Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Percentage Accurate: 97.0% → 96.9%

Time: 10.4s

Alternatives: 15

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{t}{\frac{z - y}{x - y}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.5%

   \[\frac{x - y}{z - y} \cdot t \]
2. Step-by-step derivation

   1. associate-*l/ 83.5%

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

   2. associate-/l* 88.5%

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

3. Simplified 88.5%

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

   1. associate-*r/ 83.5%

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

   2. associate-*l/ 97.5%

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

   3. *-commutative 97.5%

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

   4. clear-num 97.1%

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

   5. un-div-inv 97.6%

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

6. Applied egg-rr 97.6%

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

7. Final simplification 97.6%

   \[\leadsto \frac{t}{\frac{z - y}{x - y}} \]
8. Add Preprocessing

Alternative 2: 75.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ t_2 := t \cdot \frac{x}{z - y}\\ t_3 := t \cdot \frac{y - x}{y}\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-261}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-224}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+129}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y))))
        (t_2 (* t (/ x (- z y))))
        (t_3 (* t (/ (- y x) y))))
   (if (<= y -5.6e-49)
     t_1
     (if (<= y -7e-261)
       t_2
       (if (<= y 8.5e-224)
         (* (- x y) (/ t z))
         (if (<= y 1.7e+54)
           t_2
           (if (<= y 2.5e+129)
             t_3
             (if (<= y 1.95e+137) t_2 (if (<= y 9.2e+188) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double t_2 = t * (x / (z - y));
	double t_3 = t * ((y - x) / y);
	double tmp;
	if (y <= -5.6e-49) {
		tmp = t_1;
	} else if (y <= -7e-261) {
		tmp = t_2;
	} else if (y <= 8.5e-224) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.7e+54) {
		tmp = t_2;
	} else if (y <= 2.5e+129) {
		tmp = t_3;
	} else if (y <= 1.95e+137) {
		tmp = t_2;
	} else if (y <= 9.2e+188) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t / (1.0d0 - (z / y))
    t_2 = t * (x / (z - y))
    t_3 = t * ((y - x) / y)
    if (y <= (-5.6d-49)) then
        tmp = t_1
    else if (y <= (-7d-261)) then
        tmp = t_2
    else if (y <= 8.5d-224) then
        tmp = (x - y) * (t / z)
    else if (y <= 1.7d+54) then
        tmp = t_2
    else if (y <= 2.5d+129) then
        tmp = t_3
    else if (y <= 1.95d+137) then
        tmp = t_2
    else if (y <= 9.2d+188) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double t_2 = t * (x / (z - y));
	double t_3 = t * ((y - x) / y);
	double tmp;
	if (y <= -5.6e-49) {
		tmp = t_1;
	} else if (y <= -7e-261) {
		tmp = t_2;
	} else if (y <= 8.5e-224) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.7e+54) {
		tmp = t_2;
	} else if (y <= 2.5e+129) {
		tmp = t_3;
	} else if (y <= 1.95e+137) {
		tmp = t_2;
	} else if (y <= 9.2e+188) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (1.0 - (z / y))
	t_2 = t * (x / (z - y))
	t_3 = t * ((y - x) / y)
	tmp = 0
	if y <= -5.6e-49:
		tmp = t_1
	elif y <= -7e-261:
		tmp = t_2
	elif y <= 8.5e-224:
		tmp = (x - y) * (t / z)
	elif y <= 1.7e+54:
		tmp = t_2
	elif y <= 2.5e+129:
		tmp = t_3
	elif y <= 1.95e+137:
		tmp = t_2
	elif y <= 9.2e+188:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(1.0 - Float64(z / y)))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	t_3 = Float64(t * Float64(Float64(y - x) / y))
	tmp = 0.0
	if (y <= -5.6e-49)
		tmp = t_1;
	elseif (y <= -7e-261)
		tmp = t_2;
	elseif (y <= 8.5e-224)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 1.7e+54)
		tmp = t_2;
	elseif (y <= 2.5e+129)
		tmp = t_3;
	elseif (y <= 1.95e+137)
		tmp = t_2;
	elseif (y <= 9.2e+188)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (1.0 - (z / y));
	t_2 = t * (x / (z - y));
	t_3 = t * ((y - x) / y);
	tmp = 0.0;
	if (y <= -5.6e-49)
		tmp = t_1;
	elseif (y <= -7e-261)
		tmp = t_2;
	elseif (y <= 8.5e-224)
		tmp = (x - y) * (t / z);
	elseif (y <= 1.7e+54)
		tmp = t_2;
	elseif (y <= 2.5e+129)
		tmp = t_3;
	elseif (y <= 1.95e+137)
		tmp = t_2;
	elseif (y <= 9.2e+188)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.6e-49], t$95$1, If[LessEqual[y, -7e-261], t$95$2, If[LessEqual[y, 8.5e-224], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+54], t$95$2, If[LessEqual[y, 2.5e+129], t$95$3, If[LessEqual[y, 1.95e+137], t$95$2, If[LessEqual[y, 9.2e+188], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.59999999999999995e-49 or 1.95000000000000015e137 < y < 9.20000000000000046e188

