Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.8% → 91.0%

Time: 26.2s

Alternatives: 21

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-300}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-260}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t\_1, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
   (if (<= t_2 -2e-300)
     t_2
     (if (<= t_2 2e-260)
       (+ t (/ (- x t) (/ z (- y a))))
       (fma (- y z) t_1 x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if (t_2 <= -2e-300) {
		tmp = t_2;
	} else if (t_2 <= 2e-260) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = fma((y - z), t_1, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_2 <= -2e-300)
		tmp = t_2;
	elseif (t_2 <= 2e-260)
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = fma(Float64(y - z), t_1, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-300], t$95$2, If[LessEqual[t$95$2, 2e-260], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.00000000000000005e-300

   1. Initial program 88.2%

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

   if -2.00000000000000005e-300 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.99999999999999992e-260

   1. Initial program 6.4%

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

   3. Taylor expanded in z around inf 83.4%

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

      1. associate--l+ 83.4%

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

      2. distribute-lft-out-- 83.4%

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

      3. div-sub 83.4%

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

      4. mul-1-neg 83.4%

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

      5. unsub-neg 83.4%

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

      6. distribute-rgt-out-- 83.6%

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

      7. associate-/l* 97.1%

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

   5. Simplified 97.1%

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

   if 1.99999999999999992e-260 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.7%

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

      1. +-commutative 89.7%

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

      2. fma-def 89.7%

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

   3. Simplified 89.7%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-300}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{-260}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 50.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+147}:\\ \;\;\;\;t + \frac{a}{\frac{-z}{x}}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+94}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-61}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-261}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-244}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-204}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* y (/ (- t x) a))))
   (if (<= z -1.45e+147)
     (+ t (/ a (/ (- z) x)))
     (if (<= z -4e+94)
       (/ (- y) (/ z (- t x)))
       (if (<= z -2.3e-61)
         (- t (* t (/ y z)))
         (if (<= z -1.15e-164)
           t_1
           (if (<= z -2.3e-261)
             t_2
             (if (<= z 2.1e-244)
               t_1
               (if (<= z 4.3e-204)
                 t_2
                 (if (<= z 2.9e-114) t_1 (+ t (* y (/ x z)))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = y * ((t - x) / a);
	double tmp;
	if (z <= -1.45e+147) {
		tmp = t + (a / (-z / x));
	} else if (z <= -4e+94) {
		tmp = -y / (z / (t - x));
	} else if (z <= -2.3e-61) {
		tmp = t - (t * (y / z));
	} else if (z <= -1.15e-164) {
		tmp = t_1;
	} else if (z <= -2.3e-261) {
		tmp = t_2;
	} else if (z <= 2.1e-244) {
		tmp = t_1;
	} else if (z <= 4.3e-204) {
		tmp = t_2;
	} else if (z <= 2.9e-114) {
		tmp = t_1;
	} else {
		tmp = t + (y * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    t_2 = y * ((t - x) / a)
    if (z <= (-1.45d+147)) then
        tmp = t + (a / (-z / x))
    else if (z <= (-4d+94)) then
        tmp = -y / (z / (t - x))
    else if (z <= (-2.3d-61)) then
        tmp = t - (t * (y / z))
    else if (z <= (-1.15d-164)) then
        tmp = t_1
    else if (z <= (-2.3d-261)) then
        tmp = t_2
    else if (z <= 2.1d-244) then
        tmp = t_1
    else if (z <= 4.3d-204) then
        tmp = t_2
    else if (z <= 2.9d-114) then
        tmp = t_1
    else
        tmp = t + (y * (x / z))
    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 - (y / a));
	double t_2 = y * ((t - x) / a);
	double tmp;
	if (z <= -1.45e+147) {
		tmp = t + (a / (-z / x));
	} else if (z <= -4e+94) {
		tmp = -y / (z / (t - x));
	} else if (z <= -2.3e-61) {
		tmp = t - (t * (y / z));
	} else if (z <= -1.15e-164) {
		tmp = t_1;
	} else if (z <= -2.3e-261) {
		tmp = t_2;
	} else if (z <= 2.1e-244) {
		tmp = t_1;
	} else if (z <= 4.3e-204) {
		tmp = t_2;
	} else if (z <= 2.9e-114) {
		tmp = t_1;
	} else {
		tmp = t + (y * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = y * ((t - x) / a)
	tmp = 0
	if z <= -1.45e+147:
		tmp = t + (a / (-z / x))
	elif z <= -4e+94:
		tmp = -y / (z / (t - x))
	elif z <= -2.3e-61:
		tmp = t - (t * (y / z))
	elif z <= -1.15e-164:
		tmp = t_1
	elif z <= -2.3e-261:
		tmp = t_2
	elif z <= 2.1e-244:
		tmp = t_1
	elif z <= 4.3e-204:
		tmp = t_2
	elif z <= 2.9e-114:
		tmp = t_1
	else:
		tmp = t + (y * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (z <= -1.45e+147)
		tmp = Float64(t + Float64(a / Float64(Float64(-z) / x)));
	elseif (z <= -4e+94)
		tmp = Float64(Float64(-y) / Float64(z / Float64(t - x)));
	elseif (z <= -2.3e-61)
		tmp = Float64(t - Float64(t * Float64(y / z)));
	elseif (z <= -1.15e-164)
		tmp = t_1;
	elseif (z <= -2.3e-261)
		tmp = t_2;
	elseif (z <= 2.1e-244)
		tmp = t_1;
	elseif (z <= 4.3e-204)
		tmp = t_2;
	elseif (z <= 2.9e-114)
		tmp = t_1;
	else
		tmp = Float64(t + Float64(y * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = y * ((t - x) / a);
	tmp = 0.0;
	if (z <= -1.45e+147)
		tmp = t + (a / (-z / x));
	elseif (z <= -4e+94)
		tmp = -y / (z / (t - x));
	elseif (z <= -2.3e-61)
		tmp = t - (t * (y / z));
	elseif (z <= -1.15e-164)
		tmp = t_1;
	elseif (z <= -2.3e-261)
		tmp = t_2;
	elseif (z <= 2.1e-244)
		tmp = t_1;
	elseif (z <= 4.3e-204)
		tmp = t_2;
	elseif (z <= 2.9e-114)
		tmp = t_1;
	else
		tmp = t + (y * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+147], N[(t + N[(a / N[((-z) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4e+94], N[((-y) / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e-61], N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e-164], t$95$1, If[LessEqual[z, -2.3e-261], t$95$2, If[LessEqual[z, 2.1e-244], t$95$1, If[LessEqual[z, 4.3e-204], t$95$2, If[LessEqual[z, 2.9e-114], t$95$1, N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.4499999999999999e147

   1. Initial program 61.8%

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

   3. Taylor expanded in z around inf 59.2%

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

      1. associate--l+ 59.2%

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

      2. distribute-lft-out-- 59.2%

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

      3. div-sub 59.2%

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

      4. mul-1-neg 59.2%

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

      5. unsub-neg 59.2%

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

      6. distribute-rgt-out-- 59.2%

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

      7. associate-/l* 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in y around 0 53.0%

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

      1. sub-neg 53.0%

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

      2. mul-1-neg 53.0%

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

      3. remove-double-neg 53.0%

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

      4. associate-/l* 65.9%

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

   8. Simplified 65.9%

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

   9. Taylor expanded in t around 0 65.5%

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

       1. associate-*r/ 65.5%

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

       2. neg-mul-1 65.5%

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

   11. Simplified 65.5%

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

   if -1.4499999999999999e147 < z < -4.0000000000000001e94

   1. Initial program 91.3%

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

   3. Taylor expanded in z around inf 47.9%

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

      1. associate--l+ 47.9%

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

      2. distribute-lft-out-- 47.9%

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

      3. div-sub 47.9%

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

      4. mul-1-neg 47.9%

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

      5. unsub-neg 47.9%

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

      6. distribute-rgt-out-- 48.0%

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

      7. associate-/l* 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in y around -inf 40.1%

