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

Percentage Accurate: 97.3% → 97.3%

Time: 16.3s

Alternatives: 16

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: 97.3% 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: 97.3% 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]

Derivation

1. Initial program 96.7%

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

3. Final simplification 96.7%

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

Alternative 2: 66.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq -600000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-41}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq -3.85 \cdot 10^{-90} \lor \neg \left(y \leq 9.5 \cdot 10^{-96}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -4.4e+136)
     t_1
     (if (<= y -1.05e+79)
       (* t (/ y (- z)))
       (if (<= y -600000000.0)
         t_1
         (if (<= y -7e-41)
           (/ (* x t) z)
           (if (or (<= y -3.85e-90) (not (<= y 9.5e-96)))
             t_1
             (* x (/ t z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -4.4e+136) {
		tmp = t_1;
	} else if (y <= -1.05e+79) {
		tmp = t * (y / -z);
	} else if (y <= -600000000.0) {
		tmp = t_1;
	} else if (y <= -7e-41) {
		tmp = (x * t) / z;
	} else if ((y <= -3.85e-90) || !(y <= 9.5e-96)) {
		tmp = t_1;
	} else {
		tmp = x * (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) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-4.4d+136)) then
        tmp = t_1
    else if (y <= (-1.05d+79)) then
        tmp = t * (y / -z)
    else if (y <= (-600000000.0d0)) then
        tmp = t_1
    else if (y <= (-7d-41)) then
        tmp = (x * t) / z
    else if ((y <= (-3.85d-90)) .or. (.not. (y <= 9.5d-96))) then
        tmp = t_1
    else
        tmp = x * (t / z)
    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 - (x / y));
	double tmp;
	if (y <= -4.4e+136) {
		tmp = t_1;
	} else if (y <= -1.05e+79) {
		tmp = t * (y / -z);
	} else if (y <= -600000000.0) {
		tmp = t_1;
	} else if (y <= -7e-41) {
		tmp = (x * t) / z;
	} else if ((y <= -3.85e-90) || !(y <= 9.5e-96)) {
		tmp = t_1;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -4.4e+136:
		tmp = t_1
	elif y <= -1.05e+79:
		tmp = t * (y / -z)
	elif y <= -600000000.0:
		tmp = t_1
	elif y <= -7e-41:
		tmp = (x * t) / z
	elif (y <= -3.85e-90) or not (y <= 9.5e-96):
		tmp = t_1
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -4.4e+136)
		tmp = t_1;
	elseif (y <= -1.05e+79)
		tmp = Float64(t * Float64(y / Float64(-z)));
	elseif (y <= -600000000.0)
		tmp = t_1;
	elseif (y <= -7e-41)
		tmp = Float64(Float64(x * t) / z);
	elseif ((y <= -3.85e-90) || !(y <= 9.5e-96))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -4.4e+136)
		tmp = t_1;
	elseif (y <= -1.05e+79)
		tmp = t * (y / -z);
	elseif (y <= -600000000.0)
		tmp = t_1;
	elseif (y <= -7e-41)
		tmp = (x * t) / z;
	elseif ((y <= -3.85e-90) || ~((y <= 9.5e-96)))
		tmp = t_1;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+136], t$95$1, If[LessEqual[y, -1.05e+79], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -600000000.0], t$95$1, If[LessEqual[y, -7e-41], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[y, -3.85e-90], N[Not[LessEqual[y, 9.5e-96]], $MachinePrecision]], t$95$1, N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.3999999999999999e136 or -1.05000000000000004e79 < y < -6e8 or -6.9999999999999999e-41 < y < -3.84999999999999986e-90 or 9.4999999999999993e-96 < y

   1. Initial program 98.5%

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

      1. associate-*l/ 80.8%

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

      2. sub-neg 80.8%

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

      3. +-commutative 80.8%

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

      4. neg-sub0 80.8%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 80.8%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 80.8%

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

      7. distribute-neg-frac2 80.8%

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

      8. distribute-frac-neg 80.8%

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

      9. distribute-lft-neg-in 80.8%

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

      10. sub-neg 80.8%

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

      11. distribute-neg-in 80.8%

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

      12. remove-double-neg 80.8%

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

      13. +-commutative 80.8%

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

      14. sub-neg 80.8%

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

      15. *-commutative 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in z around 0 60.6%

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

      1. associate-/l* 72.6%

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

      2. div-sub 72.6%

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

      3. *-inverses 72.6%

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

   7. Simplified 72.6%

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

   if -4.3999999999999999e136 < y < -1.05000000000000004e79

   1. Initial program 99.8%

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

      1. associate-*l/ 84.8%

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

      2. sub-neg 84.8%

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

      3. +-commutative 84.8%

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

      4. neg-sub0 84.8%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 84.8%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 84.8%

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

      7. distribute-neg-frac2 84.8%

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

      8. distribute-frac-neg 84.8%

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

      9. distribute-lft-neg-in 84.8%

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

      10. sub-neg 84.8%

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

      11. distribute-neg-in 84.8%

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

      12. remove-double-neg 84.8%

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

      13. +-commutative 84.8%

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

      14. sub-neg 84.8%

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

      15. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in x around 0 77.2%

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

      1. associate-/l* 92.2%

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

   7. Simplified 92.2%

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

   8. Taylor expanded in y around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. associate-/l* 73.2%

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

      3. distribute-rgt-neg-in 73.2%

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

      4. distribute-neg-frac2 73.2%

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

   10. Simplified 73.2%

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

   if -6e8 < y < -6.9999999999999999e-41

   1. Initial program 99.8%

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

      1. associate-*l/ 100.0%

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

      2. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in y around 0 73.6%

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

   if -3.84999999999999986e-90 < y < 9.4999999999999993e-96

   1. Initial program 93.2%

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

      1. associate-*l/ 91.6%

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

      2. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

      1. associate-*r/ 91.6%

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

      2. associate-*l/ 93.2%

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

      3. *-commutative 93.2%

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

      4. clear-num 92.6%

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

      5. un-div-inv 92.6%

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

   6. Applied egg-rr 92.6%

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

   7. Taylor expanded in x around inf 80.2%

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

      1. associate-*l/ 82.0%

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

      2. *-commutative 82.0%

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

   9. Simplified 82.0%

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

   10. Taylor expanded in z around inf 72.9%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+136}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq -600000000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-41}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq -3.85 \cdot 10^{-90} \lor \neg \left(y \leq 9.5 \cdot 10^{-96}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;x \leq -9 \cdot 10^{+95}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+160} \lor \neg \left(x \leq 1.02 \cdot 10^{+232}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))) (t_2 (* t (/ x (- z y)))))
   (if (<= x -9e+95)
     t_2
     (if (<= x 3.7e-56)
       t_1
       (if (<= x 8e+30)
         t_2
         (if (<= x 1.35e+91)
           t_1
           (if (or (<= x 3.9e+160) (not (<= x 1.02e+232)))
             t_2
             (* t (- 1.0 (/ x y))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = t * (x / (z - y));
	double tmp;
	if (x <= -9e+95) {
		tmp = t_2;
	} else if (x <= 3.7e-56) {
		tmp = t_1;
	} else if (x <= 8e+30) {
		tmp = t_2;
	} else if (x <= 1.35e+91) {
		tmp = t_1;
	} else if ((x <= 3.9e+160) || !(x <= 1.02e+232)) {
		tmp = t_2;
	} else {
		tmp = t * (1.0 - (x / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    t_2 = t * (x / (z - y))
    if (x <= (-9d+95)) then
        tmp = t_2
    else if (x <= 3.7d-56) then
        tmp = t_1
    else if (x <= 8d+30) then
        tmp = t_2
    else if (x <= 1.35d+91) then
        tmp = t_1
    else if ((x <= 3.9d+160) .or. (.not. (x <= 1.02d+232))) then
        tmp = t_2
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = t * (x / (z - y));
	double tmp;
	if (x <= -9e+95) {
		tmp = t_2;
	} else if (x <= 3.7e-56) {
		tmp = t_1;
	} else if (x <= 8e+30) {
		tmp = t_2;
	} else if (x <= 1.35e+91) {
		tmp = t_1;
	} else if ((x <= 3.9e+160) || !(x <= 1.02e+232)) {
		tmp = t_2;
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	t_2 = t * (x / (z - y))
	tmp = 0
	if x <= -9e+95:
		tmp = t_2
	elif x <= 3.7e-56:
		tmp = t_1
	elif x <= 8e+30:
		tmp = t_2
	elif x <= 1.35e+91:
		tmp = t_1
	elif (x <= 3.9e+160) or not (x <= 1.02e+232):
		tmp = t_2
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (x <= -9e+95)
		tmp = t_2;
	elseif (x <= 3.7e-56)
		tmp = t_1;
	elseif (x <= 8e+30)
		tmp = t_2;
	elseif (x <= 1.35e+91)
		tmp = t_1;
	elseif ((x <= 3.9e+160) || !(x <= 1.02e+232))
		tmp = t_2;
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	t_2 = t * (x / (z - y));
	tmp = 0.0;
	if (x <= -9e+95)
		tmp = t_2;
	elseif (x <= 3.7e-56)
		tmp = t_1;
	elseif (x <= 8e+30)
		tmp = t_2;
	elseif (x <= 1.35e+91)
		tmp = t_1;
	elseif ((x <= 3.9e+160) || ~((x <= 1.02e+232)))
		tmp = t_2;
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -9e+95], t$95$2, If[LessEqual[x, 3.7e-56], t$95$1, If[LessEqual[x, 8e+30], t$95$2, If[LessEqual[x, 1.35e+91], t$95$1, If[Or[LessEqual[x, 3.9e+160], N[Not[LessEqual[x, 1.02e+232]], $MachinePrecision]], t$95$2, N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.00000000000000033e95 or 3.7000000000000002e-56 < x < 8.0000000000000002e30 or 1.35e91 < x < 3.90000000000000007e160 or 1.0199999999999999e232 < x