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 78.2%

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

      2. associate-/l* 80.8%

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

   3. Simplified 80.8%

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

      1. associate-*r/ 78.2%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.9%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. div-sub 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in x around 0 81.6%

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

       1. mul-1-neg 81.6%

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

       2. unsub-neg 81.6%

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

   11. Simplified 81.6%

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

   if -5.59999999999999995e-49 < y < -6.9999999999999995e-261 or 8.4999999999999996e-224 < y < 1.7e54 or 2.5000000000000001e129 < y < 1.95000000000000015e137

   1. Initial program 97.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 81.5%

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

   if -6.9999999999999995e-261 < y < 8.4999999999999996e-224

   1. Initial program 87.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

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

      2. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 96.7%

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

   7. Simplified 96.7%

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

   if 1.7e54 < y < 2.5000000000000001e129 or 9.20000000000000046e188 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 60.8%

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

      2. associate-/l* 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in z around 0 56.6%

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

      1. associate-*r/ 56.6%

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

      2. mul-1-neg 56.6%

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

      3. distribute-lft-neg-out 56.6%

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

      4. *-commutative 56.6%

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

   7. Simplified 56.6%

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

   8. Taylor expanded in x around 0 75.0%

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

      1. mul-1-neg 75.0%

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

      2. unsub-neg 75.0%

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

   10. Simplified 75.0%

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

   11. Taylor expanded in y around 0 54.0%

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

       1. distribute-lft-out-- 56.6%

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

       2. associate-/l* 95.6%

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

   13. Simplified 95.6%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-49}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-261}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-224}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+129}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+188}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z - y}\\ t_2 := t \cdot \frac{y - x}{y}\\ t_3 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -5.1 \cdot 10^{-49}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-259}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-225}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+54}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+129}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+192}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- z y))))
        (t_2 (* t (/ (- y x) y)))
        (t_3 (/ t (- 1.0 (/ z y)))))
   (if (<= y -5.1e-49)
     t_3
     (if (<= y -1.6e-259)
       t_1
       (if (<= y 9.5e-225)
         (* (- x y) (/ t z))
         (if (<= y 2.3e+54)
           (/ t (/ (- z y) x))
           (if (<= y 2.5e+129)
             t_2
             (if (<= y 1.75e+137) t_1 (if (<= y 8.6e+192) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double t_2 = t * ((y - x) / y);
	double t_3 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -5.1e-49) {
		tmp = t_3;
	} else if (y <= -1.6e-259) {
		tmp = t_1;
	} else if (y <= 9.5e-225) {
		tmp = (x - y) * (t / z);
	} else if (y <= 2.3e+54) {
		tmp = t / ((z - y) / x);
	} else if (y <= 2.5e+129) {
		tmp = t_2;
	} else if (y <= 1.75e+137) {
		tmp = t_1;
	} else if (y <= 8.6e+192) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * (x / (z - y))
    t_2 = t * ((y - x) / y)
    t_3 = t / (1.0d0 - (z / y))
    if (y <= (-5.1d-49)) then
        tmp = t_3
    else if (y <= (-1.6d-259)) then
        tmp = t_1
    else if (y <= 9.5d-225) then
        tmp = (x - y) * (t / z)
    else if (y <= 2.3d+54) then
        tmp = t / ((z - y) / x)
    else if (y <= 2.5d+129) then
        tmp = t_2
    else if (y <= 1.75d+137) then
        tmp = t_1
    else if (y <= 8.6d+192) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double t_2 = t * ((y - x) / y);
	double t_3 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -5.1e-49) {
		tmp = t_3;
	} else if (y <= -1.6e-259) {
		tmp = t_1;
	} else if (y <= 9.5e-225) {
		tmp = (x - y) * (t / z);
	} else if (y <= 2.3e+54) {
		tmp = t / ((z - y) / x);
	} else if (y <= 2.5e+129) {
		tmp = t_2;
	} else if (y <= 1.75e+137) {
		tmp = t_1;
	} else if (y <= 8.6e+192) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / (z - y))
	t_2 = t * ((y - x) / y)
	t_3 = t / (1.0 - (z / y))
	tmp = 0
	if y <= -5.1e-49:
		tmp = t_3
	elif y <= -1.6e-259:
		tmp = t_1
	elif y <= 9.5e-225:
		tmp = (x - y) * (t / z)
	elif y <= 2.3e+54:
		tmp = t / ((z - y) / x)
	elif y <= 2.5e+129:
		tmp = t_2
	elif y <= 1.75e+137:
		tmp = t_1
	elif y <= 8.6e+192:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(z - y)))
	t_2 = Float64(t * Float64(Float64(y - x) / y))
	t_3 = Float64(t / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -5.1e-49)
		tmp = t_3;
	elseif (y <= -1.6e-259)
		tmp = t_1;
	elseif (y <= 9.5e-225)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 2.3e+54)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	elseif (y <= 2.5e+129)
		tmp = t_2;
	elseif (y <= 1.75e+137)
		tmp = t_1;
	elseif (y <= 8.6e+192)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / (z - y));
	t_2 = t * ((y - x) / y);
	t_3 = t / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -5.1e-49)
		tmp = t_3;
	elseif (y <= -1.6e-259)
		tmp = t_1;
	elseif (y <= 9.5e-225)
		tmp = (x - y) * (t / z);
	elseif (y <= 2.3e+54)
		tmp = t / ((z - y) / x);
	elseif (y <= 2.5e+129)
		tmp = t_2;
	elseif (y <= 1.75e+137)
		tmp = t_1;
	elseif (y <= 8.6e+192)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.1e-49], t$95$3, If[LessEqual[y, -1.6e-259], t$95$1, If[LessEqual[y, 9.5e-225], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+54], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+129], t$95$2, If[LessEqual[y, 1.75e+137], t$95$1, If[LessEqual[y, 8.6e+192], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.10000000000000026e-49 or 1.7500000000000001e137 < y < 8.59999999999999952e192