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

      1. mul-1-neg 40.1%

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

      2. associate-/l* 65.9%

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

      3. distribute-neg-frac 65.9%

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

   8. Simplified 65.9%

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

   if -4.0000000000000001e94 < z < -2.29999999999999992e-61

   1. Initial program 80.5%

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

   3. Taylor expanded in z around inf 73.8%

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

      1. associate--l+ 73.8%

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

      2. distribute-lft-out-- 73.8%

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

      3. div-sub 73.8%

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

      4. mul-1-neg 73.8%

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

      5. unsub-neg 73.8%

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

      6. distribute-rgt-out-- 73.8%

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

      7. associate-/l* 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in y around inf 68.0%

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

   7. Taylor expanded in t around inf 58.3%

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

      1. associate-*r/ 58.3%

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

   9. Simplified 58.3%

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

   if -2.29999999999999992e-61 < z < -1.14999999999999993e-164 or -2.3e-261 < z < 2.10000000000000002e-244 or 4.3000000000000003e-204 < z < 2.89999999999999997e-114

   1. Initial program 91.0%

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

   3. Taylor expanded in x around inf 76.8%

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

      1. mul-1-neg 76.8%

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

      2. unsub-neg 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in z around 0 76.9%

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

   if -1.14999999999999993e-164 < z < -2.3e-261 or 2.10000000000000002e-244 < z < 4.3000000000000003e-204

   1. Initial program 89.4%

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

   3. Taylor expanded in a around inf 79.6%

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

   4. Taylor expanded in y around inf 70.3%

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

      1. div-sub 70.3%

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

   6. Simplified 70.3%

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

   if 2.89999999999999997e-114 < z

   1. Initial program 65.6%

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

   3. Taylor expanded in z around inf 69.6%

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

      1. associate--l+ 69.6%

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

      2. distribute-lft-out-- 69.6%

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

      3. div-sub 69.7%

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

      4. mul-1-neg 69.7%

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

      5. unsub-neg 69.7%

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

      6. distribute-rgt-out-- 69.8%

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

      7. associate-/l* 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in y around inf 67.2%

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

   7. Taylor expanded in t around 0 55.3%

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

      1. mul-1-neg 55.3%

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

      2. *-commutative 55.3%

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

      3. associate-*r/ 57.6%

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

      4. distribute-rgt-neg-in 57.6%

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

      5. distribute-neg-frac 57.6%

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

   9. Simplified 57.6%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+147}:\\ \;\;\;\;t + \frac{a}{\frac{-z}{x}}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+94}:\\ \;\;\;\;\frac{-y}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-61}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-164}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-261}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-244}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-204}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-300} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-260}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -2e-300) (not (<= t_1 2e-260)))
     t_1
     (+ t (/ (- x t) (/ z (- y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-300) || !(t_1 <= 2e-260)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-2d-300)) .or. (.not. (t_1 <= 2d-260))) then
        tmp = t_1
    else
        tmp = t + ((x - t) / (z / (y - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if ((t_1 <= -2e-300) || !(t_1 <= 2e-260)) {
		tmp = t_1;
	} else {
		tmp = t + ((x - t) / (z / (y - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if (t_1 <= -2e-300) or not (t_1 <= 2e-260):
		tmp = t_1
	else:
		tmp = t + ((x - t) / (z / (y - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if ((t_1 <= -2e-300) || !(t_1 <= 2e-260))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if ((t_1 <= -2e-300) || ~((t_1 <= 2e-260)))
		tmp = t_1;
	else
		tmp = t + ((x - t) / (z / (y - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-300], N[Not[LessEqual[t$95$1, 2e-260]], $MachinePrecision]], t$95$1, N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2.00000000000000005e-300 or 1.99999999999999992e-260 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 89.0%

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

   if -2.00000000000000005e-300 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 1.99999999999999992e-260

   1. Initial program 6.4%

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

   3. Taylor expanded in z around inf 83.4%

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

      1. associate--l+ 83.4%

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

      2. distribute-lft-out-- 83.4%

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

      3. div-sub 83.4%

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

      4. mul-1-neg 83.4%

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

      5. unsub-neg 83.4%

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

      6. distribute-rgt-out-- 83.6%

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

      7. associate-/l* 97.1%

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

   5. Simplified 97.1%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-300} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{-260}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := t - t \cdot \frac{y}{z}\\ t_3 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{-61}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-261}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-244}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-203}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a))))
        (t_2 (- t (* t (/ y z))))
        (t_3 (* y (/ (- t x) a))))
   (if (<= z -2.45e-61)
     t_2
     (if (<= z -4.6e-163)
       t_1
       (if (<= z -3.1e-261)
         t_3
         (if (<= z 9.8e-244)
           t_1
           (if (<= z 1.12e-203) t_3 (if (<= z 2.9e-114) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t - (t * (y / z));
	double t_3 = y * ((t - x) / a);
	double tmp;
	if (z <= -2.45e-61) {
		tmp = t_2;
	} else if (z <= -4.6e-163) {
		tmp = t_1;
	} else if (z <= -3.1e-261) {
		tmp = t_3;
	} else if (z <= 9.8e-244) {
		tmp = t_1;
	} else if (z <= 1.12e-203) {
		tmp = t_3;
	} else if (z <= 2.9e-114) {
		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) :: t_3
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    t_2 = t - (t * (y / z))
    t_3 = y * ((t - x) / a)
    if (z <= (-2.45d-61)) then
        tmp = t_2
    else if (z <= (-4.6d-163)) then
        tmp = t_1
    else if (z <= (-3.1d-261)) then
        tmp = t_3
    else if (z <= 9.8d-244) then
        tmp = t_1
    else if (z <= 1.12d-203) then
        tmp = t_3
    else if (z <= 2.9d-114) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = t - (t * (y / z));
	double t_3 = y * ((t - x) / a);
	double tmp;
	if (z <= -2.45e-61) {
		tmp = t_2;
	} else if (z <= -4.6e-163) {
		tmp = t_1;
	} else if (z <= -3.1e-261) {
		tmp = t_3;
	} else if (z <= 9.8e-244) {
		tmp = t_1;
	} else if (z <= 1.12e-203) {
		tmp = t_3;
	} else if (z <= 2.9e-114) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = t - (t * (y / z))
	t_3 = y * ((t - x) / a)
	tmp = 0
	if z <= -2.45e-61:
		tmp = t_2
	elif z <= -4.6e-163:
		tmp = t_1
	elif z <= -3.1e-261:
		tmp = t_3
	elif z <= 9.8e-244:
		tmp = t_1
	elif z <= 1.12e-203:
		tmp = t_3
	elif z <= 2.9e-114:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(t - Float64(t * Float64(y / z)))
	t_3 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (z <= -2.45e-61)
		tmp = t_2;
	elseif (z <= -4.6e-163)
		tmp = t_1;
	elseif (z <= -3.1e-261)
		tmp = t_3;
	elseif (z <= 9.8e-244)
		tmp = t_1;
	elseif (z <= 1.12e-203)
		tmp = t_3;
	elseif (z <= 2.9e-114)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = t - (t * (y / z));
	t_3 = y * ((t - x) / a);
	tmp = 0.0;
	if (z <= -2.45e-61)
		tmp = t_2;
	elseif (z <= -4.6e-163)
		tmp = t_1;
	elseif (z <= -3.1e-261)
		tmp = t_3;
	elseif (z <= 9.8e-244)
		tmp = t_1;
	elseif (z <= 1.12e-203)
		tmp = t_3;
	elseif (z <= 2.9e-114)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.45e-61], t$95$2, If[LessEqual[z, -4.6e-163], t$95$1, If[LessEqual[z, -3.1e-261], t$95$3, If[LessEqual[z, 9.8e-244], t$95$1, If[LessEqual[z, 1.12e-203], t$95$3, If[LessEqual[z, 2.9e-114], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.45000000000000001e-61 or 2.89999999999999997e-114 < z