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf 84.7%

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

   if -9.00000000000000033e95 < x < 3.7000000000000002e-56 or 8.0000000000000002e30 < x < 1.35e91

   1. Initial program 96.4%

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

      1. associate-*l/ 87.0%

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

      2. sub-neg 87.0%

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

      3. +-commutative 87.0%

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

      4. neg-sub0 87.0%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 87.0%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 87.0%

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

      7. distribute-neg-frac2 87.0%

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

      8. distribute-frac-neg 87.0%

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

      9. distribute-lft-neg-in 87.0%

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

      10. sub-neg 87.0%

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

      11. distribute-neg-in 87.0%

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

      12. remove-double-neg 87.0%

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

      13. +-commutative 87.0%

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

      14. sub-neg 87.0%

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

      15. *-commutative 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in x around 0 73.5%

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

      1. associate-/l* 85.4%

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

   7. Simplified 85.4%

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

   if 3.90000000000000007e160 < x < 1.0199999999999999e232

   1. Initial program 99.9%

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

      1. associate-*l/ 85.8%

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

      2. sub-neg 85.8%

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

      3. +-commutative 85.8%

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

      4. neg-sub0 85.8%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 85.8%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 85.8%

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

      7. distribute-neg-frac2 85.8%

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

      8. distribute-frac-neg 85.8%

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

      9. distribute-lft-neg-in 85.8%

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

      10. sub-neg 85.8%

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

      11. distribute-neg-in 85.8%

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

      12. remove-double-neg 85.8%

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

      13. +-commutative 85.8%

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

      14. sub-neg 85.8%

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

      15. *-commutative 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in z around 0 71.3%

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

      1. associate-/l* 76.9%

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

      2. div-sub 76.9%

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

      3. *-inverses 76.9%

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

   7. Simplified 76.9%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-56}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+160} \lor \neg \left(x \leq 1.02 \cdot 10^{+232}\right):\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+95}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+160} \lor \neg \left(x \leq 9.8 \cdot 10^{+231}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))) (t_2 (* t (/ x (- z y)))))
   (if (<= x -2.4e+95)
     t_2
     (if (<= x 5.2e-56)
       t_1
       (if (<= x 6.5e+31)
         t_2
         (if (<= x 2.75e+91)
           t_1
           (if (or (<= x 4e+160) (not (<= x 9.8e+231)))
             t_2
             (- t (* t (/ x y))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = t * (x / (z - y));
	double tmp;
	if (x <= -2.4e+95) {
		tmp = t_2;
	} else if (x <= 5.2e-56) {
		tmp = t_1;
	} else if (x <= 6.5e+31) {
		tmp = t_2;
	} else if (x <= 2.75e+91) {
		tmp = t_1;
	} else if ((x <= 4e+160) || !(x <= 9.8e+231)) {
		tmp = t_2;
	} else {
		tmp = t - (t * (x / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    t_2 = t * (x / (z - y))
    if (x <= (-2.4d+95)) then
        tmp = t_2
    else if (x <= 5.2d-56) then
        tmp = t_1
    else if (x <= 6.5d+31) then
        tmp = t_2
    else if (x <= 2.75d+91) then
        tmp = t_1
    else if ((x <= 4d+160) .or. (.not. (x <= 9.8d+231))) then
        tmp = t_2
    else
        tmp = t - (t * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = t * (x / (z - y));
	double tmp;
	if (x <= -2.4e+95) {
		tmp = t_2;
	} else if (x <= 5.2e-56) {
		tmp = t_1;
	} else if (x <= 6.5e+31) {
		tmp = t_2;
	} else if (x <= 2.75e+91) {
		tmp = t_1;
	} else if ((x <= 4e+160) || !(x <= 9.8e+231)) {
		tmp = t_2;
	} else {
		tmp = t - (t * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	t_2 = t * (x / (z - y))
	tmp = 0
	if x <= -2.4e+95:
		tmp = t_2
	elif x <= 5.2e-56:
		tmp = t_1
	elif x <= 6.5e+31:
		tmp = t_2
	elif x <= 2.75e+91:
		tmp = t_1
	elif (x <= 4e+160) or not (x <= 9.8e+231):
		tmp = t_2
	else:
		tmp = t - (t * (x / y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (x <= -2.4e+95)
		tmp = t_2;
	elseif (x <= 5.2e-56)
		tmp = t_1;
	elseif (x <= 6.5e+31)
		tmp = t_2;
	elseif (x <= 2.75e+91)
		tmp = t_1;
	elseif ((x <= 4e+160) || !(x <= 9.8e+231))
		tmp = t_2;
	else
		tmp = Float64(t - Float64(t * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	t_2 = t * (x / (z - y));
	tmp = 0.0;
	if (x <= -2.4e+95)
		tmp = t_2;
	elseif (x <= 5.2e-56)
		tmp = t_1;
	elseif (x <= 6.5e+31)
		tmp = t_2;
	elseif (x <= 2.75e+91)
		tmp = t_1;
	elseif ((x <= 4e+160) || ~((x <= 9.8e+231)))
		tmp = t_2;
	else
		tmp = t - (t * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e+95], t$95$2, If[LessEqual[x, 5.2e-56], t$95$1, If[LessEqual[x, 6.5e+31], t$95$2, If[LessEqual[x, 2.75e+91], t$95$1, If[Or[LessEqual[x, 4e+160], N[Not[LessEqual[x, 9.8e+231]], $MachinePrecision]], t$95$2, N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4e95 or 5.19999999999999994e-56 < x < 6.5000000000000004e31 or 2.7499999999999999e91 < x < 4.00000000000000003e160 or 9.80000000000000042e231 < x

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf 84.7%

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

   if -2.4e95 < x < 5.19999999999999994e-56 or 6.5000000000000004e31 < x < 2.7499999999999999e91

   1. Initial program 96.4%

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

      1. associate-*l/ 87.0%

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

      2. sub-neg 87.0%

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

      3. +-commutative 87.0%

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

      4. neg-sub0 87.0%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 87.0%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 87.0%

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

      7. distribute-neg-frac2 87.0%

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

      8. distribute-frac-neg 87.0%

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

      9. distribute-lft-neg-in 87.0%

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

      10. sub-neg 87.0%

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

      11. distribute-neg-in 87.0%

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

      12. remove-double-neg 87.0%

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

      13. +-commutative 87.0%

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

      14. sub-neg 87.0%

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

      15. *-commutative 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in x around 0 73.5%