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 78.2%

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

      2. associate-/l* 80.8%

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

   3. Simplified 80.8%

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

      1. associate-*r/ 78.2%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.9%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. div-sub 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in x around 0 81.6%

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

       1. mul-1-neg 81.6%

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

       2. unsub-neg 81.6%

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

   11. Simplified 81.6%

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

   if -5.10000000000000026e-49 < y < -1.59999999999999994e-259 or 2.5000000000000001e129 < y < 1.7500000000000001e137

   1. Initial program 97.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 88.3%

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

   if -1.59999999999999994e-259 < y < 9.50000000000000006e-225

   1. Initial program 87.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

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

      2. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 96.7%

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

   7. Simplified 96.7%

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

   if 9.50000000000000006e-225 < y < 2.29999999999999994e54

   1. Initial program 97.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 92.5%

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

      2. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

      1. associate-*r/ 92.5%

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

      2. associate-*l/ 97.8%

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

      3. *-commutative 97.8%

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

      4. clear-num 97.8%

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

      5. un-div-inv 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in x around inf 75.9%

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

   if 2.29999999999999994e54 < y < 2.5000000000000001e129 or 8.59999999999999952e192 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 60.8%

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

      2. associate-/l* 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in z around 0 56.6%

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

      1. associate-*r/ 56.6%

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

      2. mul-1-neg 56.6%

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

      3. distribute-lft-neg-out 56.6%

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

      4. *-commutative 56.6%

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

   7. Simplified 56.6%

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

   8. Taylor expanded in x around 0 75.0%

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

      1. mul-1-neg 75.0%

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

      2. unsub-neg 75.0%

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

   10. Simplified 75.0%

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

   11. Taylor expanded in y around 0 54.0%

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

       1. distribute-lft-out-- 56.6%

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

       2. associate-/l* 95.6%

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

   13. Simplified 95.6%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{-49}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-259}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-225}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+54}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+129}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+192}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+54}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+127} \lor \neg \left(y \leq 2.25 \cdot 10^{+188}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (- 1.0 (/ z y)))))
   (if (<= y -5.8e-49)
     t_1
     (if (<= y 2e+54)
       (/ (* t x) (- z y))
       (if (or (<= y 1.06e+127) (not (<= y 2.25e+188)))
         (* t (/ (- y x) y))
         t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -5.8e-49) {
		tmp = t_1;
	} else if (y <= 2e+54) {
		tmp = (t * x) / (z - y);
	} else if ((y <= 1.06e+127) || !(y <= 2.25e+188)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (1.0d0 - (z / y))
    if (y <= (-5.8d-49)) then
        tmp = t_1
    else if (y <= 2d+54) then
        tmp = (t * x) / (z - y)
    else if ((y <= 1.06d+127) .or. (.not. (y <= 2.25d+188))) then
        tmp = t * ((y - x) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -5.8e-49) {
		tmp = t_1;
	} else if (y <= 2e+54) {
		tmp = (t * x) / (z - y);
	} else if ((y <= 1.06e+127) || !(y <= 2.25e+188)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (1.0 - (z / y))
	tmp = 0
	if y <= -5.8e-49:
		tmp = t_1
	elif y <= 2e+54:
		tmp = (t * x) / (z - y)
	elif (y <= 1.06e+127) or not (y <= 2.25e+188):
		tmp = t * ((y - x) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -5.8e-49)
		tmp = t_1;
	elseif (y <= 2e+54)
		tmp = Float64(Float64(t * x) / Float64(z - y));
	elseif ((y <= 1.06e+127) || !(y <= 2.25e+188))
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -5.8e-49)
		tmp = t_1;
	elseif (y <= 2e+54)
		tmp = (t * x) / (z - y);
	elseif ((y <= 1.06e+127) || ~((y <= 2.25e+188)))
		tmp = t * ((y - x) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e-49], t$95$1, If[LessEqual[y, 2e+54], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.06e+127], N[Not[LessEqual[y, 2.25e+188]], $MachinePrecision]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8e-49 or 1.06000000000000006e127 < y < 2.25000000000000005e188

