2e-144) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 7e-170) {
		tmp = y - ((y - x) / (t / z));
	} else if (a <= 7e+34) {
		tmp = y + ((z - a) * (x / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y / (a - t)) * (t - z))
	tmp = 0
	if a <= -1.8e-17:
		tmp = t_1
	elif a <= -6.2e-144:
		tmp = z * ((y - x) / (a - t))
	elif a <= 7e-170:
		tmp = y - ((y - x) / (t / z))
	elif a <= 7e+34:
		tmp = y + ((z - a) * (x / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y / Float64(a - t)) * Float64(t - z)))
	tmp = 0.0
	if (a <= -1.8e-17)
		tmp = t_1;
	elseif (a <= -6.2e-144)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 7e-170)
		tmp = Float64(y - Float64(Float64(y - x) / Float64(t / z)));
	elseif (a <= 7e+34)
		tmp = Float64(y + Float64(Float64(z - a) * Float64(x / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y / (a - t)) * (t - z));
	tmp = 0.0;
	if (a <= -1.8e-17)
		tmp = t_1;
	elseif (a <= -6.2e-144)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 7e-170)
		tmp = y - ((y - x) / (t / z));
	elseif (a <= 7e+34)
		tmp = y + ((z - a) * (x / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.8e-17], t$95$1, If[LessEqual[a, -6.2e-144], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e-170], N[(y - N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e+34], N[(y + N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.79999999999999997e-17 or 6.99999999999999996e34 < a

   1. Initial program 70.9%

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

      1. associate-*l/ 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in y around inf 80.1%

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

   if -1.79999999999999997e-17 < a < -6.2000000000000001e-144

   1. Initial program 76.0%

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

      1. associate-*l/ 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in z around inf 71.9%

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

      1. div-sub 71.9%

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

   6. Simplified 71.9%

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

   if -6.2000000000000001e-144 < a < 6.9999999999999997e-170

   1. Initial program 63.2%

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

      1. associate-*l/ 75.1%

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

   3. Simplified 75.1%

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

      1. +-commutative 75.1%

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

      2. associate-/r/ 77.4%

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

      3. div-inv 77.3%

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

      4. fma-def 77.3%

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

      5. clear-num 77.3%

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

   5. Applied egg-rr 77.3%

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

   6. Taylor expanded in t around -inf 83.7%

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

      1. mul-1-neg 83.7%

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

      2. unsub-neg 83.7%

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

      3. associate-/l* 92.5%

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

   8. Simplified 92.5%

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

   9. Taylor expanded in z around inf 92.5%

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

   if 6.9999999999999997e-170 < a < 6.99999999999999996e34

   1. Initial program 67.7%

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

      1. associate-*l/ 67.5%

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

   3. Simplified 67.5%

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

      1. +-commutative 67.5%

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

      2. associate-/r/ 75.5%

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

      3. div-inv 75.5%

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

      4. fma-def 75.5%

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

      5. clear-num 75.6%

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

   5. Applied egg-rr 75.6%

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

   6. Taylor expanded in t around -inf 71.1%

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

      1. mul-1-neg 71.1%

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

      2. unsub-neg 71.1%

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

      3. associate-/l* 73.9%

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

   8. Simplified 73.9%

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

   9. Taylor expanded in y around 0 76.3%

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

       1. mul-1-neg 76.3%

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

       2. associate-/l* 76.3%

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

       3. associate-/r/ 78.9%

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

   11. Simplified 78.9%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-17}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-144}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-170}:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+34}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 14: 37.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -5.3 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1850000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-215}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -6.9 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z a))))
   (if (<= a -5.3e+165)
     x
     (if (<= a -1.2e+116)
       t_1
       (if (<= a -1850000000000.0)
         x
         (if (<= a -7e-146)
           t_1
           (if (<= a -3.5e-215)
             y
             (if (<= a -6.9e-292) (* z (/ x t)) (if (<= a 6.4e+77) y x)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (a <= -5.3e+165) {
		tmp = x;
	} else if (a <= -1.2e+116) {
		tmp = t_1;
	} else if (a <= -1850000000000.0) {
		tmp = x;
	} else if (a <= -7e-146) {
		tmp = t_1;
	} else if (a <= -3.5e-215) {
		tmp = y;
	} else if (a <= -6.9e-292) {
		tmp = z * (x / t);
	} else if (a <= 6.4e+77) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / a)
    if (a <= (-5.3d+165)) then
        tmp = x
    else if (a <= (-1.2d+116)) then
        tmp = t_1
    else if (a <= (-1850000000000.0d0)) then
        tmp = x
    else if (a <= (-7d-146)) then
        tmp = t_1
    else if (a <= (-3.5d-215)) then
        tmp = y
    else if (a <= (-6.9d-292)) then
        tmp = z * (x / t)
    else if (a <= 6.4d+77) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (a <= -5.3e+165) {
		tmp = x;
	} else if (a <= -1.2e+116) {
		tmp = t_1;
	} else if (a <= -1850000000000.0) {
		tmp = x;
	} else if (a <= -7e-146) {
		tmp = t_1;
	} else if (a <= -3.5e-215) {
		tmp = y;
	} else if (a <= -6.9e-292) {
		tmp = z * (x / t);
	} else if (a <= 6.4e+77) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / a)
	tmp = 0
	if a <= -5.3e+165:
		tmp = x
	elif a <= -1.2e+116:
		tmp = t_1
	elif a <= -1850000000000.0:
		tmp = x
	elif a <= -7e-146:
		tmp = t_1
	elif a <= -3.5e-215:
		tmp = y
	elif a <= -6.9e-292:
		tmp = z * (x / t)
	elif a <= 6.4e+77:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / a))
	tmp = 0.0
	if (a <= -5.3e+165)
		tmp = x;
	elseif (a <= -1.2e+116)
		tmp = t_1;
	elseif (a <= -1850000000000.0)
		tmp = x;
	elseif (a <= -7e-146)
		tmp = t_1;
	elseif (a <= -3.5e-215)
		tmp = y;
	elseif (a <= -6.9e-292)
		tmp = Float64(z * Float64(x / t));
	elseif (a <= 6.4e+77)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / a);
	tmp = 0.0;
	if (a <= -5.3e+165)
		tmp = x;
	elseif (a <= -1.2e+116)
		tmp = t_1;
	elseif (a <= -1850000000000.0)
		tmp = x;
	elseif (a <= -7e-146)
		tmp = t_1;
	elseif (a <= -3.5e-215)
		tmp = y;
	elseif (a <= -6.9e-292)
		tmp = z * (x / t);
	elseif (a <= 6.4e+77)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.3e+165], x, If[LessEqual[a, -1.2e+116], t$95$1, If[LessEqual[a, -1850000000000.0], x, If[LessEqual[a, -7e-146], t$95$1, If[LessEqual[a, -3.5e-215], y, If[LessEqual[a, -6.9e-292], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.4e+77], y, x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.3000000000000001e165 or -1.2e116 < a < -1.85e12 or 6.4000000000000003e77 < a