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

      1. associate-/l* 85.4%

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

   7. Simplified 85.4%

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

   if 4.00000000000000003e160 < x < 9.80000000000000042e231

   1. Initial program 99.9%

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

      1. associate-*l/ 85.8%

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

      2. sub-neg 85.8%

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

      3. +-commutative 85.8%

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

      4. neg-sub0 85.8%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 85.8%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 85.8%

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

      7. distribute-neg-frac2 85.8%

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

      8. distribute-frac-neg 85.8%

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

      9. distribute-lft-neg-in 85.8%

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

      10. sub-neg 85.8%

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

      11. distribute-neg-in 85.8%

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

      12. remove-double-neg 85.8%

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

      13. +-commutative 85.8%

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

      14. sub-neg 85.8%

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

      15. *-commutative 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in z around 0 71.3%

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

   6. Taylor expanded in y around 0 71.3%

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

      1. mul-1-neg 71.3%

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

      2. unsub-neg 71.3%

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

      3. associate-/l* 77.0%

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

   8. Simplified 77.0%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+95}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-56}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+160} \lor \neg \left(x \leq 9.8 \cdot 10^{+231}\right):\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ t_2 := x \cdot \frac{t}{z - y}\\ \mathbf{if}\;x \leq -5.1 \cdot 10^{+95}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+160}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+237}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))) (t_2 (* x (/ t (- z y)))))
   (if (<= x -5.1e+95)
     t_2
     (if (<= x 1e-53)
       t_1
       (if (<= x 3.8e+31)
         t_2
         (if (<= x 1.45e+91)
           t_1
           (if (<= x 3.9e+160)
             (* t (/ x z))
             (if (<= x 1.6e+237) (* t (- 1.0 (/ x y))) t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = x * (t / (z - y));
	double tmp;
	if (x <= -5.1e+95) {
		tmp = t_2;
	} else if (x <= 1e-53) {
		tmp = t_1;
	} else if (x <= 3.8e+31) {
		tmp = t_2;
	} else if (x <= 1.45e+91) {
		tmp = t_1;
	} else if (x <= 3.9e+160) {
		tmp = t * (x / z);
	} else if (x <= 1.6e+237) {
		tmp = t * (1.0 - (x / y));
	} 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) :: tmp
    t_1 = t * (y / (y - z))
    t_2 = x * (t / (z - y))
    if (x <= (-5.1d+95)) then
        tmp = t_2
    else if (x <= 1d-53) then
        tmp = t_1
    else if (x <= 3.8d+31) then
        tmp = t_2
    else if (x <= 1.45d+91) then
        tmp = t_1
    else if (x <= 3.9d+160) then
        tmp = t * (x / z)
    else if (x <= 1.6d+237) then
        tmp = t * (1.0d0 - (x / y))
    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 * (y / (y - z));
	double t_2 = x * (t / (z - y));
	double tmp;
	if (x <= -5.1e+95) {
		tmp = t_2;
	} else if (x <= 1e-53) {
		tmp = t_1;
	} else if (x <= 3.8e+31) {
		tmp = t_2;
	} else if (x <= 1.45e+91) {
		tmp = t_1;
	} else if (x <= 3.9e+160) {
		tmp = t * (x / z);
	} else if (x <= 1.6e+237) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	t_2 = x * (t / (z - y))
	tmp = 0
	if x <= -5.1e+95:
		tmp = t_2
	elif x <= 1e-53:
		tmp = t_1
	elif x <= 3.8e+31:
		tmp = t_2
	elif x <= 1.45e+91:
		tmp = t_1
	elif x <= 3.9e+160:
		tmp = t * (x / z)
	elif x <= 1.6e+237:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	t_2 = Float64(x * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (x <= -5.1e+95)
		tmp = t_2;
	elseif (x <= 1e-53)
		tmp = t_1;
	elseif (x <= 3.8e+31)
		tmp = t_2;
	elseif (x <= 1.45e+91)
		tmp = t_1;
	elseif (x <= 3.9e+160)
		tmp = Float64(t * Float64(x / z));
	elseif (x <= 1.6e+237)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	t_2 = x * (t / (z - y));
	tmp = 0.0;
	if (x <= -5.1e+95)
		tmp = t_2;
	elseif (x <= 1e-53)
		tmp = t_1;
	elseif (x <= 3.8e+31)
		tmp = t_2;
	elseif (x <= 1.45e+91)
		tmp = t_1;
	elseif (x <= 3.9e+160)
		tmp = t * (x / z);
	elseif (x <= 1.6e+237)
		tmp = t * (1.0 - (x / y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.1e+95], t$95$2, If[LessEqual[x, 1e-53], t$95$1, If[LessEqual[x, 3.8e+31], t$95$2, If[LessEqual[x, 1.45e+91], t$95$1, If[LessEqual[x, 3.9e+160], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e+237], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.10000000000000003e95 or 1.00000000000000003e-53 < x < 3.8000000000000001e31 or 1.60000000000000009e237 < x

   1. Initial program 96.0%

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

      1. associate-*l/ 82.7%

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

      2. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

      1. associate-*r/ 82.7%

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

      2. associate-*l/ 96.0%

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

      3. *-commutative 96.0%

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

      4. clear-num 95.8%

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

      5. un-div-inv 96.7%

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

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in x around inf 73.8%

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

      1. associate-*l/ 83.3%

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

      2. *-commutative 83.3%

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

   9. Simplified 83.3%

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

   if -5.10000000000000003e95 < x < 1.00000000000000003e-53 or 3.8000000000000001e31 < x < 1.45000000000000007e91

   1. Initial program 96.4%

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

      1. associate-*l/ 87.0%

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

      2. sub-neg 87.0%

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

      3. +-commutative 87.0%

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

      4. neg-sub0 87.0%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 87.0%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 87.0%

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

      7. distribute-neg-frac2 87.0%

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

      8. distribute-frac-neg 87.0%

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

      9. distribute-lft-neg-in 87.0%

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

      10. sub-neg 87.0%

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

      11. distribute-neg-in 87.0%

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

      12. remove-double-neg 87.0%

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

      13. +-commutative 87.0%

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

      14. sub-neg 87.0%

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

      15. *-commutative 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in x around 0 73.5%

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

      1. associate-/l* 85.4%

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

   7. Simplified 85.4%

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

   if 1.45000000000000007e91 < x < 3.90000000000000007e160

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 69.4%

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

   if 3.90000000000000007e160 < x < 1.60000000000000009e237

   1. Initial program 99.9%

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

      1. associate-*l/ 85.8%

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

      2. sub-neg 85.8%

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

      3. +-commutative 85.8%

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

      4. neg-sub0 85.8%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 85.8%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 85.8%

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

      7. distribute-neg-frac2 85.8%

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

      8. distribute-frac-neg 85.8%

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

      9. distribute-lft-neg-in 85.8%

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

      10. sub-neg 85.8%

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

      11. distribute-neg-in 85.8%

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

      12. remove-double-neg 85.8%

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

      13. +-commutative 85.8%

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

      14. sub-neg 85.8%

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

      15. *-commutative 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in z around 0 71.3%