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 78.1%

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

      2. associate-/l* 80.6%

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

   3. Simplified 80.6%

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

      1. associate-*r/ 78.1%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. div-sub 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in x around 0 80.1%

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

       1. mul-1-neg 80.1%

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

       2. unsub-neg 80.1%

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

   11. Simplified 80.1%

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

   if -5.8e-49 < y < 2.0000000000000002e54

   1. Initial program 95.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 95.2%

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

      2. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in x around inf 82.8%

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

   if 2.0000000000000002e54 < y < 1.06000000000000006e127 or 2.25000000000000005e188 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 60.0%

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

      2. associate-/l* 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in z around 0 55.6%

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

      1. associate-*r/ 55.6%

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

      2. mul-1-neg 55.6%

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

      3. distribute-lft-neg-out 55.6%

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

      4. *-commutative 55.6%

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

   7. Simplified 55.6%

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

   8. Taylor expanded in x around 0 74.5%

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

      1. mul-1-neg 74.5%

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

      2. unsub-neg 74.5%

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

   10. Simplified 74.5%

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

   11. Taylor expanded in y around 0 53.0%

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

       1. distribute-lft-out-- 55.6%

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

       2. associate-/l* 95.5%

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

   13. Simplified 95.5%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-49}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+54}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+127} \lor \neg \left(y \leq 2.25 \cdot 10^{+188}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+54}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+126} \lor \neg \left(y \leq 4.4 \cdot 10^{+189}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.1e-49)
   (* t (/ y (- y z)))
   (if (<= y 1.45e+54)
     (/ (* t x) (- z y))
     (if (or (<= y 8e+126) (not (<= y 4.4e+189)))
       (* t (/ (- y x) y))
       (/ t (- 1.0 (/ z y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.1e-49) {
		tmp = t * (y / (y - z));
	} else if (y <= 1.45e+54) {
		tmp = (t * x) / (z - y);
	} else if ((y <= 8e+126) || !(y <= 4.4e+189)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t / (1.0 - (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.1d-49)) then
        tmp = t * (y / (y - z))
    else if (y <= 1.45d+54) then
        tmp = (t * x) / (z - y)
    else if ((y <= 8d+126) .or. (.not. (y <= 4.4d+189))) then
        tmp = t * ((y - x) / y)
    else
        tmp = t / (1.0d0 - (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.1e-49) {
		tmp = t * (y / (y - z));
	} else if (y <= 1.45e+54) {
		tmp = (t * x) / (z - y);
	} else if ((y <= 8e+126) || !(y <= 4.4e+189)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t / (1.0 - (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.1e-49:
		tmp = t * (y / (y - z))
	elif y <= 1.45e+54:
		tmp = (t * x) / (z - y)
	elif (y <= 8e+126) or not (y <= 4.4e+189):
		tmp = t * ((y - x) / y)
	else:
		tmp = t / (1.0 - (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.1e-49)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (y <= 1.45e+54)
		tmp = Float64(Float64(t * x) / Float64(z - y));
	elseif ((y <= 8e+126) || !(y <= 4.4e+189))
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.1e-49)
		tmp = t * (y / (y - z));
	elseif (y <= 1.45e+54)
		tmp = (t * x) / (z - y);
	elseif ((y <= 8e+126) || ~((y <= 4.4e+189)))
		tmp = t * ((y - x) / y);
	else
		tmp = t / (1.0 - (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.1e-49], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+54], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 8e+126], N[Not[LessEqual[y, 4.4e+189]], $MachinePrecision]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.10000000000000026e-49

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 79.1%

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

      1. neg-mul-1 79.1%

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

      2. distribute-neg-frac2 79.1%

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

   5. Simplified 79.1%

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

   if -5.10000000000000026e-49 < y < 1.4499999999999999e54

   1. Initial program 95.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 95.2%

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

      2. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in x around inf 82.8%

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

   if 1.4499999999999999e54 < y < 7.9999999999999994e126 or 4.4000000000000001e189 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 60.0%

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

      2. associate-/l* 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in z around 0 55.6%