   1. Initial program 70.5%

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

      1. associate-*l/ 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in a around inf 54.0%

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

   if -5.3000000000000001e165 < a < -1.2e116 or -1.85e12 < a < -7.0000000000000003e-146

   1. Initial program 75.1%

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

      1. associate-*l/ 83.3%

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

   3. Simplified 83.3%

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

      1. +-commutative 83.3%

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

      2. associate-/r/ 87.2%

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

      3. div-inv 87.3%

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

      4. fma-def 87.3%

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

      5. clear-num 87.4%

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

   5. Applied egg-rr 87.4%

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

   6. Taylor expanded in y around inf 66.8%

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

      1. div-sub 66.8%

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

   8. Simplified 66.8%

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

   9. Taylor expanded in t around 0 36.8%

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

   if -7.0000000000000003e-146 < a < -3.5000000000000002e-215 or -6.89999999999999969e-292 < a < 6.4000000000000003e77

   1. Initial program 64.5%

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

      1. associate-*l/ 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in t around inf 51.9%

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

   if -3.5000000000000002e-215 < a < -6.89999999999999969e-292

   1. Initial program 69.1%

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

      1. associate-*l/ 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in z around -inf 85.3%

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

   5. Taylor expanded in a around 0 75.6%

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

      1. associate-*r/ 75.6%

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

      2. associate-*r* 75.6%

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

      3. mul-1-neg 75.6%

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

   7. Simplified 75.6%

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

   8. Taylor expanded in y around 0 50.2%

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

      1. associate-/l* 61.6%

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

   10. Simplified 61.6%

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

       1. associate-/r/ 59.8%

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

   12. Applied egg-rr 59.8%

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

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -1850000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-146}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-215}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -6.9 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+77}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 68.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -210000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-145}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-170}:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+39}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y x) (/ z a)))))
   (if (<= a -210000000000.0)
     t_1
     (if (<= a -7e-145)
       (* z (/ (- y x) (- a t)))
       (if (<= a 7.5e-170)
         (- y (/ (- y x) (/ t z)))
         (if (<= a 5.8e+39) (+ y (* (- z a) (/ x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * (z / a));
	double tmp;
	if (a <= -210000000000.0) {
		tmp = t_1;
	} else if (a <= -7e-145) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 7.5e-170) {
		tmp = y - ((y - x) / (t / z));
	} else if (a <= 5.8e+39) {
		tmp = y + ((z - a) * (x / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - x) * (z / a))
    if (a <= (-210000000000.0d0)) then
        tmp = t_1
    else if (a <= (-7d-145)) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 7.5d-170) then
        tmp = y - ((y - x) / (t / z))
    else if (a <= 5.8d+39) then
        tmp = y + ((z - a) * (x / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * (z / a));
	double tmp;
	if (a <= -210000000000.0) {
		tmp = t_1;
	} else if (a <= -7e-145) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 7.5e-170) {
		tmp = y - ((y - x) / (t / z));
	} else if (a <= 5.8e+39) {
		tmp = y + ((z - a) * (x / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) * (z / a))
	tmp = 0
	if a <= -210000000000.0:
		tmp = t_1
	elif a <= -7e-145:
		tmp = z * ((y - x) / (a - t))
	elif a <= 7.5e-170:
		tmp = y - ((y - x) / (t / z))
	elif a <= 5.8e+39:
		tmp = y + ((z - a) * (x / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) * Float64(z / a)))
	tmp = 0.0
	if (a <= -210000000000.0)
		tmp = t_1;
	elseif (a <= -7e-145)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 7.5e-170)
		tmp = Float64(y - Float64(Float64(y - x) / Float64(t / z)));
	elseif (a <= 5.8e+39)
		tmp = Float64(y + Float64(Float64(z - a) * Float64(x / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) * (z / a));
	tmp = 0.0;
	if (a <= -210000000000.0)
		tmp = t_1;
	elseif (a <= -7e-145)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 7.5e-170)
		tmp = y - ((y - x) / (t / z));
	elseif (a <= 5.8e+39)
		tmp = y + ((z - a) * (x / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -210000000000.0], t$95$1, If[LessEqual[a, -7e-145], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-170], N[(y - N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e+39], N[(y + N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.1e11 or 5.80000000000000059e39 < a

   1. Initial program 71.8%

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

      1. associate-/l* 94.8%

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

      2. clear-num 94.7%

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

      3. associate-/r/ 94.8%

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

      4. clear-num 94.9%

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

   3. Applied egg-rr 94.9%

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

   4. Taylor expanded in t around 0 71.5%

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

   if -2.1e11 < a < -6.99999999999999994e-145

   1. Initial program 74.6%

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

      1. associate-*l/ 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in z around inf 70.8%

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

      1. div-sub 70.8%

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

   6. Simplified 70.8%

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

   if -6.99999999999999994e-145 < a < 7.4999999999999998e-170

   1. Initial program 63.2%

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

      1. associate-*l/ 75.1%

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

   3. Simplified 75.1%

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

      1. +-commutative 75.1%

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

      2. associate-/r/ 77.4%

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

      3. div-inv 77.3%

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

      4. fma-def 77.3%

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

      5. clear-num 77.3%

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

   5. Applied egg-rr 77.3%

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

   6. Taylor expanded in t around -inf 83.7%

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

      1. mul-1-neg 83.7%

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

      2. unsub-neg 83.7%

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

      3. associate-/l* 92.5%

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

   8. Simplified 92.5%

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

   9. Taylor expanded in z around inf 92.5%

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

   if 7.4999999999999998e-170 < a < 5.80000000000000059e39

   1. Initial program 66.1%

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

      1. associate-*l/ 68.3%

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

   3. Simplified 68.3%

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

      1. +-commutative 68.3%

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

      2. associate-/r/ 76.1%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 76.1%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. fma-def 76.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{1}{\frac{a - t}{z - t}}, x\right)} \]

      5. clear-num 76.2%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{z - t}{a - t}}, x\right) \]