   1. Initial program 69.5%

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

   3. Taylor expanded in z around inf 66.8%

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

      1. associate--l+ 66.8%

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

      2. distribute-lft-out-- 66.8%

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

      3. div-sub 66.8%

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

      4. mul-1-neg 66.8%

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

      5. unsub-neg 66.8%

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

      6. distribute-rgt-out-- 66.9%

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

      7. associate-/l* 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in y around inf 67.3%

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

   7. Taylor expanded in t around inf 47.8%

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

      1. associate-*r/ 52.2%

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

   9. Simplified 52.2%

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

   if -2.45000000000000001e-61 < z < -4.5999999999999999e-163 or -3.0999999999999998e-261 < z < 9.80000000000000029e-244 or 1.12e-203 < z < 2.89999999999999997e-114

   1. Initial program 91.0%

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

   3. Taylor expanded in x around inf 76.8%

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

      1. mul-1-neg 76.8%

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

      2. unsub-neg 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in z around 0 76.9%

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

   if -4.5999999999999999e-163 < z < -3.0999999999999998e-261 or 9.80000000000000029e-244 < z < 1.12e-203

   1. Initial program 89.4%

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

   3. Taylor expanded in a around inf 79.6%

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

   4. Taylor expanded in y around inf 70.3%

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

      1. div-sub 70.3%

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

   6. Simplified 70.3%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-61}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-163}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-261}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-244}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-203}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ t_2 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{-61}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-165}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-262}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-244}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-202}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))) (t_2 (* y (/ (- t x) a))))
   (if (<= z -1.32e-61)
     (- t (* t (/ y z)))
     (if (<= z -3.6e-165)
       t_1
       (if (<= z -1.2e-262)
         t_2
         (if (<= z 1.1e-244)
           t_1
           (if (<= z 5.4e-202)
             t_2
             (if (<= z 2.9e-114) t_1 (+ t (* y (/ x z)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double t_2 = y * ((t - x) / a);
	double tmp;
	if (z <= -1.32e-61) {
		tmp = t - (t * (y / z));
	} else if (z <= -3.6e-165) {
		tmp = t_1;
	} else if (z <= -1.2e-262) {
		tmp = t_2;
	} else if (z <= 1.1e-244) {
		tmp = t_1;
	} else if (z <= 5.4e-202) {
		tmp = t_2;
	} else if (z <= 2.9e-114) {
		tmp = t_1;
	} else {
		tmp = t + (y * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    t_2 = y * ((t - x) / a)
    if (z <= (-1.32d-61)) then
        tmp = t - (t * (y / z))
    else if (z <= (-3.6d-165)) then
        tmp = t_1
    else if (z <= (-1.2d-262)) then
        tmp = t_2
    else if (z <= 1.1d-244) then
        tmp = t_1
    else if (z <= 5.4d-202) then
        tmp = t_2
    else if (z <= 2.9d-114) then
        tmp = t_1
    else
        tmp = t + (y * (x / z))
    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 - (y / a));
	double t_2 = y * ((t - x) / a);
	double tmp;
	if (z <= -1.32e-61) {
		tmp = t - (t * (y / z));
	} else if (z <= -3.6e-165) {
		tmp = t_1;
	} else if (z <= -1.2e-262) {
		tmp = t_2;
	} else if (z <= 1.1e-244) {
		tmp = t_1;
	} else if (z <= 5.4e-202) {
		tmp = t_2;
	} else if (z <= 2.9e-114) {
		tmp = t_1;
	} else {
		tmp = t + (y * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	t_2 = y * ((t - x) / a)
	tmp = 0
	if z <= -1.32e-61:
		tmp = t - (t * (y / z))
	elif z <= -3.6e-165:
		tmp = t_1
	elif z <= -1.2e-262:
		tmp = t_2
	elif z <= 1.1e-244:
		tmp = t_1
	elif z <= 5.4e-202:
		tmp = t_2
	elif z <= 2.9e-114:
		tmp = t_1
	else:
		tmp = t + (y * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	t_2 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (z <= -1.32e-61)
		tmp = Float64(t - Float64(t * Float64(y / z)));
	elseif (z <= -3.6e-165)
		tmp = t_1;
	elseif (z <= -1.2e-262)
		tmp = t_2;
	elseif (z <= 1.1e-244)
		tmp = t_1;
	elseif (z <= 5.4e-202)
		tmp = t_2;
	elseif (z <= 2.9e-114)
		tmp = t_1;
	else
		tmp = Float64(t + Float64(y * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	t_2 = y * ((t - x) / a);
	tmp = 0.0;
	if (z <= -1.32e-61)
		tmp = t - (t * (y / z));
	elseif (z <= -3.6e-165)
		tmp = t_1;
	elseif (z <= -1.2e-262)
		tmp = t_2;
	elseif (z <= 1.1e-244)
		tmp = t_1;
	elseif (z <= 5.4e-202)
		tmp = t_2;
	elseif (z <= 2.9e-114)
		tmp = t_1;
	else
		tmp = t + (y * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.32e-61], N[(t - N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e-165], t$95$1, If[LessEqual[z, -1.2e-262], t$95$2, If[LessEqual[z, 1.1e-244], t$95$1, If[LessEqual[z, 5.4e-202], t$95$2, If[LessEqual[z, 2.9e-114], t$95$1, N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.32000000000000002e-61

   1. Initial program 74.1%

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

   3. Taylor expanded in z around inf 63.6%

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

      1. associate--l+ 63.6%

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

      2. distribute-lft-out-- 63.6%

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

      3. div-sub 63.6%

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

      4. mul-1-neg 63.6%

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

      5. unsub-neg 63.6%

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

      6. distribute-rgt-out-- 63.6%

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

      7. associate-/l* 75.7%

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

   5. Simplified 75.7%

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

   6. Taylor expanded in y around inf 67.5%

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

   7. Taylor expanded in t around inf 51.1%

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

      1. associate-*r/ 55.1%

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

   9. Simplified 55.1%

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

   if -1.32000000000000002e-61 < z < -3.59999999999999984e-165 or -1.2e-262 < z < 1.09999999999999992e-244 or 5.3999999999999997e-202 < z < 2.89999999999999997e-114

   1. Initial program 91.0%

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

   3. Taylor expanded in x around inf 76.8%

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

      1. mul-1-neg 76.8%

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

      2. unsub-neg 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in z around 0 76.9%

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

   if -3.59999999999999984e-165 < z < -1.2e-262 or 1.09999999999999992e-244 < z < 5.3999999999999997e-202

   1. Initial program 89.4%

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

   3. Taylor expanded in a around inf 79.6%

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

   4. Taylor expanded in y around inf 70.3%

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

      1. div-sub 70.3%

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

   6. Simplified 70.3%

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

   if 2.89999999999999997e-114 < z

   1. Initial program 65.6%

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

   3. Taylor expanded in z around inf 69.6%

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

      1. associate--l+ 69.6%

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

      2. distribute-lft-out-- 69.6%

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

      3. div-sub 69.7%

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

      4. mul-1-neg 69.7%

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

      5. unsub-neg 69.7%

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

      6. distribute-rgt-out-- 69.8%

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

      7. associate-/l* 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in y around inf 67.2%