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

      1. associate-*r/ 55.6%

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

      2. mul-1-neg 55.6%

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

      3. distribute-lft-neg-out 55.6%

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

      4. *-commutative 55.6%

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

   7. Simplified 55.6%

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

   8. Taylor expanded in x around 0 74.5%

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

      1. mul-1-neg 74.5%

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

      2. unsub-neg 74.5%

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

   10. Simplified 74.5%

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

   11. Taylor expanded in y around 0 53.0%

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

       1. distribute-lft-out-- 55.6%

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

       2. associate-/l* 95.5%

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

   13. Simplified 95.5%

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

   if 7.9999999999999994e126 < y < 4.4000000000000001e189

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 79.0%

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

      2. associate-/l* 73.6%

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

   3. Simplified 73.6%

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

      1. associate-*r/ 79.0%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

      4. clear-num 99.9%

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

      5. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. div-sub 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in x around 0 84.0%

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

       1. mul-1-neg 84.0%

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

       2. unsub-neg 84.0%

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

   11. Simplified 84.0%

       \[\leadsto \color{blue}{\frac{t}{1 - \frac{z}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+54}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+126} \lor \neg \left(y \leq 4.4 \cdot 10^{+189}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+190}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.8e-49)
   (* t (/ y (- y z)))
   (if (<= y 1.5e+54)
     (/ (* t x) (- z y))
     (if (<= y 1.25e+127)
       (* t (/ (- y x) y))
       (if (<= y 2.65e+190) (/ t (- 1.0 (/ z y))) (/ t (/ y (- y x))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e-49) {
		tmp = t * (y / (y - z));
	} else if (y <= 1.5e+54) {
		tmp = (t * x) / (z - y);
	} else if (y <= 1.25e+127) {
		tmp = t * ((y - x) / y);
	} else if (y <= 2.65e+190) {
		tmp = t / (1.0 - (z / y));
	} else {
		tmp = t / (y / (y - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.8d-49)) then
        tmp = t * (y / (y - z))
    else if (y <= 1.5d+54) then
        tmp = (t * x) / (z - y)
    else if (y <= 1.25d+127) then
        tmp = t * ((y - x) / y)
    else if (y <= 2.65d+190) then
        tmp = t / (1.0d0 - (z / y))
    else
        tmp = t / (y / (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e-49) {
		tmp = t * (y / (y - z));
	} else if (y <= 1.5e+54) {
		tmp = (t * x) / (z - y);
	} else if (y <= 1.25e+127) {
		tmp = t * ((y - x) / y);
	} else if (y <= 2.65e+190) {
		tmp = t / (1.0 - (z / y));
	} else {
		tmp = t / (y / (y - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.8e-49:
		tmp = t * (y / (y - z))
	elif y <= 1.5e+54:
		tmp = (t * x) / (z - y)
	elif y <= 1.25e+127:
		tmp = t * ((y - x) / y)
	elif y <= 2.65e+190:
		tmp = t / (1.0 - (z / y))
	else:
		tmp = t / (y / (y - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.8e-49)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (y <= 1.5e+54)
		tmp = Float64(Float64(t * x) / Float64(z - y));
	elseif (y <= 1.25e+127)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	elseif (y <= 2.65e+190)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	else
		tmp = Float64(t / Float64(y / Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.8e-49)
		tmp = t * (y / (y - z));
	elseif (y <= 1.5e+54)
		tmp = (t * x) / (z - y);
	elseif (y <= 1.25e+127)
		tmp = t * ((y - x) / y);
	elseif (y <= 2.65e+190)
		tmp = t / (1.0 - (z / y));
	else
		tmp = t / (y / (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.8e-49], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+54], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+127], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.65e+190], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.8e-49

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 79.1%

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

      1. neg-mul-1 79.1%

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

      2. distribute-neg-frac2 79.1%

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

   5. Simplified 79.1%

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

   if -5.8e-49 < y < 1.4999999999999999e54

   1. Initial program 95.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 95.2%

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

      2. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in x around inf 82.8%

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

   if 1.4999999999999999e54 < y < 1.2500000000000001e127

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 74.8%

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

      2. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in z around 0 61.7%

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

      1. associate-*r/ 61.7%

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

      2. mul-1-neg 61.7%

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

      3. distribute-lft-neg-out 61.7%

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

      4. *-commutative 61.7%

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

   7. Simplified 61.7%

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

   8. Taylor expanded in x around 0 74.1%

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

      1. mul-1-neg 74.1%

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

      2. unsub-neg 74.1%

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

   10. Simplified 74.1%

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

   11. Taylor expanded in y around 0 55.0%

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

       1. distribute-lft-out-- 61.7%

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

       2. associate-/l* 86.7%

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

   13. Simplified 86.7%

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

   if 1.2500000000000001e127 < y < 2.65000000000000007e190

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 79.0%

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

      2. associate-/l* 73.6%

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

   3. Simplified 73.6%

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

      1. associate-*r/ 79.0%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

      4. clear-num 99.9%

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

      5. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. div-sub 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in x around 0 84.0%