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

      1. associate-/l* 76.9%

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

      2. div-sub 76.9%

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

      3. *-inverses 76.9%

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

   7. Simplified 76.9%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.1 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;x \leq 10^{-53}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+160}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+237}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ t_2 := t \cdot \frac{x}{z - y}\\ t_3 := \frac{t}{\frac{z - y}{x}}\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+94}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+160}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+231}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z))))
        (t_2 (* t (/ x (- z y))))
        (t_3 (/ t (/ (- z y) x))))
   (if (<= x -3.3e+94)
     t_3
     (if (<= x 1e-53)
       t_1
       (if (<= x 5.8e+29)
         t_2
         (if (<= x 4.8e+91)
           t_1
           (if (<= x 4.2e+160)
             t_2
             (if (<= x 9.8e+231) (- t (* t (/ x y))) t_3))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = t * (x / (z - y));
	double t_3 = t / ((z - y) / x);
	double tmp;
	if (x <= -3.3e+94) {
		tmp = t_3;
	} else if (x <= 1e-53) {
		tmp = t_1;
	} else if (x <= 5.8e+29) {
		tmp = t_2;
	} else if (x <= 4.8e+91) {
		tmp = t_1;
	} else if (x <= 4.2e+160) {
		tmp = t_2;
	} else if (x <= 9.8e+231) {
		tmp = t - (t * (x / y));
	} 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 * (y / (y - z))
    t_2 = t * (x / (z - y))
    t_3 = t / ((z - y) / x)
    if (x <= (-3.3d+94)) then
        tmp = t_3
    else if (x <= 1d-53) then
        tmp = t_1
    else if (x <= 5.8d+29) then
        tmp = t_2
    else if (x <= 4.8d+91) then
        tmp = t_1
    else if (x <= 4.2d+160) then
        tmp = t_2
    else if (x <= 9.8d+231) then
        tmp = t - (t * (x / y))
    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 * (y / (y - z));
	double t_2 = t * (x / (z - y));
	double t_3 = t / ((z - y) / x);
	double tmp;
	if (x <= -3.3e+94) {
		tmp = t_3;
	} else if (x <= 1e-53) {
		tmp = t_1;
	} else if (x <= 5.8e+29) {
		tmp = t_2;
	} else if (x <= 4.8e+91) {
		tmp = t_1;
	} else if (x <= 4.2e+160) {
		tmp = t_2;
	} else if (x <= 9.8e+231) {
		tmp = t - (t * (x / y));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	t_2 = t * (x / (z - y))
	t_3 = t / ((z - y) / x)
	tmp = 0
	if x <= -3.3e+94:
		tmp = t_3
	elif x <= 1e-53:
		tmp = t_1
	elif x <= 5.8e+29:
		tmp = t_2
	elif x <= 4.8e+91:
		tmp = t_1
	elif x <= 4.2e+160:
		tmp = t_2
	elif x <= 9.8e+231:
		tmp = t - (t * (x / y))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	t_3 = Float64(t / Float64(Float64(z - y) / x))
	tmp = 0.0
	if (x <= -3.3e+94)
		tmp = t_3;
	elseif (x <= 1e-53)
		tmp = t_1;
	elseif (x <= 5.8e+29)
		tmp = t_2;
	elseif (x <= 4.8e+91)
		tmp = t_1;
	elseif (x <= 4.2e+160)
		tmp = t_2;
	elseif (x <= 9.8e+231)
		tmp = Float64(t - Float64(t * Float64(x / y)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	t_2 = t * (x / (z - y));
	t_3 = t / ((z - y) / x);
	tmp = 0.0;
	if (x <= -3.3e+94)
		tmp = t_3;
	elseif (x <= 1e-53)
		tmp = t_1;
	elseif (x <= 5.8e+29)
		tmp = t_2;
	elseif (x <= 4.8e+91)
		tmp = t_1;
	elseif (x <= 4.2e+160)
		tmp = t_2;
	elseif (x <= 9.8e+231)
		tmp = t - (t * (x / y));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $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[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.3e+94], t$95$3, If[LessEqual[x, 1e-53], t$95$1, If[LessEqual[x, 5.8e+29], t$95$2, If[LessEqual[x, 4.8e+91], t$95$1, If[LessEqual[x, 4.2e+160], t$95$2, If[LessEqual[x, 9.8e+231], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.3e94 or 9.80000000000000042e231 < x

   1. Initial program 94.8%

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

      1. associate-*l/ 77.9%

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

      2. associate-/l* 90.0%

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

   3. Simplified 90.0%

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

      1. associate-*r/ 77.9%

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

      2. associate-*l/ 94.8%

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

      3. *-commutative 94.8%

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

      4. clear-num 94.7%

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

      5. un-div-inv 95.8%

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

   6. Applied egg-rr 95.8%

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

   7. Taylor expanded in x around inf 85.6%

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

   if -3.3e94 < x < 1.00000000000000003e-53 or 5.7999999999999999e29 < x < 4.79999999999999966e91

   1. Initial program 96.4%

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

      1. associate-*l/ 87.0%

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

      2. sub-neg 87.0%

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

      3. +-commutative 87.0%

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

      4. neg-sub0 87.0%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 87.0%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 87.0%

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

      7. distribute-neg-frac2 87.0%

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

      8. distribute-frac-neg 87.0%

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

      9. distribute-lft-neg-in 87.0%

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

      10. sub-neg 87.0%

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

      11. distribute-neg-in 87.0%

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

      12. remove-double-neg 87.0%

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

      13. +-commutative 87.0%

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

      14. sub-neg 87.0%

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

      15. *-commutative 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in x around 0 73.5%

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

      1. associate-/l* 85.4%

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

   7. Simplified 85.4%

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

   if 1.00000000000000003e-53 < x < 5.7999999999999999e29 or 4.79999999999999966e91 < x < 4.19999999999999993e160

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 84.7%

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

   if 4.19999999999999993e160 < x < 9.80000000000000042e231

   1. Initial program 99.9%

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

      1. associate-*l/ 85.8%

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

      2. sub-neg 85.8%

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

      3. +-commutative 85.8%

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

      4. neg-sub0 85.8%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 85.8%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 85.8%

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

      7. distribute-neg-frac2 85.8%

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

      8. distribute-frac-neg 85.8%

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

      9. distribute-lft-neg-in 85.8%

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

      10. sub-neg 85.8%

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

      11. distribute-neg-in 85.8%

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

      12. remove-double-neg 85.8%

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

      13. +-commutative 85.8%

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

      14. sub-neg 85.8%

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

      15. *-commutative 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in z around 0 71.3%

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

   6. Taylor expanded in y around 0 71.3%

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

      1. mul-1-neg 71.3%

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

      2. unsub-neg 71.3%

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

      3. associate-/l* 77.0%

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

   8. Simplified 77.0%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+94}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;x \leq 10^{-53}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+91}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+160}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+231}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{-z}\\ \mathbf{if}\;y \leq -3 \cdot 10^{+136}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.38 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-43}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- z)))))
   (if (<= y -3e+136)
     t
     (if (<= y -1.3e+77)
       t_1
       (if (<= y -1.38e+14)
         t
         (if (<= y -3.3e-43)
           (/ (* x t) z)
           (if (<= y -1.8e-107) t_1 (if (<= y 4.2) (* t (/ x z)) t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / -z);
	double tmp;
	if (y <= -3e+136) {
		tmp = t;
	} else if (y <= -1.3e+77) {
		tmp = t_1;
	} else if (y <= -1.38e+14) {
		tmp = t;
	} else if (y <= -3.3e-43) {
		tmp = (x * t) / z;
	} else if (y <= -1.8e-107) {
		tmp = t_1;
	} else if (y <= 4.2) {
		tmp = t * (x / 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) :: t_1
    real(8) :: tmp
    t_1 = t * (y / -z)
    if (y <= (-3d+136)) then
        tmp = t
    else if (y <= (-1.3d+77)) then
        tmp = t_1
    else if (y <= (-1.38d+14)) then
        tmp = t
    else if (y <= (-3.3d-43)) then
        tmp = (x * t) / z
    else if (y <= (-1.8d-107)) then
        tmp = t_1
    else if (y <= 4.2d0) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y / -z);
	double tmp;
	if (y <= -3e+136) {
		tmp = t;
	} else if (y <= -1.3e+77) {
		tmp = t_1;
	} else if (y <= -1.38e+14) {
		tmp = t;
	} else if (y <= -3.3e-43) {
		tmp = (x * t) / z;
	} else if (y <= -1.8e-107) {
		tmp = t_1;
	} else if (y <= 4.2) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / -z)
	tmp = 0
	if y <= -3e+136:
		tmp = t
	elif y <= -1.3e+77:
		tmp = t_1
	elif y <= -1.38e+14:
		tmp = t
	elif y <= -3.3e-43:
		tmp = (x * t) / z
	elif y <= -1.8e-107:
		tmp = t_1
	elif y <= 4.2:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(-z)))
	tmp = 0.0
	if (y <= -3e+136)
		tmp = t;
	elseif (y <= -1.3e+77)
		tmp = t_1;
	elseif (y <= -1.38e+14)
		tmp = t;
	elseif (y <= -3.3e-43)
		tmp = Float64(Float64(x * t) / z);
	elseif (y <= -1.8e-107)
		tmp = t_1;
	elseif (y <= 4.2)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / -z);
	tmp = 0.0;
	if (y <= -3e+136)
		tmp = t;
	elseif (y <= -1.3e+77)
		tmp = t_1;
	elseif (y <= -1.38e+14)
		tmp = t;
	elseif (y <= -3.3e-43)
		tmp = (x * t) / z;
	elseif (y <= -1.8e-107)
		tmp = t_1;
	elseif (y <= 4.2)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3e+136], t, If[LessEqual[y, -1.3e+77], t$95$1, If[LessEqual[y, -1.38e+14], t, If[LessEqual[y, -3.3e-43], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -1.8e-107], t$95$1, If[LessEqual[y, 4.2], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.99999999999999979e136 or -1.3000000000000001e77 < y < -1.38e14 or 4.20000000000000018 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 77.1%

