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

Percentage Accurate: 97.0% → 97.0%

Time: 11.8s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

3. Final simplification 97.7%

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

Alternative 2: 60.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ t_2 := \frac{t}{\frac{y}{-x}}\\ t_3 := x \cdot \frac{t}{z}\\ \mathbf{if}\;x \leq -2 \cdot 10^{+117}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.26 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.28 \cdot 10^{-30}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+169}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+217}:\\ \;\;\;\;\left(-x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+241}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))) (t_2 (/ t (/ y (- x)))) (t_3 (* x (/ t z))))
   (if (<= x -2e+117)
     t_2
     (if (<= x -1.26e+57)
       t_1
       (if (<= x -1.28e-30)
         (/ t (/ z x))
         (if (<= x 1.8e+22)
           t_1
           (if (<= x 1.02e+169)
             t_3
             (if (<= x 1.05e+217)
               (* (- x) (/ t y))
               (if (<= x 8.2e+241) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = t / (y / -x);
	double t_3 = x * (t / z);
	double tmp;
	if (x <= -2e+117) {
		tmp = t_2;
	} else if (x <= -1.26e+57) {
		tmp = t_1;
	} else if (x <= -1.28e-30) {
		tmp = t / (z / x);
	} else if (x <= 1.8e+22) {
		tmp = t_1;
	} else if (x <= 1.02e+169) {
		tmp = t_3;
	} else if (x <= 1.05e+217) {
		tmp = -x * (t / y);
	} else if (x <= 8.2e+241) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    t_2 = t / (y / -x)
    t_3 = x * (t / z)
    if (x <= (-2d+117)) then
        tmp = t_2
    else if (x <= (-1.26d+57)) then
        tmp = t_1
    else if (x <= (-1.28d-30)) then
        tmp = t / (z / x)
    else if (x <= 1.8d+22) then
        tmp = t_1
    else if (x <= 1.02d+169) then
        tmp = t_3
    else if (x <= 1.05d+217) then
        tmp = -x * (t / y)
    else if (x <= 8.2d+241) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = t / (y / -x);
	double t_3 = x * (t / z);
	double tmp;
	if (x <= -2e+117) {
		tmp = t_2;
	} else if (x <= -1.26e+57) {
		tmp = t_1;
	} else if (x <= -1.28e-30) {
		tmp = t / (z / x);
	} else if (x <= 1.8e+22) {
		tmp = t_1;
	} else if (x <= 1.02e+169) {
		tmp = t_3;
	} else if (x <= 1.05e+217) {
		tmp = -x * (t / y);
	} else if (x <= 8.2e+241) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	t_2 = t / (y / -x)
	t_3 = x * (t / z)
	tmp = 0
	if x <= -2e+117:
		tmp = t_2
	elif x <= -1.26e+57:
		tmp = t_1
	elif x <= -1.28e-30:
		tmp = t / (z / x)
	elif x <= 1.8e+22:
		tmp = t_1
	elif x <= 1.02e+169:
		tmp = t_3
	elif x <= 1.05e+217:
		tmp = -x * (t / y)
	elif x <= 8.2e+241:
		tmp = t_3
	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(t / Float64(y / Float64(-x)))
	t_3 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (x <= -2e+117)
		tmp = t_2;
	elseif (x <= -1.26e+57)
		tmp = t_1;
	elseif (x <= -1.28e-30)
		tmp = Float64(t / Float64(z / x));
	elseif (x <= 1.8e+22)
		tmp = t_1;
	elseif (x <= 1.02e+169)
		tmp = t_3;
	elseif (x <= 1.05e+217)
		tmp = Float64(Float64(-x) * Float64(t / y));
	elseif (x <= 8.2e+241)
		tmp = t_3;
	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 = t / (y / -x);
	t_3 = x * (t / z);
	tmp = 0.0;
	if (x <= -2e+117)
		tmp = t_2;
	elseif (x <= -1.26e+57)
		tmp = t_1;
	elseif (x <= -1.28e-30)
		tmp = t / (z / x);
	elseif (x <= 1.8e+22)
		tmp = t_1;
	elseif (x <= 1.02e+169)
		tmp = t_3;
	elseif (x <= 1.05e+217)
		tmp = -x * (t / y);
	elseif (x <= 8.2e+241)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(y / (-x)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2e+117], t$95$2, If[LessEqual[x, -1.26e+57], t$95$1, If[LessEqual[x, -1.28e-30], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e+22], t$95$1, If[LessEqual[x, 1.02e+169], t$95$3, If[LessEqual[x, 1.05e+217], N[((-x) * N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e+241], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.0000000000000001e117 or 8.2000000000000003e241 < x