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

       1. mul-1-neg 84.0%

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

       2. unsub-neg 84.0%

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

   11. Simplified 84.0%

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

   if 2.65000000000000007e190 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 52.6%

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

      2. associate-/l* 75.2%

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

   3. Simplified 75.2%

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

      1. associate-*r/ 52.6%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 100.0%

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

      5. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. distribute-neg-frac 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+127}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+190}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-41}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-135}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.5e-41)
   t
   (if (<= y 1.05e-135)
     (/ (* t x) z)
     (if (<= y 9.6e+137) (* t (/ x (- y))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e-41) {
		tmp = t;
	} else if (y <= 1.05e-135) {
		tmp = (t * x) / z;
	} else if (y <= 9.6e+137) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.5d-41)) then
        tmp = t
    else if (y <= 1.05d-135) then
        tmp = (t * x) / z
    else if (y <= 9.6d+137) then
        tmp = t * (x / -y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e-41) {
		tmp = t;
	} else if (y <= 1.05e-135) {
		tmp = (t * x) / z;
	} else if (y <= 9.6e+137) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.5e-41:
		tmp = t
	elif y <= 1.05e-135:
		tmp = (t * x) / z
	elif y <= 9.6e+137:
		tmp = t * (x / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.5e-41)
		tmp = t;
	elseif (y <= 1.05e-135)
		tmp = Float64(Float64(t * x) / z);
	elseif (y <= 9.6e+137)
		tmp = Float64(t * Float64(x / Float64(-y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.5e-41)
		tmp = t;
	elseif (y <= 1.05e-135)
		tmp = (t * x) / z;
	elseif (y <= 9.6e+137)
		tmp = t * (x / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.5e-41], t, If[LessEqual[y, 1.05e-135], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 9.6e+137], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4999999999999998e-41 or 9.59999999999999932e137 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 70.6%

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

      2. associate-/l* 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in y around inf 66.3%

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

   if -2.4999999999999998e-41 < y < 1.05e-135

   1. Initial program 94.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 97.4%

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

      2. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in y around 0 82.3%

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

   if 1.05e-135 < y < 9.59999999999999932e137

   1. Initial program 98.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 86.2%

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

      2. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in z around 0 57.2%

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

      1. associate-*r/ 57.2%

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

      2. mul-1-neg 57.2%

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

      3. distribute-lft-neg-out 57.2%

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

      4. *-commutative 57.2%

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

   7. Simplified 57.2%

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

   8. Taylor expanded in x around inf 42.3%

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

      1. mul-1-neg 42.3%

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

      2. associate-/l* 44.8%

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

      3. distribute-rgt-neg-in 44.8%

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

      4. distribute-neg-frac2 44.8%

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

   10. Simplified 44.8%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-41}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-135}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-33}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-135}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+143}:\\ \;\;\;\;\frac{t}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1e-33)
   t
   (if (<= y 2.1e-135)
     (/ (* t x) z)
     (if (<= y 1.12e+143) (/ t (/ (- y) x)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1e-33) {
		tmp = t;
	} else if (y <= 2.1e-135) {
		tmp = (t * x) / z;
	} else if (y <= 1.12e+143) {
		tmp = t / (-y / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1d-33)) then
        tmp = t
    else if (y <= 2.1d-135) then
        tmp = (t * x) / z
    else if (y <= 1.12d+143) then
        tmp = t / (-y / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1e-33) {
		tmp = t;
	} else if (y <= 2.1e-135) {
		tmp = (t * x) / z;
	} else if (y <= 1.12e+143) {
		tmp = t / (-y / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1e-33:
		tmp = t
	elif y <= 2.1e-135:
		tmp = (t * x) / z
	elif y <= 1.12e+143:
		tmp = t / (-y / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1e-33)
		tmp = t;
	elseif (y <= 2.1e-135)
		tmp = Float64(Float64(t * x) / z);
	elseif (y <= 1.12e+143)
		tmp = Float64(t / Float64(Float64(-y) / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1e-33)
		tmp = t;
	elseif (y <= 2.1e-135)
		tmp = (t * x) / z;
	elseif (y <= 1.12e+143)
		tmp = t / (-y / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1e-33], t, If[LessEqual[y, 2.1e-135], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.12e+143], N[(t / N[((-y) / x), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0000000000000001e-33 or 1.12e143 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 70.6%

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

      2. associate-/l* 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in y around inf 66.3%