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

      2. associate-/l* 74.5%

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

   3. Simplified 74.5%

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

   5. Taylor expanded in y around inf 62.9%

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

   if -2.99999999999999979e136 < y < -1.3000000000000001e77 or -3.30000000000000016e-43 < y < -1.79999999999999988e-107

   1. Initial program 96.5%

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

      1. associate-*l/ 93.0%

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

      2. sub-neg 93.0%

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

      3. +-commutative 93.0%

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

      4. neg-sub0 93.0%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 93.0%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 93.0%

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

      7. distribute-neg-frac2 93.0%

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

      8. distribute-frac-neg 93.0%

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

      9. distribute-lft-neg-in 93.0%

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

      10. sub-neg 93.0%

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

      11. distribute-neg-in 93.0%

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

      12. remove-double-neg 93.0%

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

      13. +-commutative 93.0%

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

      14. sub-neg 93.0%

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

      15. *-commutative 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in x around 0 63.0%

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

      1. associate-/l* 69.7%

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

   7. Simplified 69.7%

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

   8. Taylor expanded in y around 0 46.7%

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

      1. mul-1-neg 46.7%

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

      2. associate-/l* 53.3%

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

      3. distribute-rgt-neg-in 53.3%

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

      4. distribute-neg-frac2 53.3%

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

   10. Simplified 53.3%

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

   if -1.38e14 < y < -3.30000000000000016e-43

   1. Initial program 99.9%

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

      1. associate-*l/ 99.9%

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

      2. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around 0 62.5%

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

   if -1.79999999999999988e-107 < y < 4.20000000000000018

   1. Initial program 93.1%

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

   3. Taylor expanded in y around 0 68.9%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+136}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq -1.38 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-43}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq 4.2:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+136}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq -300000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-43}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-90}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq 4.8:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.2e+136)
   t
   (if (<= y -6.8e+69)
     (* t (/ y (- z)))
     (if (<= y -300000000000.0)
       t
       (if (<= y -3e-43)
         (/ (* x t) z)
         (if (<= y -6.7e-90)
           (* t (/ (- x) y))
           (if (<= y 4.8) (* t (/ x z)) t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.2e+136) {
		tmp = t;
	} else if (y <= -6.8e+69) {
		tmp = t * (y / -z);
	} else if (y <= -300000000000.0) {
		tmp = t;
	} else if (y <= -3e-43) {
		tmp = (x * t) / z;
	} else if (y <= -6.7e-90) {
		tmp = t * (-x / y);
	} else if (y <= 4.8) {
		tmp = t * (x / 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 <= (-4.2d+136)) then
        tmp = t
    else if (y <= (-6.8d+69)) then
        tmp = t * (y / -z)
    else if (y <= (-300000000000.0d0)) then
        tmp = t
    else if (y <= (-3d-43)) then
        tmp = (x * t) / z
    else if (y <= (-6.7d-90)) then
        tmp = t * (-x / y)
    else if (y <= 4.8d0) then
        tmp = t * (x / 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 <= -4.2e+136) {
		tmp = t;
	} else if (y <= -6.8e+69) {
		tmp = t * (y / -z);
	} else if (y <= -300000000000.0) {
		tmp = t;
	} else if (y <= -3e-43) {
		tmp = (x * t) / z;
	} else if (y <= -6.7e-90) {
		tmp = t * (-x / y);
	} else if (y <= 4.8) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.2e+136:
		tmp = t
	elif y <= -6.8e+69:
		tmp = t * (y / -z)
	elif y <= -300000000000.0:
		tmp = t
	elif y <= -3e-43:
		tmp = (x * t) / z
	elif y <= -6.7e-90:
		tmp = t * (-x / y)
	elif y <= 4.8:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.2e+136)
		tmp = t;
	elseif (y <= -6.8e+69)
		tmp = Float64(t * Float64(y / Float64(-z)));
	elseif (y <= -300000000000.0)
		tmp = t;
	elseif (y <= -3e-43)
		tmp = Float64(Float64(x * t) / z);
	elseif (y <= -6.7e-90)
		tmp = Float64(t * Float64(Float64(-x) / y));
	elseif (y <= 4.8)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.2e+136)
		tmp = t;
	elseif (y <= -6.8e+69)
		tmp = t * (y / -z);
	elseif (y <= -300000000000.0)
		tmp = t;
	elseif (y <= -3e-43)
		tmp = (x * t) / z;
	elseif (y <= -6.7e-90)
		tmp = t * (-x / y);
	elseif (y <= 4.8)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.2e+136], t, If[LessEqual[y, -6.8e+69], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -300000000000.0], t, If[LessEqual[y, -3e-43], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -6.7e-90], N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.1999999999999998e136 or -6.79999999999999973e69 < y < -3e11 or 4.79999999999999982 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 77.1%

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

      2. associate-/l* 74.5%

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

   3. Simplified 74.5%

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

   5. Taylor expanded in y around inf 62.9%

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

   if -4.1999999999999998e136 < y < -6.79999999999999973e69

   1. Initial program 99.8%

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

      1. associate-*l/ 84.8%

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

      2. sub-neg 84.8%

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

      3. +-commutative 84.8%

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

      4. neg-sub0 84.8%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 84.8%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 84.8%

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

      7. distribute-neg-frac2 84.8%

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

      8. distribute-frac-neg 84.8%

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

      9. distribute-lft-neg-in 84.8%

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

      10. sub-neg 84.8%

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

      11. distribute-neg-in 84.8%

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

      12. remove-double-neg 84.8%

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

      13. +-commutative 84.8%

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

      14. sub-neg 84.8%

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

      15. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in x around 0 77.2%

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

      1. associate-/l* 92.2%

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

   7. Simplified 92.2%

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

   8. Taylor expanded in y around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. associate-/l* 73.2%

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

      3. distribute-rgt-neg-in 73.2%

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

      4. distribute-neg-frac2 73.2%

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

   10. Simplified 73.2%

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

   if -3e11 < y < -3.00000000000000003e-43

   1. Initial program 99.9%

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

      1. associate-*l/ 99.9%

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

      2. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around 0 62.5%

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

   if -3.00000000000000003e-43 < y < -6.7000000000000004e-90

   1. Initial program 91.9%

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

      1. associate-*l/ 99.6%

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

      2. sub-neg 99.6%

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

      3. +-commutative 99.6%

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

      4. neg-sub0 99.6%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 99.6%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 99.6%