   1. Initial program 99.7%

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

      1. associate-*l/ 82.3%

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

      2. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

      1. associate-*r/ 82.3%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. clear-num 99.7%

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

      5. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 89.9%

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

   8. Taylor expanded in z around 0 59.0%

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

      1. neg-mul-1 59.0%

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

      2. distribute-neg-frac2 59.0%

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

   10. Simplified 59.0%

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

   if -2.0000000000000001e117 < x < -1.26e57 or -1.28000000000000007e-30 < x < 1.8e22

   1. Initial program 97.3%

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

   3. Taylor expanded in x around 0 80.1%

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

      1. neg-mul-1 80.1%

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

      2. distribute-neg-frac 80.1%

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

   5. Simplified 80.1%

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

      1. *-commutative 80.1%

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

      2. distribute-frac-neg 80.1%

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

      3. distribute-frac-neg2 80.1%

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

      4. associate-*r/ 67.3%

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

      5. sub-neg 67.3%

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

      6. distribute-neg-in 67.3%

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

      7. remove-double-neg 67.3%

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

   7. Applied egg-rr 67.3%

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

      1. associate-/l* 80.1%

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

      2. +-commutative 80.1%

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

      3. unsub-neg 80.1%

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

   9. Simplified 80.1%

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

   if -1.26e57 < x < -1.28000000000000007e-30

   1. Initial program 99.4%

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

      1. associate-*l/ 89.4%

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

      2. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

      1. associate-*r/ 89.4%

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

      2. associate-*l/ 99.4%

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

      3. *-commutative 99.4%

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

      4. clear-num 99.3%

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

      5. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 78.5%

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

   if 1.8e22 < x < 1.02000000000000005e169 or 1.05e217 < x < 8.2000000000000003e241

   1. Initial program 95.1%

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

   3. Taylor expanded in y around 0 64.2%

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

      1. *-commutative 64.2%

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

      2. clear-num 64.2%

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

      3. un-div-inv 64.1%

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

   5. Applied egg-rr 64.1%

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

      1. associate-/r/ 68.5%

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

   7. Simplified 68.5%

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

   if 1.02000000000000005e169 < x < 1.05e217

   1. Initial program 99.2%

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

      1. associate-*l/ 90.4%

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

      2. associate-/l* 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in x around inf 90.4%

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

   6. Taylor expanded in z around 0 71.4%

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

      1. associate-*r/ 71.4%

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

      2. mul-1-neg 71.4%

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

      3. distribute-rgt-neg-out 71.4%

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

   8. Simplified 71.4%

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

      1. frac-2neg 71.4%

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

      2. distribute-frac-neg 71.4%

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

      3. add-sqr-sqrt 11.5%

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

      4. sqrt-unprod 12.1%

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

      5. sqr-neg 12.1%

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

      6. sqrt-unprod 0.6%

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

      7. add-sqr-sqrt 1.1%

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

      8. div-inv 1.1%

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

      9. *-commutative 1.1%

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

      10. associate-*l* 1.3%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 23.2%