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

   if -1.0000000000000001e-33 < y < 2.1e-135

   1. Initial program 94.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 97.4%

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

      2. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in y around 0 82.3%

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

   if 2.1e-135 < y < 1.12e143

   1. Initial program 98.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 86.2%

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

      2. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

      1. associate-*r/ 86.2%

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

      2. associate-*l/ 98.2%

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

      3. *-commutative 98.2%

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

      4. clear-num 98.1%

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

      5. un-div-inv 98.3%

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

   6. Applied egg-rr 98.3%

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

   7. Taylor expanded in x around inf 67.4%

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

   8. Taylor expanded in z around 0 44.8%

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

      1. neg-mul-1 44.8%

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

      2. distribute-neg-frac2 44.8%

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

   10. Simplified 44.8%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-33}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-135}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+143}:\\ \;\;\;\;\frac{t}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+228}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+167}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.6e+228)
   (/ t (- 1.0 (/ z y)))
   (if (<= y 4.3e+167) (* (- x y) (/ t (- z y))) (/ t (/ y (- y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.6e+228) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 4.3e+167) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t / (y / (y - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-8.6d+228)) then
        tmp = t / (1.0d0 - (z / y))
    else if (y <= 4.3d+167) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t / (y / (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.6e+228) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 4.3e+167) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t / (y / (y - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.6e+228:
		tmp = t / (1.0 - (z / y))
	elif y <= 4.3e+167:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t / (y / (y - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.6e+228)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	elseif (y <= 4.3e+167)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t / Float64(y / Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.6e+228)
		tmp = t / (1.0 - (z / y));
	elseif (y <= 4.3e+167)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t / (y / (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.6e+228], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e+167], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.60000000000000063e228

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 57.8%

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

      2. associate-/l* 54.6%

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

   3. Simplified 54.6%

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

      1. associate-*r/ 57.8%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

      4. clear-num 100.0%

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

      5. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

      1. div-sub 100.0%

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

   8. Applied egg-rr 100.0%

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

   9. Taylor expanded in x around 0 100.0%

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

       1. mul-1-neg 100.0%

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

       2. unsub-neg 100.0%

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

   11. Simplified 100.0%

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

   if -8.60000000000000063e228 < y < 4.3000000000000002e167

   1. Initial program 96.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 90.0%

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

      2. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   if 4.3000000000000002e167 < y

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 57.9%

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

      2. associate-/l* 74.1%

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

   3. Simplified 74.1%

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

      1. associate-*r/ 57.9%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

      4. clear-num 100.0%

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

      5. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around 0 95.7%

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

      1. neg-mul-1 95.7%

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

      2. distribute-neg-frac 95.7%

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

   9. Simplified 95.7%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+228}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+167}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-74} \lor \neg \left(y \leq 1.05 \cdot 10^{-135}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.2e-74) (not (<= y 1.05e-135)))
   (* t (/ (- y x) y))
   (/ (* t x) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.2e-74) || !(y <= 1.05e-135)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.2d-74)) .or. (.not. (y <= 1.05d-135))) then
        tmp = t * ((y - x) / y)
    else
        tmp = (t * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.2e-74) || !(y <= 1.05e-135)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.2e-74) or not (y <= 1.05e-135):
		tmp = t * ((y - x) / y)
	else:
		tmp = (t * x) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.2e-74) || !(y <= 1.05e-135))
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = Float64(Float64(t * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.2e-74) || ~((y <= 1.05e-135)))
		tmp = t * ((y - x) / y);
	else
		tmp = (t * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.2e-74], N[Not[LessEqual[y, 1.05e-135]], $MachinePrecision]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e-74 or 1.05e-135 < y

   1. Initial program 99.3%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 77.3%

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

      2. associate-/l* 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in z around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. mul-1-neg 57.9%

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

      3. distribute-lft-neg-out 57.9%

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

      4. *-commutative 57.9%

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

   7. Simplified 57.9%

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

   8. Taylor expanded in x around 0 68.7%

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

      1. mul-1-neg 68.7%

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

      2. unsub-neg 68.7%

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

   10. Simplified 68.7%

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

   11. Taylor expanded in y around 0 56.6%

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

       1. distribute-lft-out-- 57.9%

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

       2. associate-/l* 74.8%

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

   13. Simplified 74.8%

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

   if -4.2e-74 < y < 1.05e-135

   1. Initial program 93.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 97.2%

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

      2. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in y around 0 86.8%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-74} \lor \neg \left(y \leq 1.05 \cdot 10^{-135}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-76} \lor \neg \left(y \leq 2.1 \cdot 10^{-135}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.6e-76) (not (<= y 2.1e-135)))
   (* t (/ (- y x) y))
   (* (- x y) (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.6e-76) || !(y <= 2.1e-135)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.6d-76)) .or. (.not. (y <= 2.1d-135))) then
        tmp = t * ((y - x) / y)
    else
        tmp = (x - y) * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.6e-76) || !(y <= 2.1e-135)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.6e-76) or not (y <= 2.1e-135):
		tmp = t * ((y - x) / y)
	else:
		tmp = (x - y) * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.6e-76) || !(y <= 2.1e-135))
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = Float64(Float64(x - y) * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.6e-76) || ~((y <= 2.1e-135)))
		tmp = t * ((y - x) / y);
	else
		tmp = (x - y) * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.6e-76], N[Not[LessEqual[y, 2.1e-135]], $MachinePrecision]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5999999999999999e-76 or 2.1e-135 < y