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

      7. distribute-neg-frac2 99.6%

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

      8. distribute-frac-neg 99.6%

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

      9. distribute-lft-neg-in 99.6%

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

      10. sub-neg 99.6%

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

      11. distribute-neg-in 99.6%

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

      12. remove-double-neg 99.6%

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

      13. +-commutative 99.6%

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

      14. sub-neg 99.6%

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

      15. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 75.9%

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

   6. Taylor expanded in y around 0 59.9%

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

      1. mul-1-neg 59.9%

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

      2. associate-/l* 52.3%

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

      3. distribute-rgt-neg-in 52.3%

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

      4. distribute-frac-neg 52.3%

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

   8. Simplified 52.3%

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

   if -6.7000000000000004e-90 < y < 4.79999999999999982

   1. Initial program 93.3%

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

   3. Taylor expanded in y around 0 68.2%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+136}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+69}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq -300000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-43}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-90}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq 4.8:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+136}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq -16500000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-43}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{elif}\;y \leq 2.55:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.6e+136)
   t
   (if (<= y -7e+71)
     (* t (/ y (- z)))
     (if (<= y -16500000000.0)
       t
       (if (<= y -3.1e-43)
         (/ (* x t) z)
         (if (<= y -6.7e-90)
           (* x (/ t (- y)))
           (if (<= y 2.55) (* t (/ x z)) t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.6e+136) {
		tmp = t;
	} else if (y <= -7e+71) {
		tmp = t * (y / -z);
	} else if (y <= -16500000000.0) {
		tmp = t;
	} else if (y <= -3.1e-43) {
		tmp = (x * t) / z;
	} else if (y <= -6.7e-90) {
		tmp = x * (t / -y);
	} else if (y <= 2.55) {
		tmp = t * (x / 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 <= (-7.6d+136)) then
        tmp = t
    else if (y <= (-7d+71)) then
        tmp = t * (y / -z)
    else if (y <= (-16500000000.0d0)) then
        tmp = t
    else if (y <= (-3.1d-43)) then
        tmp = (x * t) / z
    else if (y <= (-6.7d-90)) then
        tmp = x * (t / -y)
    else if (y <= 2.55d0) then
        tmp = t * (x / 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 <= -7.6e+136) {
		tmp = t;
	} else if (y <= -7e+71) {
		tmp = t * (y / -z);
	} else if (y <= -16500000000.0) {
		tmp = t;
	} else if (y <= -3.1e-43) {
		tmp = (x * t) / z;
	} else if (y <= -6.7e-90) {
		tmp = x * (t / -y);
	} else if (y <= 2.55) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.6e+136:
		tmp = t
	elif y <= -7e+71:
		tmp = t * (y / -z)
	elif y <= -16500000000.0:
		tmp = t
	elif y <= -3.1e-43:
		tmp = (x * t) / z
	elif y <= -6.7e-90:
		tmp = x * (t / -y)
	elif y <= 2.55:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.6e+136)
		tmp = t;
	elseif (y <= -7e+71)
		tmp = Float64(t * Float64(y / Float64(-z)));
	elseif (y <= -16500000000.0)
		tmp = t;
	elseif (y <= -3.1e-43)
		tmp = Float64(Float64(x * t) / z);
	elseif (y <= -6.7e-90)
		tmp = Float64(x * Float64(t / Float64(-y)));
	elseif (y <= 2.55)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.6e+136)
		tmp = t;
	elseif (y <= -7e+71)
		tmp = t * (y / -z);
	elseif (y <= -16500000000.0)
		tmp = t;
	elseif (y <= -3.1e-43)
		tmp = (x * t) / z;
	elseif (y <= -6.7e-90)
		tmp = x * (t / -y);
	elseif (y <= 2.55)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.6e+136], t, If[LessEqual[y, -7e+71], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -16500000000.0], t, If[LessEqual[y, -3.1e-43], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -6.7e-90], N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.55], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.60000000000000029e136 or -6.9999999999999998e71 < y < -1.65e10 or 2.5499999999999998 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 77.1%

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

      2. associate-/l* 74.5%

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

   3. Simplified 74.5%

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

   5. Taylor expanded in y around inf 62.9%

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

   if -7.60000000000000029e136 < y < -6.9999999999999998e71

   1. Initial program 99.8%

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

      1. associate-*l/ 84.8%

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

      2. sub-neg 84.8%

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

      3. +-commutative 84.8%

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

      4. neg-sub0 84.8%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 84.8%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 84.8%

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

      7. distribute-neg-frac2 84.8%

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

      8. distribute-frac-neg 84.8%

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

      9. distribute-lft-neg-in 84.8%

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

      10. sub-neg 84.8%

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

      11. distribute-neg-in 84.8%

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

      12. remove-double-neg 84.8%

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

      13. +-commutative 84.8%

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

      14. sub-neg 84.8%

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

      15. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in x around 0 77.2%

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

      1. associate-/l* 92.2%

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

   7. Simplified 92.2%

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

   8. Taylor expanded in y around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. associate-/l* 73.2%

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

      3. distribute-rgt-neg-in 73.2%

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

      4. distribute-neg-frac2 73.2%

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

   10. Simplified 73.2%

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

   if -1.65e10 < y < -3.0999999999999999e-43

   1. Initial program 99.9%

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

      1. associate-*l/ 99.9%

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

      2. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around 0 62.5%

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

   if -3.0999999999999999e-43 < y < -6.7000000000000004e-90

   1. Initial program 91.9%

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

      1. associate-*l/ 99.6%

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

      2. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

      1. associate-*r/ 99.6%

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

      2. associate-*l/ 91.9%

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

      3. *-commutative 91.9%

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

      4. clear-num 91.6%

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

      5. un-div-inv 91.5%

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

   6. Applied egg-rr 91.5%

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

   7. Taylor expanded in x around inf 60.6%

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

      1. associate-*l/ 60.4%

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

      2. *-commutative 60.4%

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

   9. Simplified 60.4%

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

   10. Taylor expanded in z around 0 59.8%

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

       1. mul-1-neg 59.8%

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

       2. distribute-neg-frac2 59.8%

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

   12. Simplified 59.8%

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

   if -6.7000000000000004e-90 < y < 2.5499999999999998

   1. Initial program 93.3%

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

   3. Taylor expanded in y around 0 68.2%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+136}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq -16500000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-43}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{elif}\;y \leq 2.55:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+140}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-43}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-90}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;y \leq 4.8:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.9e+140)
   t
   (if (<= y -1.95e+71)
     (* t (/ y (- z)))
     (if (<= y -5.3e+14)
       t
       (if (<= y -3.3e-43)
         (/ (* x t) z)
         (if (<= y -6.5e-90)
           (/ (* x t) (- y))
           (if (<= y 4.8) (* t (/ x z)) t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.9e+140) {
		tmp = t;
	} else if (y <= -1.95e+71) {
		tmp = t * (y / -z);
	} else if (y <= -5.3e+14) {
		tmp = t;
	} else if (y <= -3.3e-43) {
		tmp = (x * t) / z;
	} else if (y <= -6.5e-90) {
		tmp = (x * t) / -y;
	} else if (y <= 4.8) {
		tmp = t * (x / 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 <= (-1.9d+140)) then
        tmp = t
    else if (y <= (-1.95d+71)) then
        tmp = t * (y / -z)
    else if (y <= (-5.3d+14)) then
        tmp = t
    else if (y <= (-3.3d-43)) then
        tmp = (x * t) / z
    else if (y <= (-6.5d-90)) then
        tmp = (x * t) / -y
    else if (y <= 4.8d0) then
        tmp = t * (x / 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 <= -1.9e+140) {
		tmp = t;
	} else if (y <= -1.95e+71) {
		tmp = t * (y / -z);
	} else if (y <= -5.3e+14) {
		tmp = t;
	} else if (y <= -3.3e-43) {
		tmp = (x * t) / z;
	} else if (y <= -6.5e-90) {
		tmp = (x * t) / -y;
	} else if (y <= 4.8) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.9e+140:
		tmp = t
	elif y <= -1.95e+71:
		tmp = t * (y / -z)
	elif y <= -5.3e+14:
		tmp = t
	elif y <= -3.3e-43:
		tmp = (x * t) / z
	elif y <= -6.5e-90:
		tmp = (x * t) / -y
	elif y <= 4.8:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.9e+140)
		tmp = t;
	elseif (y <= -1.95e+71)
		tmp = Float64(t * Float64(y / Float64(-z)));
	elseif (y <= -5.3e+14)
		tmp = t;
	elseif (y <= -3.3e-43)
		tmp = Float64(Float64(x * t) / z);
	elseif (y <= -6.5e-90)
		tmp = Float64(Float64(x * t) / Float64(-y));
	elseif (y <= 4.8)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.9e+140)
		tmp = t;
	elseif (y <= -1.95e+71)
		tmp = t * (y / -z);
	elseif (y <= -5.3e+14)
		tmp = t;
	elseif (y <= -3.3e-43)
		tmp = (x * t) / z;
	elseif (y <= -6.5e-90)
		tmp = (x * t) / -y;
	elseif (y <= 4.8)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.9e+140], t, If[LessEqual[y, -1.95e+71], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.3e+14], t, If[LessEqual[y, -3.3e-43], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -6.5e-90], N[(N[(x * t), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[y, 4.8], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.9e140 or -1.9500000000000001e71 < y < -5.3e14 or 4.79999999999999982 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 77.1%