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

   7. Taylor expanded in t around 0 55.3%

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

      1. mul-1-neg 55.3%

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

      2. *-commutative 55.3%

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

      3. associate-*r/ 57.6%

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

      4. distribute-rgt-neg-in 57.6%

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

      5. distribute-neg-frac 57.6%

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

   9. Simplified 57.6%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-61}:\\ \;\;\;\;t - t \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-165}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-262}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-244}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-202}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-265}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-242}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-44}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5600000000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.05e+62)
   x
   (if (<= a -3.5e-265)
     t
     (if (<= a 1.15e-242)
       (* x (/ y z))
       (if (<= a 1.22e-44) t (if (<= a 5600000000.0) (* t (/ y a)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.05e+62) {
		tmp = x;
	} else if (a <= -3.5e-265) {
		tmp = t;
	} else if (a <= 1.15e-242) {
		tmp = x * (y / z);
	} else if (a <= 1.22e-44) {
		tmp = t;
	} else if (a <= 5600000000.0) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.05d+62)) then
        tmp = x
    else if (a <= (-3.5d-265)) then
        tmp = t
    else if (a <= 1.15d-242) then
        tmp = x * (y / z)
    else if (a <= 1.22d-44) then
        tmp = t
    else if (a <= 5600000000.0d0) then
        tmp = t * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.05e+62) {
		tmp = x;
	} else if (a <= -3.5e-265) {
		tmp = t;
	} else if (a <= 1.15e-242) {
		tmp = x * (y / z);
	} else if (a <= 1.22e-44) {
		tmp = t;
	} else if (a <= 5600000000.0) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.05e+62:
		tmp = x
	elif a <= -3.5e-265:
		tmp = t
	elif a <= 1.15e-242:
		tmp = x * (y / z)
	elif a <= 1.22e-44:
		tmp = t
	elif a <= 5600000000.0:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.05e+62)
		tmp = x;
	elseif (a <= -3.5e-265)
		tmp = t;
	elseif (a <= 1.15e-242)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.22e-44)
		tmp = t;
	elseif (a <= 5600000000.0)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.05e+62)
		tmp = x;
	elseif (a <= -3.5e-265)
		tmp = t;
	elseif (a <= 1.15e-242)
		tmp = x * (y / z);
	elseif (a <= 1.22e-44)
		tmp = t;
	elseif (a <= 5600000000.0)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.05e+62], x, If[LessEqual[a, -3.5e-265], t, If[LessEqual[a, 1.15e-242], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.22e-44], t, If[LessEqual[a, 5600000000.0], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.05e62 or 5.6e9 < a

   1. Initial program 86.1%

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

   3. Taylor expanded in a around inf 49.0%

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

   if -1.05e62 < a < -3.50000000000000015e-265 or 1.14999999999999992e-242 < a < 1.22e-44

   1. Initial program 70.1%

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

   3. Taylor expanded in z around inf 37.7%

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

   if -3.50000000000000015e-265 < a < 1.14999999999999992e-242

   1. Initial program 75.0%

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

   3. Taylor expanded in x around inf 33.1%

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

      1. mul-1-neg 33.1%

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

      2. unsub-neg 33.1%

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

   5. Simplified 33.1%

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

   6. Taylor expanded in a around 0 44.3%

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

   if 1.22e-44 < a < 5.6e9

   1. Initial program 93.1%

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

   3. Taylor expanded in a around inf 73.0%

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

   4. Taylor expanded in t around inf 53.7%

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

      1. div-sub 53.7%

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

   6. Simplified 53.7%

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

   7. Taylor expanded in y around inf 54.3%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-265}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-242}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-44}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5600000000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+66}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-263}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.7 \cdot 10^{-243}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-46}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5600000000:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.2e+66)
   x
   (if (<= a -1.25e-263)
     t
     (if (<= a 6.7e-243)
       (* x (/ y z))
       (if (<= a 1.85e-46) t (if (<= a 5600000000.0) (/ t (/ a y)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.2e+66) {
		tmp = x;
	} else if (a <= -1.25e-263) {
		tmp = t;
	} else if (a <= 6.7e-243) {
		tmp = x * (y / z);
	} else if (a <= 1.85e-46) {
		tmp = t;
	} else if (a <= 5600000000.0) {
		tmp = t / (a / 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 <= (-9.2d+66)) then
        tmp = x
    else if (a <= (-1.25d-263)) then
        tmp = t
    else if (a <= 6.7d-243) then
        tmp = x * (y / z)
    else if (a <= 1.85d-46) then
        tmp = t
    else if (a <= 5600000000.0d0) then
        tmp = t / (a / 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 <= -9.2e+66) {
		tmp = x;
	} else if (a <= -1.25e-263) {
		tmp = t;
	} else if (a <= 6.7e-243) {
		tmp = x * (y / z);
	} else if (a <= 1.85e-46) {
		tmp = t;
	} else if (a <= 5600000000.0) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.2e+66:
		tmp = x
	elif a <= -1.25e-263:
		tmp = t
	elif a <= 6.7e-243:
		tmp = x * (y / z)
	elif a <= 1.85e-46:
		tmp = t
	elif a <= 5600000000.0:
		tmp = t / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.2e+66)
		tmp = x;
	elseif (a <= -1.25e-263)
		tmp = t;
	elseif (a <= 6.7e-243)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.85e-46)
		tmp = t;
	elseif (a <= 5600000000.0)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.2e+66)
		tmp = x;
	elseif (a <= -1.25e-263)
		tmp = t;
	elseif (a <= 6.7e-243)
		tmp = x * (y / z);
	elseif (a <= 1.85e-46)
		tmp = t;
	elseif (a <= 5600000000.0)
		tmp = t / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.2e+66], x, If[LessEqual[a, -1.25e-263], t, If[LessEqual[a, 6.7e-243], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e-46], t, If[LessEqual[a, 5600000000.0], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.2e66 or 5.6e9 < a

   1. Initial program 86.1%

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

   3. Taylor expanded in a around inf 49.0%

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

   if -9.2e66 < a < -1.25000000000000002e-263 or 6.70000000000000009e-243 < a < 1.84999999999999992e-46

   1. Initial program 70.1%

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

   3. Taylor expanded in z around inf 37.7%

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

   if -1.25000000000000002e-263 < a < 6.70000000000000009e-243

   1. Initial program 75.0%

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

   3. Taylor expanded in x around inf 33.1%

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

      1. mul-1-neg 33.1%

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

      2. unsub-neg 33.1%

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

   5. Simplified 33.1%

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

   6. Taylor expanded in a around 0 44.3%

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

   if 1.84999999999999992e-46 < a < 5.6e9

   1. Initial program 93.1%

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

   3. Taylor expanded in x around 0 74.0%

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

      1. associate-/l* 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in z around 0 54.5%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.2 \cdot 10^{+66}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-263}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 6.7 \cdot 10^{-243}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-46}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5600000000:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-265}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-247}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-41}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4500000000:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.2e+61)
   x
   (if (<= a -4.7e-265)
     t
     (if (<= a 2.5e-247)
       (/ x (/ z y))
       (if (<= a 2.2e-41) t (if (<= a 4500000000.0) (/ t (/ a y)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.2e+61) {
		tmp = x;
	} else if (a <= -4.7e-265) {
		tmp = t;
	} else if (a <= 2.5e-247) {
		tmp = x / (z / y);
	} else if (a <= 2.2e-41) {
		tmp = t;
	} else if (a <= 4500000000.0) {
		tmp = t / (a / 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 <= (-7.2d+61)) then
        tmp = x
    else if (a <= (-4.7d-265)) then
        tmp = t
    else if (a <= 2.5d-247) then
        tmp = x / (z / y)
    else if (a <= 2.2d-41) then
        tmp = t
    else if (a <= 4500000000.0d0) then
        tmp = t / (a / 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 <= -7.2e+61) {
		tmp = x;
	} else if (a <= -4.7e-265) {
		tmp = t;
	} else if (a <= 2.5e-247) {
		tmp = x / (z / y);
	} else if (a <= 2.2e-41) {
		tmp = t;
	} else if (a <= 4500000000.0) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.2e+61:
		tmp = x
	elif a <= -4.7e-265:
		tmp = t
	elif a <= 2.5e-247:
		tmp = x / (z / y)
	elif a <= 2.2e-41:
		tmp = t
	elif a <= 4500000000.0:
		tmp = t / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.2e+61)
		tmp = x;
	elseif (a <= -4.7e-265)
		tmp = t;
	elseif (a <= 2.5e-247)
		tmp = Float64(x / Float64(z / y));
	elseif (a <= 2.2e-41)
		tmp = t;
	elseif (a <= 4500000000.0)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.2e+61)
		tmp = x;
	elseif (a <= -4.7e-265)
		tmp = t;
	elseif (a <= 2.5e-247)
		tmp = x / (z / y);
	elseif (a <= 2.2e-41)
		tmp = t;
	elseif (a <= 4500000000.0)
		tmp = t / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.2e+61], x, If[LessEqual[a, -4.7e-265], t, If[LessEqual[a, 2.5e-247], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e-41], t, If[LessEqual[a, 4500000000.0], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.20000000000000021e61 or 4.5e9 < a