   1. Initial program 99.3%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 77.3%

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

      2. associate-/l* 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in z around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. mul-1-neg 57.9%

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

      3. distribute-lft-neg-out 57.9%

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

      4. *-commutative 57.9%

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

   7. Simplified 57.9%

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

   8. Taylor expanded in x around 0 68.7%

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

      1. mul-1-neg 68.7%

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

      2. unsub-neg 68.7%

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

   10. Simplified 68.7%

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

   11. Taylor expanded in y around 0 56.6%

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

       1. distribute-lft-out-- 57.9%

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

       2. associate-/l* 74.8%

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

   13. Simplified 74.8%

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

   if -1.5999999999999999e-76 < y < 2.1e-135

   1. Initial program 93.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 97.2%

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

      2. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around inf 90.7%

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

      1. *-commutative 90.7%

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

      2. associate-/l* 89.2%

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

   7. Simplified 89.2%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-76} \lor \neg \left(y \leq 2.1 \cdot 10^{-135}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-38} \lor \neg \left(y \leq 2.15 \cdot 10^{+54}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.5e-38) (not (<= y 2.15e+54)))
   (* t (/ (- y x) y))
   (* t (/ x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.5e-38) || !(y <= 2.15e+54)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.5d-38)) .or. (.not. (y <= 2.15d+54))) then
        tmp = t * ((y - x) / y)
    else
        tmp = t * (x / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.5e-38) || !(y <= 2.15e+54)) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.5e-38) or not (y <= 2.15e+54):
		tmp = t * ((y - x) / y)
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.5e-38) || !(y <= 2.15e+54))
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.5e-38) || ~((y <= 2.15e+54)))
		tmp = t * ((y - x) / y);
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.5e-38], N[Not[LessEqual[y, 2.15e+54]], $MachinePrecision]], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.50000000000000009e-38 or 2.14999999999999988e54 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 71.5%

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

      2. associate-/l* 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in z around 0 57.6%

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

      1. associate-*r/ 57.6%

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

      2. mul-1-neg 57.6%

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

      3. distribute-lft-neg-out 57.6%

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

      4. *-commutative 57.6%

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

   7. Simplified 57.6%

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

   8. Taylor expanded in x around 0 73.4%

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

      1. mul-1-neg 73.4%

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

      2. unsub-neg 73.4%

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

   10. Simplified 73.4%

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

   11. Taylor expanded in y around 0 56.6%

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

       1. distribute-lft-out-- 57.6%

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

       2. associate-/l* 81.8%

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

   13. Simplified 81.8%

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

   if -4.50000000000000009e-38 < y < 2.14999999999999988e54

   1. Initial program 95.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 81.2%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-38} \lor \neg \left(y \leq 2.15 \cdot 10^{+54}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-33}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.15e-33) t (if (<= y 1.55e+54) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e-33) {
		tmp = t;
	} else if (y <= 1.55e+54) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.15d-33)) then
        tmp = t
    else if (y <= 1.55d+54) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e-33) {
		tmp = t;
	} else if (y <= 1.55e+54) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.15e-33:
		tmp = t
	elif y <= 1.55e+54:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.15e-33)
		tmp = t;
	elseif (y <= 1.55e+54)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.15e-33)
		tmp = t;
	elseif (y <= 1.55e+54)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.15e-33], t, If[LessEqual[y, 1.55e+54], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.14999999999999993e-33 or 1.55e54 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 71.5%

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

      2. associate-/l* 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in y around inf 60.3%

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

   if -1.14999999999999993e-33 < y < 1.55e54

   1. Initial program 95.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 95.2%

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

      2. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around 0 64.6%

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

      1. *-commutative 64.6%

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

      2. associate-/l* 64.7%

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

   7. Simplified 64.7%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-33}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ t \cdot \frac{x - y}{z - y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.5%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing

3. Final simplification 97.5%

   \[\leadsto t \cdot \frac{x - y}{z - y} \]
4. Add Preprocessing

Alternative 15: 35.0% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.5%

   \[\frac{x - y}{z - y} \cdot t \]
2. Step-by-step derivation

   1. associate-*l/ 83.5%

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

   2. associate-/l* 88.5%

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

3. Simplified 88.5%

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

5. Taylor expanded in y around inf 35.2%

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

6. Final simplification 35.2%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{t}{\frac{z - y}{x - y}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024067 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (/ t (/ (- z y) (- x y)))

  (* (/ (- x y) (- z y)) t))