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

      13. sqr-neg 23.2%

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

      14. sqrt-unprod 80.3%

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

      15. add-sqr-sqrt 79.9%

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

      16. add-sqr-sqrt 59.4%

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

      17. sqrt-unprod 60.3%

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

      18. sqr-neg 60.3%

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

      19. sqrt-unprod 0.7%

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

      20. add-sqr-sqrt 1.3%

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

      21. div-inv 1.3%

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

      22. add-sqr-sqrt 0.7%

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

      23. sqrt-unprod 60.7%

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

      24. sqr-neg 60.7%

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

      25. sqrt-unprod 59.6%

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

      26. add-sqr-sqrt 80.5%

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

   10. Applied egg-rr 80.5%

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

       1. distribute-rgt-neg-in 80.5%

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

       2. mul-1-neg 80.5%

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

       3. associate-*r/ 80.5%

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

       4. neg-mul-1 80.5%

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

   12. Simplified 80.5%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+117}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{elif}\;x \leq -1.26 \cdot 10^{+57}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq -1.28 \cdot 10^{-30}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+22}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+169}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+217}:\\ \;\;\;\;\left(-x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+241}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1900000000000:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-15}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5000000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+86}:\\ \;\;\;\;\left(-x\right) \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.85e+112)
   t
   (if (<= y -1900000000000.0)
     (* t (/ x z))
     (if (<= y -7.6e-15)
       t
       (if (<= y 5000000.0)
         (* x (/ t z))
         (if (<= y 1.5e+86) (* (- x) (/ t y)) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.85e+112) {
		tmp = t;
	} else if (y <= -1900000000000.0) {
		tmp = t * (x / z);
	} else if (y <= -7.6e-15) {
		tmp = t;
	} else if (y <= 5000000.0) {
		tmp = x * (t / z);
	} else if (y <= 1.5e+86) {
		tmp = -x * (t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.85d+112)) then
        tmp = t
    else if (y <= (-1900000000000.0d0)) then
        tmp = t * (x / z)
    else if (y <= (-7.6d-15)) then
        tmp = t
    else if (y <= 5000000.0d0) then
        tmp = x * (t / z)
    else if (y <= 1.5d+86) then
        tmp = -x * (t / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.85e+112) {
		tmp = t;
	} else if (y <= -1900000000000.0) {
		tmp = t * (x / z);
	} else if (y <= -7.6e-15) {
		tmp = t;
	} else if (y <= 5000000.0) {
		tmp = x * (t / z);
	} else if (y <= 1.5e+86) {
		tmp = -x * (t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.85e+112:
		tmp = t
	elif y <= -1900000000000.0:
		tmp = t * (x / z)
	elif y <= -7.6e-15:
		tmp = t
	elif y <= 5000000.0:
		tmp = x * (t / z)
	elif y <= 1.5e+86:
		tmp = -x * (t / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.85e+112)
		tmp = t;
	elseif (y <= -1900000000000.0)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= -7.6e-15)
		tmp = t;
	elseif (y <= 5000000.0)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= 1.5e+86)
		tmp = Float64(Float64(-x) * Float64(t / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.85e+112)
		tmp = t;
	elseif (y <= -1900000000000.0)
		tmp = t * (x / z);
	elseif (y <= -7.6e-15)
		tmp = t;
	elseif (y <= 5000000.0)
		tmp = x * (t / z);
	elseif (y <= 1.5e+86)
		tmp = -x * (t / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.85e+112], t, If[LessEqual[y, -1900000000000.0], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.6e-15], t, If[LessEqual[y, 5000000.0], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+86], N[((-x) * N[(t / y), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.85000000000000002e112 or -1.9e12 < y < -7.6000000000000004e-15 or 1.49999999999999988e86 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 73.2%

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

      2. associate-/l* 73.2%

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

   3. Simplified 73.2%

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

   5. Taylor expanded in y around inf 68.9%

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

   if -1.85000000000000002e112 < y < -1.9e12

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 49.2%

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

   if -7.6000000000000004e-15 < y < 5e6

   1. Initial program 95.7%

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

   3. Taylor expanded in y around 0 65.5%

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

      1. *-commutative 65.5%

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

      2. clear-num 65.4%

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

      3. un-div-inv 65.5%

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

   5. Applied egg-rr 65.5%

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

      1. associate-/r/ 65.8%

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

   7. Simplified 65.8%

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

   if 5e6 < y < 1.49999999999999988e86

   1. Initial program 99.5%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in x around inf 57.4%

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

   6. Taylor expanded in z around 0 49.7%

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

      1. associate-*r/ 49.7%

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

      2. mul-1-neg 49.7%

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

      3. distribute-rgt-neg-out 49.7%

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

   8. Simplified 49.7%

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

      1. frac-2neg 49.7%

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

      2. distribute-frac-neg 49.7%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 7.1%