   1. Initial program 86.1%

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

   3. Taylor expanded in a around inf 49.0%

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

   if -7.20000000000000021e61 < a < -4.69999999999999986e-265 or 2.49999999999999989e-247 < a < 2.2e-41

   1. Initial program 70.1%

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

   3. Taylor expanded in z around inf 37.7%

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

   if -4.69999999999999986e-265 < a < 2.49999999999999989e-247

   1. Initial program 75.0%

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

   3. Taylor expanded in x around inf 33.1%

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

      1. mul-1-neg 33.1%

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

      2. unsub-neg 33.1%

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

   5. Simplified 33.1%

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

   6. Taylor expanded in a around 0 39.5%

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

      1. associate-/l* 44.4%

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

   8. Simplified 44.4%

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

   if 2.2e-41 < a < 4.5e9

   1. Initial program 93.1%

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

   3. Taylor expanded in x around 0 74.0%

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

      1. associate-/l* 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in z around 0 54.5%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-265}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-247}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-41}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4500000000:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.46 \cdot 10^{-279}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{-247}:\\ \;\;\;\;\frac{-t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5500000000:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.1e+67)
   x
   (if (<= a -1.46e-279)
     t
     (if (<= a 9.4e-247)
       (/ (- t) (/ z y))
       (if (<= a 1.75e-45) t (if (<= a 5500000000.0) (/ t (/ a y)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e+67) {
		tmp = x;
	} else if (a <= -1.46e-279) {
		tmp = t;
	} else if (a <= 9.4e-247) {
		tmp = -t / (z / y);
	} else if (a <= 1.75e-45) {
		tmp = t;
	} else if (a <= 5500000000.0) {
		tmp = t / (a / 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 <= (-2.1d+67)) then
        tmp = x
    else if (a <= (-1.46d-279)) then
        tmp = t
    else if (a <= 9.4d-247) then
        tmp = -t / (z / y)
    else if (a <= 1.75d-45) then
        tmp = t
    else if (a <= 5500000000.0d0) then
        tmp = t / (a / 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 <= -2.1e+67) {
		tmp = x;
	} else if (a <= -1.46e-279) {
		tmp = t;
	} else if (a <= 9.4e-247) {
		tmp = -t / (z / y);
	} else if (a <= 1.75e-45) {
		tmp = t;
	} else if (a <= 5500000000.0) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.1e+67:
		tmp = x
	elif a <= -1.46e-279:
		tmp = t
	elif a <= 9.4e-247:
		tmp = -t / (z / y)
	elif a <= 1.75e-45:
		tmp = t
	elif a <= 5500000000.0:
		tmp = t / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.1e+67)
		tmp = x;
	elseif (a <= -1.46e-279)
		tmp = t;
	elseif (a <= 9.4e-247)
		tmp = Float64(Float64(-t) / Float64(z / y));
	elseif (a <= 1.75e-45)
		tmp = t;
	elseif (a <= 5500000000.0)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.1e+67)
		tmp = x;
	elseif (a <= -1.46e-279)
		tmp = t;
	elseif (a <= 9.4e-247)
		tmp = -t / (z / y);
	elseif (a <= 1.75e-45)
		tmp = t;
	elseif (a <= 5500000000.0)
		tmp = t / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.1e+67], x, If[LessEqual[a, -1.46e-279], t, If[LessEqual[a, 9.4e-247], N[((-t) / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.75e-45], t, If[LessEqual[a, 5500000000.0], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.1000000000000001e67 or 5.5e9 < a

   1. Initial program 86.1%

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

   3. Taylor expanded in a around inf 49.0%

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

   if -2.1000000000000001e67 < a < -1.46000000000000005e-279 or 9.3999999999999996e-247 < a < 1.75e-45

   1. Initial program 70.5%

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

   3. Taylor expanded in z around inf 37.1%

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

   if -1.46000000000000005e-279 < a < 9.3999999999999996e-247

   1. Initial program 73.0%

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

   3. Taylor expanded in x around 0 59.9%

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

      1. associate-/l* 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in y around inf 51.8%

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

      1. associate-/l* 58.1%

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

   8. Simplified 58.1%

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

   9. Taylor expanded in a around 0 51.8%

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

       1. mul-1-neg 51.8%

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

       2. associate-/l* 58.1%

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

       3. distribute-neg-frac 58.1%

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

   11. Simplified 58.1%

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

   if 1.75e-45 < a < 5.5e9

   1. Initial program 93.1%

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

   3. Taylor expanded in x around 0 74.0%

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

      1. associate-/l* 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in z around 0 54.5%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.46 \cdot 10^{-279}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 9.4 \cdot 10^{-247}:\\ \;\;\;\;\frac{-t}{\frac{z}{y}}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 5500000000:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+168}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-309}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= y -4.4e+168)
     (* y (/ t (- a z)))
     (if (<= y -1.6e-39)
       t_1
       (if (<= y 8e-309) t (if (<= y 3.5e+82) t_1 (* y (/ (- t x) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (y <= -4.4e+168) {
		tmp = y * (t / (a - z));
	} else if (y <= -1.6e-39) {
		tmp = t_1;
	} else if (y <= 8e-309) {
		tmp = t;
	} else if (y <= 3.5e+82) {
		tmp = t_1;
	} else {
		tmp = y * ((t - x) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (y <= (-4.4d+168)) then
        tmp = y * (t / (a - z))
    else if (y <= (-1.6d-39)) then
        tmp = t_1
    else if (y <= 8d-309) then
        tmp = t
    else if (y <= 3.5d+82) then
        tmp = t_1
    else
        tmp = y * ((t - x) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (y <= -4.4e+168) {
		tmp = y * (t / (a - z));
	} else if (y <= -1.6e-39) {
		tmp = t_1;
	} else if (y <= 8e-309) {
		tmp = t;
	} else if (y <= 3.5e+82) {
		tmp = t_1;
	} else {
		tmp = y * ((t - x) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if y <= -4.4e+168:
		tmp = y * (t / (a - z))
	elif y <= -1.6e-39:
		tmp = t_1
	elif y <= 8e-309:
		tmp = t
	elif y <= 3.5e+82:
		tmp = t_1
	else:
		tmp = y * ((t - x) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (y <= -4.4e+168)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (y <= -1.6e-39)
		tmp = t_1;
	elseif (y <= 8e-309)
		tmp = t;
	elseif (y <= 3.5e+82)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(t - x) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (y <= -4.4e+168)
		tmp = y * (t / (a - z));
	elseif (y <= -1.6e-39)
		tmp = t_1;
	elseif (y <= 8e-309)
		tmp = t;
	elseif (y <= 3.5e+82)
		tmp = t_1;
	else
		tmp = y * ((t - x) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+168], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.6e-39], t$95$1, If[LessEqual[y, 8e-309], t, If[LessEqual[y, 3.5e+82], t$95$1, N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.4000000000000004e168

   1. Initial program 87.7%

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

   3. Taylor expanded in x around 0 39.9%

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

      1. associate-/l* 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in y around inf 39.9%

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

      1. associate-/l* 52.6%

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

   8. Simplified 52.6%

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

      1. associate-/r/ 49.5%

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

   10. Applied egg-rr 49.5%

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

   if -4.4000000000000004e168 < y < -1.5999999999999999e-39 or 8.0000000000000003e-309 < y < 3.5e82