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

      2. associate-/l* 74.5%

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

   3. Simplified 74.5%

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

   5. Taylor expanded in y around inf 62.9%

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

   if -1.9e140 < y < -1.9500000000000001e71

   1. Initial program 99.8%

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

      1. associate-*l/ 84.8%

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

      2. sub-neg 84.8%

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

      3. +-commutative 84.8%

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

      4. neg-sub0 84.8%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 84.8%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 84.8%

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

      7. distribute-neg-frac2 84.8%

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

      8. distribute-frac-neg 84.8%

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

      9. distribute-lft-neg-in 84.8%

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

      10. sub-neg 84.8%

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

      11. distribute-neg-in 84.8%

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

      12. remove-double-neg 84.8%

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

      13. +-commutative 84.8%

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

      14. sub-neg 84.8%

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

      15. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in x around 0 77.2%

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

      1. associate-/l* 92.2%

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

   7. Simplified 92.2%

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

   8. Taylor expanded in y around 0 58.4%

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

      1. mul-1-neg 58.4%

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

      2. associate-/l* 73.2%

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

      3. distribute-rgt-neg-in 73.2%

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

      4. distribute-neg-frac2 73.2%

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

   10. Simplified 73.2%

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

   if -5.3e14 < y < -3.30000000000000016e-43

   1. Initial program 99.9%

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

      1. associate-*l/ 99.9%

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

      2. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around 0 62.5%

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

   if -3.30000000000000016e-43 < y < -6.4999999999999996e-90

   1. Initial program 91.9%

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

      1. associate-*l/ 99.6%

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

      2. sub-neg 99.6%

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

      3. +-commutative 99.6%

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

      4. neg-sub0 99.6%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 99.6%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 99.6%

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

      7. distribute-neg-frac2 99.6%

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

      8. distribute-frac-neg 99.6%

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

      9. distribute-lft-neg-in 99.6%

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

      10. sub-neg 99.6%

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

      11. distribute-neg-in 99.6%

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

      12. remove-double-neg 99.6%

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

      13. +-commutative 99.6%

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

      14. sub-neg 99.6%

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

      15. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 75.9%

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

   6. Taylor expanded in y around 0 59.9%

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

      1. associate-*r/ 59.9%

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

      2. associate-*r* 59.9%

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

      3. neg-mul-1 59.9%

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

   8. Simplified 59.9%

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

   if -6.4999999999999996e-90 < y < 4.79999999999999982

   1. Initial program 93.3%

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

   3. Taylor expanded in y around 0 68.2%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+140}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{+14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-43}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-90}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;y \leq 4.8:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+220}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+194}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.4e+220)
   (* t (- 1.0 (/ x y)))
   (if (<= y 2e+194) (* (- y x) (/ t (- y z))) (- t (* t (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.4e+220) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 2e+194) {
		tmp = (y - x) * (t / (y - z));
	} else {
		tmp = t - (t * (x / 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 <= (-4.4d+220)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= 2d+194) then
        tmp = (y - x) * (t / (y - z))
    else
        tmp = t - (t * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.4e+220) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 2e+194) {
		tmp = (y - x) * (t / (y - z));
	} else {
		tmp = t - (t * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.4e+220:
		tmp = t * (1.0 - (x / y))
	elif y <= 2e+194:
		tmp = (y - x) * (t / (y - z))
	else:
		tmp = t - (t * (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.4e+220)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= 2e+194)
		tmp = Float64(Float64(y - x) * Float64(t / Float64(y - z)));
	else
		tmp = Float64(t - Float64(t * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.4e+220)
		tmp = t * (1.0 - (x / y));
	elseif (y <= 2e+194)
		tmp = (y - x) * (t / (y - z));
	else
		tmp = t - (t * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.4e+220], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+194], N[(N[(y - x), $MachinePrecision] * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.39999999999999978e220

   1. Initial program 99.9%

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

      1. associate-*l/ 64.1%

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

      2. sub-neg 64.1%

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

      3. +-commutative 64.1%

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

      4. neg-sub0 64.1%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 64.1%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 64.1%

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

      7. distribute-neg-frac2 64.1%

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

      8. distribute-frac-neg 64.1%

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

      9. distribute-lft-neg-in 64.1%

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

      10. sub-neg 64.1%

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

      11. distribute-neg-in 64.1%

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

      12. remove-double-neg 64.1%

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

      13. +-commutative 64.1%

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

      14. sub-neg 64.1%

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

      15. *-commutative 64.1%

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

   3. Simplified 64.1%

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

   5. Taylor expanded in z around 0 64.1%

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

      1. associate-/l* 96.5%

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

      2. div-sub 96.5%

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

      3. *-inverses 96.5%

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

   7. Simplified 96.5%

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

   if -4.39999999999999978e220 < y < 1.99999999999999989e194

   1. Initial program 96.0%

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

      1. associate-*l/ 89.8%

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

      2. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   if 1.99999999999999989e194 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 70.4%

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

      2. sub-neg 70.4%

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

      3. +-commutative 70.4%

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

      4. neg-sub0 70.4%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 70.4%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 70.4%

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

      7. distribute-neg-frac2 70.4%

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

      8. distribute-frac-neg 70.4%

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

      9. distribute-lft-neg-in 70.4%

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

      10. sub-neg 70.4%

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

      11. distribute-neg-in 70.4%

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

      12. remove-double-neg 70.4%

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

      13. +-commutative 70.4%

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

      14. sub-neg 70.4%

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

      15. *-commutative 70.4%

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

   3. Simplified 70.4%

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

   5. Taylor expanded in z around 0 63.9%

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

   6. Taylor expanded in y around 0 83.6%

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

      1. mul-1-neg 83.6%

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

      2. unsub-neg 83.6%

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

      3. associate-/l* 90.5%

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

   8. Simplified 90.5%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+220}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+194}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-133}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.9e-133)
   (* t (/ y (- y z)))
   (if (<= y 5.2e-98) (* x (/ t z)) (* t (- 1.0 (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.9e-133) {
		tmp = t * (y / (y - z));
	} else if (y <= 5.2e-98) {
		tmp = x * (t / z);
	} else {
		tmp = t * (1.0 - (x / 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 <= (-2.9d-133)) then
        tmp = t * (y / (y - z))
    else if (y <= 5.2d-98) then
        tmp = x * (t / z)
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.9e-133) {
		tmp = t * (y / (y - z));
	} else if (y <= 5.2e-98) {
		tmp = x * (t / z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.9e-133:
		tmp = t * (y / (y - z))
	elif y <= 5.2e-98:
		tmp = x * (t / z)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.9e-133)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (y <= 5.2e-98)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.9e-133)
		tmp = t * (y / (y - z));
	elseif (y <= 5.2e-98)
		tmp = x * (t / z);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.9e-133], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e-98], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8999999999999998e-133

   1. Initial program 98.8%

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

      1. associate-*l/ 85.1%

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

      2. sub-neg 85.1%

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

      3. +-commutative 85.1%

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

      4. neg-sub0 85.1%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 85.1%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 85.1%

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

      7. distribute-neg-frac2 85.1%

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

      8. distribute-frac-neg 85.1%

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

      9. distribute-lft-neg-in 85.1%

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

      10. sub-neg 85.1%

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

      11. distribute-neg-in 85.1%

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

      12. remove-double-neg 85.1%

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

      13. +-commutative 85.1%

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

      14. sub-neg 85.1%

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

      15. *-commutative 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in x around 0 59.7%