   5. Applied egg-rr 76.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   6. Taylor expanded in t around -inf 71.9%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
   7. Step-by-step derivation

      1. mul-1-neg 71.9%

         \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)} \]

      2. unsub-neg 71.9%

         \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

      3. associate-/l* 74.6%

         \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   8. Simplified 74.6%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   9. Taylor expanded in y around 0 76.9%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   10. Step-by-step derivation

       1. mul-1-neg 76.9%

          \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

       2. associate-/l* 77.0%

          \[\leadsto y - \left(-\color{blue}{\frac{x}{\frac{t}{z - a}}}\right) \]

       3. associate-/r/ 79.5%

          \[\leadsto y - \left(-\color{blue}{\frac{x}{t} \cdot \left(z - a\right)}\right) \]

   11. Simplified 79.5%

       \[\leadsto y - \color{blue}{\left(-\frac{x}{t} \cdot \left(z - a\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -210000000000:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-145}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-170}:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+39}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \end{array} \]

Alternative 16: 78.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+18}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+89}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (* (- z a) (/ x t)))))
   (if (<= t -6.5e+193)
     t_1
     (if (<= t -5.2e+18)
       (- x (* (/ y (- a t)) (- t z)))
       (if (<= t 1.35e+89) (+ x (/ (- y x) (/ (- a t) z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * (x / t));
	double tmp;
	if (t <= -6.5e+193) {
		tmp = t_1;
	} else if (t <= -5.2e+18) {
		tmp = x - ((y / (a - t)) * (t - z));
	} else if (t <= 1.35e+89) {
		tmp = x + ((y - x) / ((a - t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + ((z - a) * (x / t))
    if (t <= (-6.5d+193)) then
        tmp = t_1
    else if (t <= (-5.2d+18)) then
        tmp = x - ((y / (a - t)) * (t - z))
    else if (t <= 1.35d+89) then
        tmp = x + ((y - x) / ((a - t) / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((z - a) * (x / t));
	double tmp;
	if (t <= -6.5e+193) {
		tmp = t_1;
	} else if (t <= -5.2e+18) {
		tmp = x - ((y / (a - t)) * (t - z));
	} else if (t <= 1.35e+89) {
		tmp = x + ((y - x) / ((a - t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((z - a) * (x / t))
	tmp = 0
	if t <= -6.5e+193:
		tmp = t_1
	elif t <= -5.2e+18:
		tmp = x - ((y / (a - t)) * (t - z))
	elif t <= 1.35e+89:
		tmp = x + ((y - x) / ((a - t) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(z - a) * Float64(x / t)))
	tmp = 0.0
	if (t <= -6.5e+193)
		tmp = t_1;
	elseif (t <= -5.2e+18)
		tmp = Float64(x - Float64(Float64(y / Float64(a - t)) * Float64(t - z)));
	elseif (t <= 1.35e+89)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((z - a) * (x / t));
	tmp = 0.0;
	if (t <= -6.5e+193)
		tmp = t_1;
	elseif (t <= -5.2e+18)
		tmp = x - ((y / (a - t)) * (t - z));
	elseif (t <= 1.35e+89)
		tmp = x + ((y - x) / ((a - t) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+193], t$95$1, If[LessEqual[t, -5.2e+18], N[(x - N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e+89], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.4999999999999997e193 or 1.35e89 < t

   1. Initial program 34.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 57.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 57.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Step-by-step derivation

      1. +-commutative 57.8%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 64.1%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 64.1%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. fma-def 64.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{1}{\frac{a - t}{z - t}}, x\right)} \]

      5. clear-num 64.2%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{z - t}{a - t}}, x\right) \]

   5. Applied egg-rr 64.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   6. Taylor expanded in t around -inf 67.8%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
   7. Step-by-step derivation

      1. mul-1-neg 67.8%

         \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)} \]

      2. unsub-neg 67.8%

         \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

      3. associate-/l* 89.4%

         \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   8. Simplified 89.4%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   9. Taylor expanded in y around 0 74.1%

      \[\leadsto y - \color{blue}{-1 \cdot \frac{x \cdot \left(z - a\right)}{t}} \]
   10. Step-by-step derivation

       1. mul-1-neg 74.1%

          \[\leadsto y - \color{blue}{\left(-\frac{x \cdot \left(z - a\right)}{t}\right)} \]

       2. associate-/l* 85.1%

          \[\leadsto y - \left(-\color{blue}{\frac{x}{\frac{t}{z - a}}}\right) \]

       3. associate-/r/ 86.4%

          \[\leadsto y - \left(-\color{blue}{\frac{x}{t} \cdot \left(z - a\right)}\right) \]

   11. Simplified 86.4%

       \[\leadsto y - \color{blue}{\left(-\frac{x}{t} \cdot \left(z - a\right)\right)} \]

   if -6.4999999999999997e193 < t < -5.2e18

   1. Initial program 56.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 88.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   4. Taylor expanded in y around inf 81.1%

      \[\leadsto x + \color{blue}{\frac{y}{a - t}} \cdot \left(z - t\right) \]

   if -5.2e18 < t < 1.35e89

   1. Initial program 88.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 96.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 96.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around inf 83.3%

      \[\leadsto x + \frac{y - x}{\color{blue}{\frac{a - t}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+193}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{+18}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+89}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z - a\right) \cdot \frac{x}{t}\\ \end{array} \]