   1. Initial program 75.6%

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

   3. Taylor expanded in x around inf 48.3%

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

      1. mul-1-neg 48.3%

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

      2. unsub-neg 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in z around 0 46.9%

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

   if -1.5999999999999999e-39 < y < 8.0000000000000003e-309

   1. Initial program 62.5%

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

   3. Taylor expanded in z around inf 55.1%

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

   if 3.5e82 < y

   1. Initial program 95.9%

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

   3. Taylor expanded in a around inf 63.9%

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

   4. Taylor expanded in y around inf 59.9%

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

      1. div-sub 61.9%

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

   6. Simplified 61.9%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+168}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-309}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.9 \cdot 10^{-78}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+63}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= x -2.2e+59)
     t_1
     (if (<= x -5.9e-78)
       (* (- t x) (/ y (- a z)))
       (if (<= x 6.8e+63) (* (- y z) (/ t (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -2.2e+59) {
		tmp = t_1;
	} else if (x <= -5.9e-78) {
		tmp = (t - x) * (y / (a - z));
	} else if (x <= 6.8e+63) {
		tmp = (y - z) * (t / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (x <= (-2.2d+59)) then
        tmp = t_1
    else if (x <= (-5.9d-78)) then
        tmp = (t - x) * (y / (a - z))
    else if (x <= 6.8d+63) then
        tmp = (y - z) * (t / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (x <= -2.2e+59) {
		tmp = t_1;
	} else if (x <= -5.9e-78) {
		tmp = (t - x) * (y / (a - z));
	} else if (x <= 6.8e+63) {
		tmp = (y - z) * (t / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if x <= -2.2e+59:
		tmp = t_1
	elif x <= -5.9e-78:
		tmp = (t - x) * (y / (a - z))
	elif x <= 6.8e+63:
		tmp = (y - z) * (t / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (x <= -2.2e+59)
		tmp = t_1;
	elseif (x <= -5.9e-78)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (x <= 6.8e+63)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (x <= -2.2e+59)
		tmp = t_1;
	elseif (x <= -5.9e-78)
		tmp = (t - x) * (y / (a - z));
	elseif (x <= 6.8e+63)
		tmp = (y - z) * (t / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.2e+59], t$95$1, If[LessEqual[x, -5.9e-78], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e+63], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2e59 or 6.7999999999999997e63 < x

   1. Initial program 70.2%

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

   3. Taylor expanded in x around inf 62.6%

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

      1. mul-1-neg 62.6%

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

      2. unsub-neg 62.6%

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

   5. Simplified 62.6%

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

   6. Taylor expanded in z around 0 55.5%

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

   if -2.2e59 < x < -5.9000000000000004e-78

   1. Initial program 88.1%

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

   3. Taylor expanded in y around inf 78.3%

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

      1. div-sub 78.3%

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

      2. associate-*r/ 67.6%

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

      3. associate-/l* 78.4%

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

      4. associate-/r/ 78.4%

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

   5. Simplified 78.4%

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

   if -5.9000000000000004e-78 < x < 6.7999999999999997e63

   1. Initial program 82.4%

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

      1. add-cube-cbrt 81.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \cdot \sqrt[3]{x + \left(y - z\right) \cdot \frac{t - x}{a - z}}\right) \cdot \sqrt[3]{x + \left(y - z\right) \cdot \frac{t - x}{a - z}}} \]

      2. pow3 81.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(y - z\right) \cdot \frac{t - x}{a - z}}\right)}^{3}} \]

      3. +-commutative 81.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x}}\right)}^{3} \]

      4. fma-udef 81.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 81.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in x around 0 65.5%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. pow-base-1 65.5%

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

      2. associate-*l/ 65.0%

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

      3. *-lft-identity 65.0%

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

   7. Simplified 65.0%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -5.9 \cdot 10^{-78}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+63}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+151}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-61}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.6e+151)
   (+ t (/ a (/ z (- t x))))
   (if (<= z -4.1e-61)
     (* (- y z) (/ t (- a z)))
     (if (<= z 9.2e-99) (+ x (/ y (/ a (- t x)))) (+ t (* y (/ x z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.6e+151) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -4.1e-61) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 9.2e-99) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + (y * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.6d+151)) then
        tmp = t + (a / (z / (t - x)))
    else if (z <= (-4.1d-61)) then
        tmp = (y - z) * (t / (a - z))
    else if (z <= 9.2d-99) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t + (y * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.6e+151) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -4.1e-61) {
		tmp = (y - z) * (t / (a - z));
	} else if (z <= 9.2e-99) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + (y * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.6e+151:
		tmp = t + (a / (z / (t - x)))
	elif z <= -4.1e-61:
		tmp = (y - z) * (t / (a - z))
	elif z <= 9.2e-99:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t + (y * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.6e+151)
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	elseif (z <= -4.1e-61)
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	elseif (z <= 9.2e-99)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t + Float64(y * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.6e+151)
		tmp = t + (a / (z / (t - x)));
	elseif (z <= -4.1e-61)
		tmp = (y - z) * (t / (a - z));
	elseif (z <= 9.2e-99)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t + (y * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.6e+151], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.1e-61], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-99], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.6e151

   1. Initial program 61.8%

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

   3. Taylor expanded in z around inf 59.2%

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

      1. associate--l+ 59.2%

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

      2. distribute-lft-out-- 59.2%

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

      3. div-sub 59.2%

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

      4. mul-1-neg 59.2%

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

      5. unsub-neg 59.2%

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

      6. distribute-rgt-out-- 59.2%

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

      7. associate-/l* 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in y around 0 53.0%

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

      1. sub-neg 53.0%

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

      2. mul-1-neg 53.0%

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

      3. remove-double-neg 53.0%

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

      4. associate-/l* 65.9%

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

   8. Simplified 65.9%

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

   if -3.6e151 < z < -4.09999999999999999e-61

   1. Initial program 83.4%

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

      1. add-cube-cbrt 82.3%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \cdot \sqrt[3]{x + \left(y - z\right) \cdot \frac{t - x}{a - z}}\right) \cdot \sqrt[3]{x + \left(y - z\right) \cdot \frac{t - x}{a - z}}} \]

      2. pow3 82.2%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(y - z\right) \cdot \frac{t - x}{a - z}}\right)}^{3}} \]

      3. +-commutative 82.2%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x}}\right)}^{3} \]

      4. fma-udef 82.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 82.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in x around 0 54.3%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. pow-base-1 54.3%

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

      2. associate-*l/ 61.0%

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

      3. *-lft-identity 61.0%

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

   7. Simplified 61.0%

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

   if -4.09999999999999999e-61 < z < 9.1999999999999994e-99

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 78.9%

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

      1. associate-/l* 80.5%

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

   5. Simplified 80.5%

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

   if 9.1999999999999994e-99 < z

   1. Initial program 63.9%

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

   3. Taylor expanded in z around inf 72.8%

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

      1. associate--l+ 72.8%

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

      2. distribute-lft-out-- 72.8%

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

      3. div-sub 72.9%

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

      4. mul-1-neg 72.9%

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

      5. unsub-neg 72.9%

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

      6. distribute-rgt-out-- 73.0%

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

      7. associate-/l* 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in y around inf 69.1%