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

      1. associate-/l* 71.4%

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

   7. Simplified 71.4%

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

   if -2.8999999999999998e-133 < y < 5.20000000000000027e-98

   1. Initial program 92.6%

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

      1. associate-*l/ 90.9%

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

      2. associate-/l* 90.8%

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

   3. Simplified 90.8%

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

      1. associate-*r/ 90.9%

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

      2. associate-*l/ 92.6%

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

      3. *-commutative 92.6%

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

      4. clear-num 92.0%

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

      5. un-div-inv 92.0%

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

   6. Applied egg-rr 92.0%

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

   7. Taylor expanded in x around inf 80.9%

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

      1. associate-*l/ 82.8%

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

      2. *-commutative 82.8%

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

   9. Simplified 82.8%

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

   10. Taylor expanded in z around inf 75.3%

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

   if 5.20000000000000027e-98 < y

   1. Initial program 98.7%

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

      1. associate-*l/ 80.4%

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

      2. sub-neg 80.4%

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

      3. +-commutative 80.4%

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

      4. neg-sub0 80.4%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 80.4%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 80.4%

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

      7. distribute-neg-frac2 80.4%

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

      8. distribute-frac-neg 80.4%

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

      9. distribute-lft-neg-in 80.4%

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

      10. sub-neg 80.4%

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

      11. distribute-neg-in 80.4%

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

      12. remove-double-neg 80.4%

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

      13. +-commutative 80.4%

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

      14. sub-neg 80.4%

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

      15. *-commutative 80.4%

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

   3. Simplified 80.4%

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

   5. Taylor expanded in z around 0 60.0%

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

      1. associate-/l* 71.7%

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

      2. div-sub 71.7%

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

      3. *-inverses 71.7%

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

   7. Simplified 71.7%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-133}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-90}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.98:\\ \;\;\;\;t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.6e-90) t (if (<= y 1.98) (* t (/ y z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e-90) {
		tmp = t;
	} else if (y <= 1.98) {
		tmp = t * (y / 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 <= (-1.6d-90)) then
        tmp = t
    else if (y <= 1.98d0) then
        tmp = t * (y / 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 <= -1.6e-90) {
		tmp = t;
	} else if (y <= 1.98) {
		tmp = t * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.6e-90:
		tmp = t
	elif y <= 1.98:
		tmp = t * (y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.6e-90)
		tmp = t;
	elseif (y <= 1.98)
		tmp = Float64(t * Float64(y / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.6e-90)
		tmp = t;
	elseif (y <= 1.98)
		tmp = t * (y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.6e-90], t, If[LessEqual[y, 1.98], N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.60000000000000004e-90 or 1.98 < y

   1. Initial program 99.2%

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

      1. associate-*l/ 81.3%

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

      2. associate-/l* 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in y around inf 51.8%

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

   if -1.60000000000000004e-90 < y < 1.98

   1. Initial program 93.3%

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

      1. associate-*l/ 91.2%

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

      2. sub-neg 91.2%

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

      3. +-commutative 91.2%

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

      4. neg-sub0 91.2%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{\left(0 - y\right)} + z} \]

      5. associate-+l- 91.2%

         \[\leadsto \frac{\left(x - y\right) \cdot t}{\color{blue}{0 - \left(y - z\right)}} \]

      6. neg-sub0 91.2%

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

      7. distribute-neg-frac2 91.2%

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

      8. distribute-frac-neg 91.2%

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

      9. distribute-lft-neg-in 91.2%

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

      10. sub-neg 91.2%

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

      11. distribute-neg-in 91.2%

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

      12. remove-double-neg 91.2%

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

      13. +-commutative 91.2%

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

      14. sub-neg 91.2%

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

      15. *-commutative 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in x around 0 39.3%

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

      1. associate-/l* 40.7%

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

   7. Simplified 40.7%

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

   8. Taylor expanded in y around 0 35.9%

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

      1. mul-1-neg 35.9%

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

      2. associate-/l* 34.6%

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

      3. distribute-rgt-neg-in 34.6%

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

      4. distribute-neg-frac2 34.6%

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

   10. Simplified 34.6%

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

       1. add0 34.6%

          \[\leadsto \color{blue}{t \cdot \frac{y}{-z} + 0} \]

       2. clear-num 34.1%

          \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{-z}{y}}} + 0 \]

       3. un-div-inv 34.1%

          \[\leadsto \color{blue}{\frac{t}{\frac{-z}{y}}} + 0 \]

       4. add-sqr-sqrt 14.7%

          \[\leadsto \frac{t}{\frac{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}{y}} + 0 \]

       5. sqrt-unprod 32.3%

          \[\leadsto \frac{t}{\frac{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}}{y}} + 0 \]

       6. sqr-neg 32.3%

          \[\leadsto \frac{t}{\frac{\sqrt{\color{blue}{z \cdot z}}}{y}} + 0 \]

       7. sqrt-unprod 13.3%

          \[\leadsto \frac{t}{\frac{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}{y}} + 0 \]

       8. add-sqr-sqrt 27.9%

          \[\leadsto \frac{t}{\frac{\color{blue}{z}}{y}} + 0 \]

   12. Applied egg-rr 27.9%

       \[\leadsto \color{blue}{\frac{t}{\frac{z}{y}} + 0} \]
   13. Step-by-step derivation

       1. associate-/r/ 32.2%

          \[\leadsto \color{blue}{\frac{t}{z} \cdot y} + 0 \]

       2. mul0-lft 32.2%

          \[\leadsto \frac{t}{z} \cdot y + \color{blue}{0 \cdot y} \]

       3. distribute-rgt-in 32.2%

          \[\leadsto \color{blue}{y \cdot \left(\frac{t}{z} + 0\right)} \]

       4. add0 32.2%

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

       5. associate-/l* 27.8%

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

       6. *-commutative 27.8%

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

       7. associate-/l* 27.9%

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

   14. Simplified 27.9%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-90}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.98:\\ \;\;\;\;t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.115:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.98:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.115) t (if (<= y 0.98) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.115) {
		tmp = t;
	} else if (y <= 0.98) {
		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 <= (-0.115d0)) then
        tmp = t
    else if (y <= 0.98d0) 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 <= -0.115) {
		tmp = t;
	} else if (y <= 0.98) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.115:
		tmp = t
	elif y <= 0.98:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.115)
		tmp = t;
	elseif (y <= 0.98)
		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 <= -0.115)
		tmp = t;
	elseif (y <= 0.98)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.115], t, If[LessEqual[y, 0.98], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -0.115000000000000005 or 0.97999999999999998 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in y around inf 57.9%

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

   if -0.115000000000000005 < y < 0.97999999999999998

   1. Initial program 93.7%

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

      1. associate-*l/ 92.7%

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

      2. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

      1. associate-*r/ 92.7%

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

      2. associate-*l/ 93.7%

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

      3. *-commutative 93.7%

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

      4. clear-num 93.2%

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

      5. un-div-inv 93.6%

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

   6. Applied egg-rr 93.6%

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

   7. Taylor expanded in x around inf 73.4%

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

      1. associate-*l/ 74.6%

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

      2. *-commutative 74.6%

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

   9. Simplified 74.6%

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

   10. Taylor expanded in z around inf 61.0%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.115:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 0.98:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -510000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.5:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -510000000000.0) t (if (<= y 4.5) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -510000000000.0) {
		tmp = t;
	} else if (y <= 4.5) {
		tmp = t * (x / 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 <= (-510000000000.0d0)) then
        tmp = t
    else if (y <= 4.5d0) then
        tmp = t * (x / 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 <= -510000000000.0) {
		tmp = t;
	} else if (y <= 4.5) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -510000000000.0:
		tmp = t
	elif y <= 4.5:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -510000000000.0)
		tmp = t;
	elseif (y <= 4.5)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -510000000000.0)
		tmp = t;
	elseif (y <= 4.5)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -510000000000.0], t, If[LessEqual[y, 4.5], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -5.1e11 or 4.5 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 77.9%

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

      2. associate-/l* 75.6%

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

   3. Simplified 75.6%

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

   5. Taylor expanded in y around inf 58.3%

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

   if -5.1e11 < y < 4.5

   1. Initial program 93.7%

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

   3. Taylor expanded in y around 0 62.0%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -510000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.5:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 35.6% 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 96.7%

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

   1. associate-*l/ 85.5%

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

   2. associate-/l* 83.9%

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

3. Simplified 83.9%

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

5. Taylor expanded in y around inf 34.4%

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

6. Final simplification 34.4%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 97.3% 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 2024046 
(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))