Alternative 17: 79.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{if}\;t \leq -9 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+22}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (- x y) (/ t (- z a))))))
   (if (<= t -9e+192)
     t_1
     (if (<= t -2.2e+22)
       (- x (* (/ y (- a t)) (- t z)))
       (if (<= t 9.2e+25) (+ x (/ (- y x) (/ (- a t) z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / (z - a)));
	double tmp;
	if (t <= -9e+192) {
		tmp = t_1;
	} else if (t <= -2.2e+22) {
		tmp = x - ((y / (a - t)) * (t - z));
	} else if (t <= 9.2e+25) {
		tmp = x + ((y - x) / ((a - t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + ((x - y) / (t / (z - a)))
    if (t <= (-9d+192)) then
        tmp = t_1
    else if (t <= (-2.2d+22)) then
        tmp = x - ((y / (a - t)) * (t - z))
    else if (t <= 9.2d+25) then
        tmp = x + ((y - x) / ((a - t) / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / (z - a)));
	double tmp;
	if (t <= -9e+192) {
		tmp = t_1;
	} else if (t <= -2.2e+22) {
		tmp = x - ((y / (a - t)) * (t - z));
	} else if (t <= 9.2e+25) {
		tmp = x + ((y - x) / ((a - t) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((x - y) / (t / (z - a)))
	tmp = 0
	if t <= -9e+192:
		tmp = t_1
	elif t <= -2.2e+22:
		tmp = x - ((y / (a - t)) * (t - z))
	elif t <= 9.2e+25:
		tmp = x + ((y - x) / ((a - t) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))))
	tmp = 0.0
	if (t <= -9e+192)
		tmp = t_1;
	elseif (t <= -2.2e+22)
		tmp = Float64(x - Float64(Float64(y / Float64(a - t)) * Float64(t - z)));
	elseif (t <= 9.2e+25)
		tmp = Float64(x + Float64(Float64(y - x) / Float64(Float64(a - t) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((x - y) / (t / (z - a)));
	tmp = 0.0;
	if (t <= -9e+192)
		tmp = t_1;
	elseif (t <= -2.2e+22)
		tmp = x - ((y / (a - t)) * (t - z));
	elseif (t <= 9.2e+25)
		tmp = x + ((y - x) / ((a - t) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e+192], t$95$1, If[LessEqual[t, -2.2e+22], N[(x - N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e+25], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9e192 or 9.1999999999999992e25 < t

   1. Initial program 42.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 62.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 62.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Step-by-step derivation

      1. +-commutative 62.2%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 67.5%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 67.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. fma-def 67.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{1}{\frac{a - t}{z - t}}, x\right)} \]

      5. clear-num 67.6%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{z - t}{a - t}}, x\right) \]

   5. Applied egg-rr 67.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   6. Taylor expanded in t around -inf 66.4%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
   7. Step-by-step derivation

      1. mul-1-neg 66.4%

         \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)} \]

      2. unsub-neg 66.4%

         \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

      3. associate-/l* 84.2%

         \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   8. Simplified 84.2%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   if -9e192 < t < -2.2e22

   1. Initial program 56.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 88.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   4. Taylor expanded in y around inf 81.1%

      \[\leadsto x + \color{blue}{\frac{y}{a - t}} \cdot \left(z - t\right) \]

   if -2.2e22 < t < 9.1999999999999992e25

   1. Initial program 89.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 97.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

   3. Simplified 97.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a - t}{z - t}}} \]

   4. Taylor expanded in z around inf 86.4%

      \[\leadsto x + \frac{y - x}{\color{blue}{\frac{a - t}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+192}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+22}:\\ \;\;\;\;x - \frac{y}{a - t} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]

Alternative 18: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+192} \lor \neg \left(t \leq 2.5 \cdot 10^{+91}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.2e+192) (not (<= t 2.5e+91)))
   (+ y (/ (- x y) (/ t (- z a))))
   (+ x (* (- z t) (/ (- y x) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.2e+192) || !(t <= 2.5e+91)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-8.2d+192)) .or. (.not. (t <= 2.5d+91))) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x + ((z - t) * ((y - x) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.2e+192) || !(t <= 2.5e+91)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.2e+192) or not (t <= 2.5e+91):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x + ((z - t) * ((y - x) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.2e+192) || !(t <= 2.5e+91))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(Float64(y - x) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.2e+192) || ~((t <= 2.5e+91)))
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x + ((z - t) * ((y - x) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.2e+192], N[Not[LessEqual[t, 2.5e+91]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.20000000000000006e192 or 2.5000000000000001e91 < t

   1. Initial program 34.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 57.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 57.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Step-by-step derivation

      1. +-commutative 57.8%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 64.1%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 64.1%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. fma-def 64.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{1}{\frac{a - t}{z - t}}, x\right)} \]

      5. clear-num 64.2%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{z - t}{a - t}}, x\right) \]

   5. Applied egg-rr 64.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   6. Taylor expanded in t around -inf 67.8%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
   7. Step-by-step derivation

      1. mul-1-neg 67.8%

         \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)} \]

      2. unsub-neg 67.8%

         \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

      3. associate-/l* 89.4%

         \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   8. Simplified 89.4%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   if -8.20000000000000006e192 < t < 2.5000000000000001e91

   1. Initial program 82.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+192} \lor \neg \left(t \leq 2.5 \cdot 10^{+91}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y - x}{a - t}\\ \end{array} \]

Alternative 19: 89.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+194} \lor \neg \left(t \leq 5.5 \cdot 10^{+90}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2e+194) (not (<= t 5.5e+90)))
   (+ y (/ (- x y) (/ t (- z a))))
   (+ x (* (- y x) (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2e+194) || !(t <= 5.5e+90)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2d+194)) .or. (.not. (t <= 5.5d+90))) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x + ((y - x) * ((z - t) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2e+194) || !(t <= 5.5e+90)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2e+194) or not (t <= 5.5e+90):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x + ((y - x) * ((z - t) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2e+194) || !(t <= 5.5e+90))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(Float64(z - t) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2e+194) || ~((t <= 5.5e+90)))
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x + ((y - x) * ((z - t) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2e+194], N[Not[LessEqual[t, 5.5e+90]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.99999999999999989e194 or 5.49999999999999999e90 < t

   1. Initial program 34.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 57.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 57.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Step-by-step derivation

      1. +-commutative 57.8%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 64.1%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 64.1%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. fma-def 64.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{1}{\frac{a - t}{z - t}}, x\right)} \]

      5. clear-num 64.2%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{z - t}{a - t}}, x\right) \]

   5. Applied egg-rr 64.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   6. Taylor expanded in t around -inf 67.8%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
   7. Step-by-step derivation

      1. mul-1-neg 67.8%

         \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)} \]

      2. unsub-neg 67.8%

         \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

      3. associate-/l* 89.4%

         \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   8. Simplified 89.4%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   if -1.99999999999999989e194 < t < 5.49999999999999999e90

   1. Initial program 82.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 94.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

      2. clear-num 94.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - t}{z - t}}{y - x}}} \]

      3. associate-/r/ 94.8%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - t}{z - t}} \cdot \left(y - x\right)} \]

      4. clear-num 94.8%

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t}} \cdot \left(y - x\right) \]

   3. Applied egg-rr 94.8%

      \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+194} \lor \neg \left(t \leq 5.5 \cdot 10^{+90}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array} \]