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

   7. Taylor expanded in t around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. *-commutative 57.9%

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

      3. associate-*r/ 59.2%

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

      4. distribute-rgt-neg-in 59.2%

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

      5. distribute-neg-frac 59.2%

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

   9. Simplified 59.2%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+151}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-61}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-308}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+250}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= y -5.5e-39)
     t_1
     (if (<= y 2e-308) t (if (<= y 9.8e+250) t_1 (* t (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (y <= -5.5e-39) {
		tmp = t_1;
	} else if (y <= 2e-308) {
		tmp = t;
	} else if (y <= 9.8e+250) {
		tmp = t_1;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (y <= (-5.5d-39)) then
        tmp = t_1
    else if (y <= 2d-308) then
        tmp = t
    else if (y <= 9.8d+250) then
        tmp = t_1
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (y <= -5.5e-39) {
		tmp = t_1;
	} else if (y <= 2e-308) {
		tmp = t;
	} else if (y <= 9.8e+250) {
		tmp = t_1;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if y <= -5.5e-39:
		tmp = t_1
	elif y <= 2e-308:
		tmp = t
	elif y <= 9.8e+250:
		tmp = t_1
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (y <= -5.5e-39)
		tmp = t_1;
	elseif (y <= 2e-308)
		tmp = t;
	elseif (y <= 9.8e+250)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (y <= -5.5e-39)
		tmp = t_1;
	elseif (y <= 2e-308)
		tmp = t;
	elseif (y <= 9.8e+250)
		tmp = t_1;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e-39], t$95$1, If[LessEqual[y, 2e-308], t, If[LessEqual[y, 9.8e+250], t$95$1, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.50000000000000018e-39 or 1.9999999999999998e-308 < y < 9.79999999999999986e250

   1. Initial program 81.0%

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

   3. Taylor expanded in x around inf 49.5%

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

      1. mul-1-neg 49.5%

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

      2. unsub-neg 49.5%

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

   5. Simplified 49.5%

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

   6. Taylor expanded in z around 0 43.6%

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

   if -5.50000000000000018e-39 < y < 1.9999999999999998e-308

   1. Initial program 62.5%

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

   3. Taylor expanded in z around inf 55.1%

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

   if 9.79999999999999986e250 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in a around inf 75.1%

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

   4. Taylor expanded in t around inf 62.4%

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

      1. div-sub 62.4%

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

   6. Simplified 62.4%

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

   7. Taylor expanded in y around inf 62.4%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-308}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+250}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 38.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-307}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y a)))))
   (if (<= y -2.6e-39)
     t_1
     (if (<= y -8.2e-307) t (if (<= y 2.9e+87) t_1 (* y (/ (- t x) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (y <= -2.6e-39) {
		tmp = t_1;
	} else if (y <= -8.2e-307) {
		tmp = t;
	} else if (y <= 2.9e+87) {
		tmp = t_1;
	} else {
		tmp = y * ((t - x) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / a))
    if (y <= (-2.6d-39)) then
        tmp = t_1
    else if (y <= (-8.2d-307)) then
        tmp = t
    else if (y <= 2.9d+87) then
        tmp = t_1
    else
        tmp = y * ((t - x) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (1.0 - (y / a));
	double tmp;
	if (y <= -2.6e-39) {
		tmp = t_1;
	} else if (y <= -8.2e-307) {
		tmp = t;
	} else if (y <= 2.9e+87) {
		tmp = t_1;
	} else {
		tmp = y * ((t - x) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (1.0 - (y / a))
	tmp = 0
	if y <= -2.6e-39:
		tmp = t_1
	elif y <= -8.2e-307:
		tmp = t
	elif y <= 2.9e+87:
		tmp = t_1
	else:
		tmp = y * ((t - x) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(1.0 - Float64(y / a)))
	tmp = 0.0
	if (y <= -2.6e-39)
		tmp = t_1;
	elseif (y <= -8.2e-307)
		tmp = t;
	elseif (y <= 2.9e+87)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(t - x) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (1.0 - (y / a));
	tmp = 0.0;
	if (y <= -2.6e-39)
		tmp = t_1;
	elseif (y <= -8.2e-307)
		tmp = t;
	elseif (y <= 2.9e+87)
		tmp = t_1;
	else
		tmp = y * ((t - x) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e-39], t$95$1, If[LessEqual[y, -8.2e-307], t, If[LessEqual[y, 2.9e+87], t$95$1, N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e-39 or -8.20000000000000064e-307 < y < 2.8999999999999998e87

   1. Initial program 78.0%

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

   3. Taylor expanded in x around inf 48.8%

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

      1. mul-1-neg 48.8%

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

      2. unsub-neg 48.8%

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

   5. Simplified 48.8%

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

   6. Taylor expanded in z around 0 43.4%

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

   if -2.6e-39 < y < -8.20000000000000064e-307

   1. Initial program 62.5%

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

   3. Taylor expanded in z around inf 55.1%

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

   if 2.8999999999999998e87 < y

   1. Initial program 95.9%

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

   3. Taylor expanded in a around inf 63.9%

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

   4. Taylor expanded in y around inf 59.9%

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

      1. div-sub 61.9%

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

   6. Simplified 61.9%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-307}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-65} \lor \neg \left(z \leq 8 \cdot 10^{-99}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.8e-65) (not (<= z 8e-99)))
   (+ t (/ (- x t) (/ z (- y a))))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.8e-65) || !(z <= 8e-99)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.8d-65)) .or. (.not. (z <= 8d-99))) then
        tmp = t + ((x - t) / (z / (y - a)))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.8e-65) || !(z <= 8e-99)) {
		tmp = t + ((x - t) / (z / (y - a)));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.8e-65) or not (z <= 8e-99):
		tmp = t + ((x - t) / (z / (y - a)))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.8e-65) || !(z <= 8e-99))
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / Float64(y - a))));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.8e-65) || ~((z <= 8e-99)))
		tmp = t + ((x - t) / (z / (y - a)));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.8e-65], N[Not[LessEqual[z, 8e-99]], $MachinePrecision]], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8000000000000003e-65 or 8.0000000000000002e-99 < z

   1. Initial program 68.7%

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

   3. Taylor expanded in z around inf 68.4%

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

      1. associate--l+ 68.4%

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

      2. distribute-lft-out-- 68.4%

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

      3. div-sub 68.5%

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

      4. mul-1-neg 68.5%

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

      5. unsub-neg 68.5%

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

      6. distribute-rgt-out-- 68.5%

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

      7. associate-/l* 78.0%

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

   5. Simplified 78.0%

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

   if -4.8000000000000003e-65 < z < 8.0000000000000002e-99

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 78.9%

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

      1. associate-/l* 80.5%

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

   5. Simplified 80.5%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-65} \lor \neg \left(z \leq 8 \cdot 10^{-99}\right):\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y - a}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 38.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.15 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4400000000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.15e+62)
   x
   (if (<= a 3.5e-45) t (if (<= a 4400000000.0) (* t (/ y a)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.15e+62) {
		tmp = x;
	} else if (a <= 3.5e-45) {
		tmp = t;
	} else if (a <= 4400000000.0) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.15d+62)) then
        tmp = x
    else if (a <= 3.5d-45) then
        tmp = t
    else if (a <= 4400000000.0d0) then
        tmp = t * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.15e+62) {
		tmp = x;
	} else if (a <= 3.5e-45) {
		tmp = t;
	} else if (a <= 4400000000.0) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.15e+62:
		tmp = x
	elif a <= 3.5e-45:
		tmp = t
	elif a <= 4400000000.0:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.15e+62)
		tmp = x;
	elseif (a <= 3.5e-45)
		tmp = t;
	elseif (a <= 4400000000.0)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.15e+62)
		tmp = x;
	elseif (a <= 3.5e-45)
		tmp = t;
	elseif (a <= 4400000000.0)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.15e+62], x, If[LessEqual[a, 3.5e-45], t, If[LessEqual[a, 4400000000.0], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.14999999999999999e62 or 4.4e9 < a