Alternative 20: 62.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -23000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-291}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y x) (/ z a)))))
   (if (<= a -23000000000.0)
     t_1
     (if (<= a -1.35e-291)
       (* z (/ (- y x) (- a t)))
       (if (<= a 3.2e+50) (* y (/ (- z t) (- a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * (z / a));
	double tmp;
	if (a <= -23000000000.0) {
		tmp = t_1;
	} else if (a <= -1.35e-291) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 3.2e+50) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - x) * (z / a))
    if (a <= (-23000000000.0d0)) then
        tmp = t_1
    else if (a <= (-1.35d-291)) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 3.2d+50) then
        tmp = y * ((z - t) / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * (z / a));
	double tmp;
	if (a <= -23000000000.0) {
		tmp = t_1;
	} else if (a <= -1.35e-291) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 3.2e+50) {
		tmp = y * ((z - t) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) * (z / a))
	tmp = 0
	if a <= -23000000000.0:
		tmp = t_1
	elif a <= -1.35e-291:
		tmp = z * ((y - x) / (a - t))
	elif a <= 3.2e+50:
		tmp = y * ((z - t) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) * Float64(z / a)))
	tmp = 0.0
	if (a <= -23000000000.0)
		tmp = t_1;
	elseif (a <= -1.35e-291)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 3.2e+50)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) * (z / a));
	tmp = 0.0;
	if (a <= -23000000000.0)
		tmp = t_1;
	elseif (a <= -1.35e-291)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 3.2e+50)
		tmp = y * ((z - t) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -23000000000.0], t$95$1, If[LessEqual[a, -1.35e-291], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e+50], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.3e10 or 3.19999999999999983e50 < a

   1. Initial program 71.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 94.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

      2. clear-num 94.6%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - t}{z - t}}{y - x}}} \]

      3. associate-/r/ 94.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - t}{z - t}} \cdot \left(y - x\right)} \]

      4. clear-num 94.8%

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t}} \cdot \left(y - x\right) \]

   3. Applied egg-rr 94.8%

      \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} \]

   4. Taylor expanded in t around 0 71.9%

      \[\leadsto x + \color{blue}{\frac{z}{a}} \cdot \left(y - x\right) \]

   if -2.3e10 < a < -1.34999999999999996e-291

   1. Initial program 70.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 73.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 73.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   4. Taylor expanded in z around inf 70.3%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 70.3%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   6. Simplified 70.3%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if -1.34999999999999996e-291 < a < 3.19999999999999983e50

   1. Initial program 64.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 74.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 74.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Step-by-step derivation

      1. +-commutative 74.5%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 80.1%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 80.1%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. fma-def 80.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{1}{\frac{a - t}{z - t}}, x\right)} \]

      5. clear-num 80.1%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{z - t}{a - t}}, x\right) \]

   5. Applied egg-rr 80.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 68.8%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 68.8%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 68.8%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -23000000000:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-291}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \end{array} \]

Alternative 21: 69.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -80000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-145}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+38}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y x) (/ z a)))))
   (if (<= a -80000000000.0)
     t_1
     (if (<= a -7e-145)
       (* z (/ (- y x) (- a t)))
       (if (<= a 2.25e+38) (+ y (* (/ z t) (- x y))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * (z / a));
	double tmp;
	if (a <= -80000000000.0) {
		tmp = t_1;
	} else if (a <= -7e-145) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 2.25e+38) {
		tmp = y + ((z / t) * (x - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - x) * (z / a))
    if (a <= (-80000000000.0d0)) then
        tmp = t_1
    else if (a <= (-7d-145)) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 2.25d+38) then
        tmp = y + ((z / t) * (x - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * (z / a));
	double tmp;
	if (a <= -80000000000.0) {
		tmp = t_1;
	} else if (a <= -7e-145) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 2.25e+38) {
		tmp = y + ((z / t) * (x - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) * (z / a))
	tmp = 0
	if a <= -80000000000.0:
		tmp = t_1
	elif a <= -7e-145:
		tmp = z * ((y - x) / (a - t))
	elif a <= 2.25e+38:
		tmp = y + ((z / t) * (x - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) * Float64(z / a)))
	tmp = 0.0
	if (a <= -80000000000.0)
		tmp = t_1;
	elseif (a <= -7e-145)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 2.25e+38)
		tmp = Float64(y + Float64(Float64(z / t) * Float64(x - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) * (z / a));
	tmp = 0.0;
	if (a <= -80000000000.0)
		tmp = t_1;
	elseif (a <= -7e-145)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 2.25e+38)
		tmp = y + ((z / t) * (x - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -80000000000.0], t$95$1, If[LessEqual[a, -7e-145], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.25e+38], N[(y + N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8e10 or 2.2499999999999999e38 < a

   1. Initial program 71.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 94.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

      2. clear-num 94.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - t}{z - t}}{y - x}}} \]

      3. associate-/r/ 94.8%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - t}{z - t}} \cdot \left(y - x\right)} \]

      4. clear-num 94.9%

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t}} \cdot \left(y - x\right) \]

   3. Applied egg-rr 94.9%

      \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} \]

   4. Taylor expanded in t around 0 71.5%

      \[\leadsto x + \color{blue}{\frac{z}{a}} \cdot \left(y - x\right) \]

   if -8e10 < a < -6.99999999999999994e-145

   1. Initial program 74.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 77.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 77.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   4. Taylor expanded in z around inf 70.8%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 70.8%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   6. Simplified 70.8%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if -6.99999999999999994e-145 < a < 2.2499999999999999e38

   1. Initial program 64.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 72.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 72.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Step-by-step derivation

      1. +-commutative 72.6%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 76.9%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 76.9%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. fma-def 76.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{1}{\frac{a - t}{z - t}}, x\right)} \]

      5. clear-num 76.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{z - t}{a - t}}, x\right) \]

   5. Applied egg-rr 76.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   6. Taylor expanded in t around -inf 79.4%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
   7. Step-by-step derivation

      1. mul-1-neg 79.4%

         \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)} \]

      2. unsub-neg 79.4%

         \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

      3. associate-/l* 85.9%

         \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   8. Simplified 85.9%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   9. Taylor expanded in z around inf 75.0%

      \[\leadsto y - \color{blue}{\frac{z \cdot \left(y - x\right)}{t}} \]
   10. Step-by-step derivation

       1. *-commutative 75.0%

          \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot z}}{t} \]

       2. associate-*r/ 82.4%

          \[\leadsto y - \color{blue}{\left(y - x\right) \cdot \frac{z}{t}} \]

   11. Simplified 82.4%

       \[\leadsto y - \color{blue}{\left(y - x\right) \cdot \frac{z}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -80000000000:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-145}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+38}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \end{array} \]

Alternative 22: 69.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -10000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-144}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+39}:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y x) (/ z a)))))
   (if (<= a -10000000000.0)
     t_1
     (if (<= a -6.2e-144)
       (* z (/ (- y x) (- a t)))
       (if (<= a 5.8e+39) (- y (/ (- y x) (/ t z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * (z / a));
	double tmp;
	if (a <= -10000000000.0) {
		tmp = t_1;
	} else if (a <= -6.2e-144) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 5.8e+39) {
		tmp = y - ((y - x) / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - x) * (z / a))
    if (a <= (-10000000000.0d0)) then
        tmp = t_1
    else if (a <= (-6.2d-144)) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 5.8d+39) then
        tmp = y - ((y - x) / (t / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - x) * (z / a));
	double tmp;
	if (a <= -10000000000.0) {
		tmp = t_1;
	} else if (a <= -6.2e-144) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 5.8e+39) {
		tmp = y - ((y - x) / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - x) * (z / a))
	tmp = 0
	if a <= -10000000000.0:
		tmp = t_1
	elif a <= -6.2e-144:
		tmp = z * ((y - x) / (a - t))
	elif a <= 5.8e+39:
		tmp = y - ((y - x) / (t / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - x) * Float64(z / a)))
	tmp = 0.0
	if (a <= -10000000000.0)
		tmp = t_1;
	elseif (a <= -6.2e-144)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 5.8e+39)
		tmp = Float64(y - Float64(Float64(y - x) / Float64(t / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - x) * (z / a));
	tmp = 0.0;
	if (a <= -10000000000.0)
		tmp = t_1;
	elseif (a <= -6.2e-144)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 5.8e+39)
		tmp = y - ((y - x) / (t / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -10000000000.0], t$95$1, If[LessEqual[a, -6.2e-144], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e+39], N[(y - N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1e10 or 5.80000000000000059e39 < a

   1. Initial program 71.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 94.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} \]

      2. clear-num 94.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - t}{z - t}}{y - x}}} \]

      3. associate-/r/ 94.8%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - t}{z - t}} \cdot \left(y - x\right)} \]

      4. clear-num 94.9%

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t}} \cdot \left(y - x\right) \]

   3. Applied egg-rr 94.9%

      \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} \]

   4. Taylor expanded in t around 0 71.5%

      \[\leadsto x + \color{blue}{\frac{z}{a}} \cdot \left(y - x\right) \]

   if -1e10 < a < -6.2000000000000001e-144

   1. Initial program 74.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 77.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 77.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   4. Taylor expanded in z around inf 70.8%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   5. Step-by-step derivation

      1. div-sub 70.8%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   6. Simplified 70.8%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if -6.2000000000000001e-144 < a < 5.80000000000000059e39

   1. Initial program 64.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 72.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 72.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Step-by-step derivation

      1. +-commutative 72.6%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 76.9%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 76.9%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. fma-def 76.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{1}{\frac{a - t}{z - t}}, x\right)} \]

      5. clear-num 76.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{z - t}{a - t}}, x\right) \]

   5. Applied egg-rr 76.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   6. Taylor expanded in t around -inf 79.4%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]
   7. Step-by-step derivation

      1. mul-1-neg 79.4%

         \[\leadsto y + \color{blue}{\left(-\frac{\left(y - x\right) \cdot \left(z - a\right)}{t}\right)} \]

      2. unsub-neg 79.4%

         \[\leadsto \color{blue}{y - \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

      3. associate-/l* 85.9%

         \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   8. Simplified 85.9%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   9. Taylor expanded in z around inf 82.4%

      \[\leadsto y - \frac{y - x}{\color{blue}{\frac{t}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -10000000000:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-144}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+39}:\\ \;\;\;\;y - \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{a}\\ \end{array} \]

Alternative 23: 38.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+74}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z a))))
   (if (<= a -3.5e+165)
     x
     (if (<= a -1.25e+116)
       t_1
       (if (<= a -5500000000000.0)
         x
         (if (<= a -6.2e-144) t_1 (if (<= a 6.2e+74) y x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (a <= -3.5e+165) {
		tmp = x;
	} else if (a <= -1.25e+116) {
		tmp = t_1;
	} else if (a <= -5500000000000.0) {
		tmp = x;
	} else if (a <= -6.2e-144) {
		tmp = t_1;
	} else if (a <= 6.2e+74) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / a)
    if (a <= (-3.5d+165)) then
        tmp = x
    else if (a <= (-1.25d+116)) then
        tmp = t_1
    else if (a <= (-5500000000000.0d0)) then
        tmp = x
    else if (a <= (-6.2d-144)) then
        tmp = t_1
    else if (a <= 6.2d+74) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (a <= -3.5e+165) {
		tmp = x;
	} else if (a <= -1.25e+116) {
		tmp = t_1;
	} else if (a <= -5500000000000.0) {
		tmp = x;
	} else if (a <= -6.2e-144) {
		tmp = t_1;
	} else if (a <= 6.2e+74) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / a)
	tmp = 0
	if a <= -3.5e+165:
		tmp = x
	elif a <= -1.25e+116:
		tmp = t_1
	elif a <= -5500000000000.0:
		tmp = x
	elif a <= -6.2e-144:
		tmp = t_1
	elif a <= 6.2e+74:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / a))
	tmp = 0.0
	if (a <= -3.5e+165)
		tmp = x;
	elseif (a <= -1.25e+116)
		tmp = t_1;
	elseif (a <= -5500000000000.0)
		tmp = x;
	elseif (a <= -6.2e-144)
		tmp = t_1;
	elseif (a <= 6.2e+74)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / a);
	tmp = 0.0;
	if (a <= -3.5e+165)
		tmp = x;
	elseif (a <= -1.25e+116)
		tmp = t_1;
	elseif (a <= -5500000000000.0)
		tmp = x;
	elseif (a <= -6.2e-144)
		tmp = t_1;
	elseif (a <= 6.2e+74)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e+165], x, If[LessEqual[a, -1.25e+116], t$95$1, If[LessEqual[a, -5500000000000.0], x, If[LessEqual[a, -6.2e-144], t$95$1, If[LessEqual[a, 6.2e+74], y, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.49999999999999996e165 or -1.25000000000000006e116 < a < -5.5e12 or 6.20000000000000043e74 < a

   1. Initial program 70.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 89.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   4. Taylor expanded in a around inf 54.0%

      \[\leadsto \color{blue}{x} \]

   if -3.49999999999999996e165 < a < -1.25000000000000006e116 or -5.5e12 < a < -6.2000000000000001e-144