   1. Initial program 86.1%

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

   3. Taylor expanded in a around inf 49.0%

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

   if -3.14999999999999999e62 < a < 3.5e-45

   1. Initial program 70.7%

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

   3. Taylor expanded in z around inf 35.3%

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

   if 3.5e-45 < a < 4.4e9

   1. Initial program 93.1%

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

   3. Taylor expanded in a around inf 73.0%

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

   4. Taylor expanded in t around inf 53.7%

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

      1. div-sub 53.7%

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

   6. Simplified 53.7%

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

   7. Taylor expanded in y around inf 54.3%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.15 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{elif}\;a \leq 4400000000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 57.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+60} \lor \neg \left(x \leq 6.3 \cdot 10^{+66}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -5.5e+60) (not (<= x 6.3e+66)))
   (* x (- 1.0 (/ y a)))
   (* (- y z) (/ t (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -5.5e+60) || !(x <= 6.3e+66)) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = (y - z) * (t / (a - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-5.5d+60)) .or. (.not. (x <= 6.3d+66))) then
        tmp = x * (1.0d0 - (y / a))
    else
        tmp = (y - z) * (t / (a - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -5.5e+60) || !(x <= 6.3e+66)) {
		tmp = x * (1.0 - (y / a));
	} else {
		tmp = (y - z) * (t / (a - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -5.5e+60) or not (x <= 6.3e+66):
		tmp = x * (1.0 - (y / a))
	else:
		tmp = (y - z) * (t / (a - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -5.5e+60) || !(x <= 6.3e+66))
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	else
		tmp = Float64(Float64(y - z) * Float64(t / Float64(a - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -5.5e+60) || ~((x <= 6.3e+66)))
		tmp = x * (1.0 - (y / a));
	else
		tmp = (y - z) * (t / (a - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -5.5e+60], N[Not[LessEqual[x, 6.3e+66]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5000000000000001e60 or 6.2999999999999998e66 < x

   1. Initial program 70.0%

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

   3. Taylor expanded in x around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. unsub-neg 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in z around 0 55.9%

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

   if -5.5000000000000001e60 < x < 6.2999999999999998e66

   1. Initial program 83.5%

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

      1. add-cube-cbrt 82.3%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \left(y - z\right) \cdot \frac{t - x}{a - z}} \cdot \sqrt[3]{x + \left(y - z\right) \cdot \frac{t - x}{a - z}}\right) \cdot \sqrt[3]{x + \left(y - z\right) \cdot \frac{t - x}{a - z}}} \]

      2. pow3 82.3%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(y - z\right) \cdot \frac{t - x}{a - z}}\right)}^{3}} \]

      3. +-commutative 82.3%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z} + x}}\right)}^{3} \]

      4. fma-udef 82.3%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)}}\right)}^{3} \]

   4. Applied egg-rr 82.3%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)}\right)}^{3}} \]

   5. Taylor expanded in x around 0 61.3%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \frac{t \cdot \left(y - z\right)}{a - z}} \]
   6. Step-by-step derivation

      1. pow-base-1 61.3%

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

      2. associate-*l/ 64.0%

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

      3. *-lft-identity 64.0%

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

   7. Simplified 64.0%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+60} \lor \neg \left(x \leq 6.3 \cdot 10^{+66}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 67.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-63} \lor \neg \left(z \leq 3.45 \cdot 10^{-99}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.3e-63) (not (<= z 3.45e-99)))
   (+ t (* y (/ (- x t) z)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e-63) || !(z <= 3.45e-99)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.3d-63)) .or. (.not. (z <= 3.45d-99))) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.3e-63) || !(z <= 3.45e-99)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.3e-63) or not (z <= 3.45e-99):
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.3e-63) || !(z <= 3.45e-99))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.3e-63) || ~((z <= 3.45e-99)))
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.3e-63], N[Not[LessEqual[z, 3.45e-99]], $MachinePrecision]], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3000000000000001e-63 or 3.4500000000000002e-99 < z

   1. Initial program 68.7%

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

   3. Taylor expanded in z around inf 68.4%

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

      1. associate--l+ 68.4%

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

      2. distribute-lft-out-- 68.4%

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

      3. div-sub 68.5%

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

      4. mul-1-neg 68.5%

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

      5. unsub-neg 68.5%

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

      6. distribute-rgt-out-- 68.5%

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

      7. associate-/l* 78.0%

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

   5. Simplified 78.0%

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

   6. Taylor expanded in y around inf 68.3%

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

      1. associate-/r/ 67.5%

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

   8. Applied egg-rr 67.5%

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

   if -1.3000000000000001e-63 < z < 3.4500000000000002e-99

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 78.9%

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

      1. associate-/l* 80.5%

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

   5. Simplified 80.5%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-63} \lor \neg \left(z \leq 3.45 \cdot 10^{-99}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 68.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-61}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e-61)
   (+ t (* y (/ (- x t) z)))
   (if (<= z 2.75e-99) (+ x (/ y (/ a (- t x)))) (+ t (/ (- x t) (/ z y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e-61) {
		tmp = t + (y * ((x - t) / z));
	} else if (z <= 2.75e-99) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2d-61)) then
        tmp = t + (y * ((x - t) / z))
    else if (z <= 2.75d-99) then
        tmp = x + (y / (a / (t - x)))
    else
        tmp = t + ((x - t) / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e-61) {
		tmp = t + (y * ((x - t) / z));
	} else if (z <= 2.75e-99) {
		tmp = x + (y / (a / (t - x)));
	} else {
		tmp = t + ((x - t) / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e-61:
		tmp = t + (y * ((x - t) / z))
	elif z <= 2.75e-99:
		tmp = x + (y / (a / (t - x)))
	else:
		tmp = t + ((x - t) / (z / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e-61)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	elseif (z <= 2.75e-99)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	else
		tmp = Float64(t + Float64(Float64(x - t) / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e-61)
		tmp = t + (y * ((x - t) / z));
	elseif (z <= 2.75e-99)
		tmp = x + (y / (a / (t - x)));
	else
		tmp = t + ((x - t) / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e-61], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.75e-99], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x - t), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0000000000000001e-61

   1. Initial program 74.1%

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

   3. Taylor expanded in z around inf 63.6%

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

      1. associate--l+ 63.6%

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

      2. distribute-lft-out-- 63.6%

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

      3. div-sub 63.6%

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

      4. mul-1-neg 63.6%

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

      5. unsub-neg 63.6%

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

      6. distribute-rgt-out-- 63.6%

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

      7. associate-/l* 75.7%

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

   5. Simplified 75.7%

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

   6. Taylor expanded in y around inf 67.5%

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

      1. associate-/r/ 67.5%

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

   8. Applied egg-rr 67.5%

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

   if -2.0000000000000001e-61 < z < 2.74999999999999995e-99

   1. Initial program 90.7%

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

   3. Taylor expanded in z around 0 78.9%

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

      1. associate-/l* 80.5%

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

   5. Simplified 80.5%

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

   if 2.74999999999999995e-99 < z

   1. Initial program 63.9%

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

   3. Taylor expanded in z around inf 72.8%

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

      1. associate--l+ 72.8%

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

      2. distribute-lft-out-- 72.8%

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

      3. div-sub 72.9%

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

      4. mul-1-neg 72.9%

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

      5. unsub-neg 72.9%

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

      6. distribute-rgt-out-- 73.0%

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

      7. associate-/l* 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in y around inf 69.1%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-61}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-99}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x - t}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 38.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+155}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.1e+64) x (if (<= a 6.4e+155) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e+64) {
		tmp = x;
	} else if (a <= 6.4e+155) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.1d+64)) then
        tmp = x
    else if (a <= 6.4d+155) then
        tmp = t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e+64) {
		tmp = x;
	} else if (a <= 6.4e+155) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.1e+64:
		tmp = x
	elif a <= 6.4e+155:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.1e+64)
		tmp = x;
	elseif (a <= 6.4e+155)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.1e+64)
		tmp = x;
	elseif (a <= 6.4e+155)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.1e+64], x, If[LessEqual[a, 6.4e+155], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.10000000000000001e64 or 6.40000000000000024e155 < a

   1. Initial program 87.1%

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

   3. Taylor expanded in a around inf 52.9%

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

   if -1.10000000000000001e64 < a < 6.40000000000000024e155

   1. Initial program 73.8%

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

   3. Taylor expanded in z around inf 33.7%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+155}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 25.5% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.7%

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

3. Taylor expanded in z around inf 26.4%

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

4. Final simplification 26.4%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024040 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))