   1. Initial program 75.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 83.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 83.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Step-by-step derivation

      1. +-commutative 83.3%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 87.2%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 87.3%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. fma-def 87.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{1}{\frac{a - t}{z - t}}, x\right)} \]

      5. clear-num 87.4%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{z - t}{a - t}}, x\right) \]

   5. Applied egg-rr 87.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 66.8%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 66.8%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 66.8%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   9. Taylor expanded in t around 0 36.8%

      \[\leadsto y \cdot \color{blue}{\frac{z}{a}} \]

   if -6.2000000000000001e-144 < a < 6.20000000000000043e74

   1. Initial program 65.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 74.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   4. Taylor expanded in t around inf 44.0%

      \[\leadsto \color{blue}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -5500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+74}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24: 37.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-292}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+74}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.5e+165)
   x
   (if (<= a -1.25e+116)
     (* y (/ z a))
     (if (<= a -3.8e-16)
       x
       (if (<= a -6.5e-292) (/ x (/ t z)) (if (<= a 5.8e+74) y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e+165) {
		tmp = x;
	} else if (a <= -1.25e+116) {
		tmp = y * (z / a);
	} else if (a <= -3.8e-16) {
		tmp = x;
	} else if (a <= -6.5e-292) {
		tmp = x / (t / z);
	} else if (a <= 5.8e+74) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.5d+165)) then
        tmp = x
    else if (a <= (-1.25d+116)) then
        tmp = y * (z / a)
    else if (a <= (-3.8d-16)) then
        tmp = x
    else if (a <= (-6.5d-292)) then
        tmp = x / (t / z)
    else if (a <= 5.8d+74) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e+165) {
		tmp = x;
	} else if (a <= -1.25e+116) {
		tmp = y * (z / a);
	} else if (a <= -3.8e-16) {
		tmp = x;
	} else if (a <= -6.5e-292) {
		tmp = x / (t / z);
	} else if (a <= 5.8e+74) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.5e+165:
		tmp = x
	elif a <= -1.25e+116:
		tmp = y * (z / a)
	elif a <= -3.8e-16:
		tmp = x
	elif a <= -6.5e-292:
		tmp = x / (t / z)
	elif a <= 5.8e+74:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.5e+165)
		tmp = x;
	elseif (a <= -1.25e+116)
		tmp = Float64(y * Float64(z / a));
	elseif (a <= -3.8e-16)
		tmp = x;
	elseif (a <= -6.5e-292)
		tmp = Float64(x / Float64(t / z));
	elseif (a <= 5.8e+74)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.5e+165)
		tmp = x;
	elseif (a <= -1.25e+116)
		tmp = y * (z / a);
	elseif (a <= -3.8e-16)
		tmp = x;
	elseif (a <= -6.5e-292)
		tmp = x / (t / z);
	elseif (a <= 5.8e+74)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.5e+165], x, If[LessEqual[a, -1.25e+116], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.8e-16], x, If[LessEqual[a, -6.5e-292], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e+74], y, x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.49999999999999996e165 or -1.25000000000000006e116 < a < -3.80000000000000012e-16 or 5.8000000000000005e74 < a

   1. Initial program 70.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 89.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   4. Taylor expanded in a around inf 53.0%

      \[\leadsto \color{blue}{x} \]

   if -3.49999999999999996e165 < a < -1.25000000000000006e116

   1. Initial program 76.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 99.6%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. fma-def 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{1}{\frac{a - t}{z - t}}, x\right)} \]

      5. clear-num 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{z - t}{a - t}}, x\right) \]

   5. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   6. Taylor expanded in y around inf 83.8%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. div-sub 83.8%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   8. Simplified 83.8%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   9. Taylor expanded in t around 0 51.1%

      \[\leadsto y \cdot \color{blue}{\frac{z}{a}} \]

   if -3.80000000000000012e-16 < a < -6.4999999999999997e-292

   1. Initial program 71.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 73.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 73.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   4. Taylor expanded in z around -inf 67.8%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   5. Taylor expanded in a around 0 46.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate-*r/ 46.7%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} \]

      2. associate-*r* 46.7%

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot z\right) \cdot \left(y - x\right)}}{t} \]

      3. mul-1-neg 46.7%

         \[\leadsto \frac{\color{blue}{\left(-z\right)} \cdot \left(y - x\right)}{t} \]

   7. Simplified 46.7%

      \[\leadsto \color{blue}{\frac{\left(-z\right) \cdot \left(y - x\right)}{t}} \]

   8. Taylor expanded in y around 0 34.6%

      \[\leadsto \color{blue}{\frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. associate-/l* 42.3%

         \[\leadsto \color{blue}{\frac{x}{\frac{t}{z}}} \]

   10. Simplified 42.3%

       \[\leadsto \color{blue}{\frac{x}{\frac{t}{z}}} \]

   if -6.4999999999999997e-292 < a < 5.8000000000000005e74

   1. Initial program 64.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 75.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 75.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   4. Taylor expanded in t around inf 51.3%

      \[\leadsto \color{blue}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{+116}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-292}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+74}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 25: 37.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{+116}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+74}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.5e+165)
   x
   (if (<= a -1.12e+116)
     (/ z (/ a y))
     (if (<= a -6.2e-16)
       x
       (if (<= a -1.1e-291) (/ x (/ t z)) (if (<= a 4.5e+74) y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e+165) {
		tmp = x;
	} else if (a <= -1.12e+116) {
		tmp = z / (a / y);
	} else if (a <= -6.2e-16) {
		tmp = x;
	} else if (a <= -1.1e-291) {
		tmp = x / (t / z);
	} else if (a <= 4.5e+74) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.5d+165)) then
        tmp = x
    else if (a <= (-1.12d+116)) then
        tmp = z / (a / y)
    else if (a <= (-6.2d-16)) then
        tmp = x
    else if (a <= (-1.1d-291)) then
        tmp = x / (t / z)
    else if (a <= 4.5d+74) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e+165) {
		tmp = x;
	} else if (a <= -1.12e+116) {
		tmp = z / (a / y);
	} else if (a <= -6.2e-16) {
		tmp = x;
	} else if (a <= -1.1e-291) {
		tmp = x / (t / z);
	} else if (a <= 4.5e+74) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.5e+165:
		tmp = x
	elif a <= -1.12e+116:
		tmp = z / (a / y)
	elif a <= -6.2e-16:
		tmp = x
	elif a <= -1.1e-291:
		tmp = x / (t / z)
	elif a <= 4.5e+74:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.5e+165)
		tmp = x;
	elseif (a <= -1.12e+116)
		tmp = Float64(z / Float64(a / y));
	elseif (a <= -6.2e-16)
		tmp = x;
	elseif (a <= -1.1e-291)
		tmp = Float64(x / Float64(t / z));
	elseif (a <= 4.5e+74)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.5e+165)
		tmp = x;
	elseif (a <= -1.12e+116)
		tmp = z / (a / y);
	elseif (a <= -6.2e-16)
		tmp = x;
	elseif (a <= -1.1e-291)
		tmp = x / (t / z);
	elseif (a <= 4.5e+74)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.5e+165], x, If[LessEqual[a, -1.12e+116], N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.2e-16], x, If[LessEqual[a, -1.1e-291], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e+74], y, x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.49999999999999996e165 or -1.12e116 < a < -6.2000000000000002e-16 or 4.5e74 < a

   1. Initial program 70.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 89.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   4. Taylor expanded in a around inf 53.0%

      \[\leadsto \color{blue}{x} \]

   if -3.49999999999999996e165 < a < -1.12e116

   1. Initial program 76.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   4. Taylor expanded in z around -inf 43.7%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   5. Taylor expanded in a around inf 43.5%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 59.1%

         \[\leadsto \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   7. Simplified 59.1%

      \[\leadsto \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   8. Taylor expanded in y around inf 51.1%

      \[\leadsto \frac{z}{\color{blue}{\frac{a}{y}}} \]

   if -6.2000000000000002e-16 < a < -1.10000000000000001e-291

   1. Initial program 71.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 73.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 73.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   4. Taylor expanded in z around -inf 67.8%

      \[\leadsto \color{blue}{\frac{z \cdot \left(y - x\right)}{a - t}} \]

   5. Taylor expanded in a around 0 46.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate-*r/ 46.7%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} \]

      2. associate-*r* 46.7%

         \[\leadsto \frac{\color{blue}{\left(-1 \cdot z\right) \cdot \left(y - x\right)}}{t} \]

      3. mul-1-neg 46.7%

         \[\leadsto \frac{\color{blue}{\left(-z\right)} \cdot \left(y - x\right)}{t} \]

   7. Simplified 46.7%

      \[\leadsto \color{blue}{\frac{\left(-z\right) \cdot \left(y - x\right)}{t}} \]

   8. Taylor expanded in y around 0 34.6%

      \[\leadsto \color{blue}{\frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. associate-/l* 42.3%

         \[\leadsto \color{blue}{\frac{x}{\frac{t}{z}}} \]

   10. Simplified 42.3%

       \[\leadsto \color{blue}{\frac{x}{\frac{t}{z}}} \]

   if -1.10000000000000001e-291 < a < 4.5e74

   1. Initial program 64.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 75.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 75.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   4. Taylor expanded in t around inf 51.3%

      \[\leadsto \color{blue}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+165}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{+116}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+74}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 26: 50.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+99}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.5e+99) y (if (<= t 4.4e+88) (* x (- 1.0 (/ z a))) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.5e+99) {
		tmp = y;
	} else if (t <= 4.4e+88) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = 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 (t <= (-9.5d+99)) then
        tmp = y
    else if (t <= 4.4d+88) then
        tmp = x * (1.0d0 - (z / a))
    else
        tmp = 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 (t <= -9.5e+99) {
		tmp = y;
	} else if (t <= 4.4e+88) {
		tmp = x * (1.0 - (z / a));
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.5e+99:
		tmp = y
	elif t <= 4.4e+88:
		tmp = x * (1.0 - (z / a))
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.5e+99)
		tmp = y;
	elseif (t <= 4.4e+88)
		tmp = Float64(x * Float64(1.0 - Float64(z / a)));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.5e+99)
		tmp = y;
	elseif (t <= 4.4e+88)
		tmp = x * (1.0 - (z / a));
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.5e+99], y, If[LessEqual[t, 4.4e+88], N[(x * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if t < -9.49999999999999908e99 or 4.40000000000000017e88 < t

   1. Initial program 36.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 63.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 63.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   4. Taylor expanded in t around inf 57.2%

      \[\leadsto \color{blue}{y} \]

   if -9.49999999999999908e99 < t < 4.40000000000000017e88

   1. Initial program 86.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 91.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Step-by-step derivation

      1. +-commutative 91.8%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 95.4%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 95.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. fma-def 95.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{1}{\frac{a - t}{z - t}}, x\right)} \]

      5. clear-num 95.5%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{z - t}{a - t}}, x\right) \]

   5. Applied egg-rr 95.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]

   6. Taylor expanded in x around inf 60.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{z - t}{a - t}\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 60.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-\frac{z - t}{a - t}\right)}\right) \]

      2. unsub-neg 60.6%

         \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z - t}{a - t}\right)} \]

   8. Simplified 60.6%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z - t}{a - t}\right)} \]

   9. Taylor expanded in t around 0 50.7%

      \[\leadsto x \cdot \color{blue}{\left(1 - \frac{z}{a}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+99}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 27: 40.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -15500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -15500000000000.0) x (if (<= a 5.2e+75) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -15500000000000.0) {
		tmp = x;
	} else if (a <= 5.2e+75) {
		tmp = y;
	} 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 <= (-15500000000000.0d0)) then
        tmp = x
    else if (a <= 5.2d+75) then
        tmp = y
    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 <= -15500000000000.0) {
		tmp = x;
	} else if (a <= 5.2e+75) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -15500000000000.0:
		tmp = x
	elif a <= 5.2e+75:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -15500000000000.0)
		tmp = x;
	elseif (a <= 5.2e+75)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -15500000000000.0)
		tmp = x;
	elseif (a <= 5.2e+75)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -15500000000000.0], x, If[LessEqual[a, 5.2e+75], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.55e13 or 5.1999999999999997e75 < a

   1. Initial program 71.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 90.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   4. Taylor expanded in a around inf 49.5%

      \[\leadsto \color{blue}{x} \]

   if -1.55e13 < a < 5.1999999999999997e75

   1. Initial program 67.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 74.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 74.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   4. Taylor expanded in t around inf 37.8%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -15500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+75}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 28: 25.5% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

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
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x;
}

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 69.1%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. associate-*l/ 81.9%

      \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

3. Simplified 81.9%

   \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]

4. Taylor expanded in a around inf 25.1%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 25.1%

   \[\leadsto x \]

Developer target: 87.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - 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 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - 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 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))