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

      5. sqr-neg 7.1%

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

      6. sqrt-unprod 7.1%

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

      7. add-sqr-sqrt 7.1%

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

      8. div-inv 7.1%

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

      9. *-commutative 7.1%

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

      10. associate-*l* 7.1%

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

      11. add-sqr-sqrt 6.4%

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

      12. sqrt-unprod 21.8%

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

      13. sqr-neg 21.8%

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

      14. sqrt-unprod 39.3%

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

      15. add-sqr-sqrt 53.9%

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

      16. add-sqr-sqrt 53.7%

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

      17. sqrt-unprod 53.9%

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

      18. sqr-neg 53.9%

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

      19. sqrt-unprod 0.0%

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

      20. add-sqr-sqrt 7.1%

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

      21. div-inv 7.1%

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

      22. add-sqr-sqrt 0.0%

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

      23. sqrt-unprod 54.1%

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

      24. sqr-neg 54.1%

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

      25. sqrt-unprod 53.8%

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

      26. add-sqr-sqrt 54.1%

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

   10. Applied egg-rr 54.1%

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

       1. distribute-rgt-neg-in 54.1%

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

       2. mul-1-neg 54.1%

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

       3. associate-*r/ 54.1%

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

       4. neg-mul-1 54.1%

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

   12. Simplified 54.1%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1900000000000:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-15}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5000000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+86}:\\ \;\;\;\;\left(-x\right) \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+114}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2000000000000:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-15}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6200000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+86}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.2e+114)
   t
   (if (<= y -2000000000000.0)
     (* t (/ x z))
     (if (<= y -1.02e-15)
       t
       (if (<= y 6200000.0)
         (* x (/ t z))
         (if (<= y 1.05e+86) (/ t (/ y (- x))) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e+114) {
		tmp = t;
	} else if (y <= -2000000000000.0) {
		tmp = t * (x / z);
	} else if (y <= -1.02e-15) {
		tmp = t;
	} else if (y <= 6200000.0) {
		tmp = x * (t / z);
	} else if (y <= 1.05e+86) {
		tmp = t / (y / -x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.2d+114)) then
        tmp = t
    else if (y <= (-2000000000000.0d0)) then
        tmp = t * (x / z)
    else if (y <= (-1.02d-15)) then
        tmp = t
    else if (y <= 6200000.0d0) then
        tmp = x * (t / z)
    else if (y <= 1.05d+86) then
        tmp = t / (y / -x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e+114) {
		tmp = t;
	} else if (y <= -2000000000000.0) {
		tmp = t * (x / z);
	} else if (y <= -1.02e-15) {
		tmp = t;
	} else if (y <= 6200000.0) {
		tmp = x * (t / z);
	} else if (y <= 1.05e+86) {
		tmp = t / (y / -x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.2e+114:
		tmp = t
	elif y <= -2000000000000.0:
		tmp = t * (x / z)
	elif y <= -1.02e-15:
		tmp = t
	elif y <= 6200000.0:
		tmp = x * (t / z)
	elif y <= 1.05e+86:
		tmp = t / (y / -x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.2e+114)
		tmp = t;
	elseif (y <= -2000000000000.0)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= -1.02e-15)
		tmp = t;
	elseif (y <= 6200000.0)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= 1.05e+86)
		tmp = Float64(t / Float64(y / Float64(-x)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.2e+114)
		tmp = t;
	elseif (y <= -2000000000000.0)
		tmp = t * (x / z);
	elseif (y <= -1.02e-15)
		tmp = t;
	elseif (y <= 6200000.0)
		tmp = x * (t / z);
	elseif (y <= 1.05e+86)
		tmp = t / (y / -x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.2e+114], t, If[LessEqual[y, -2000000000000.0], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.02e-15], t, If[LessEqual[y, 6200000.0], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+86], N[(t / N[(y / (-x)), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.2e114 or -2e12 < y < -1.02e-15 or 1.0499999999999999e86 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 73.2%

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

      2. associate-/l* 73.2%

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

   3. Simplified 73.2%

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

   5. Taylor expanded in y around inf 68.9%

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

   if -1.2e114 < y < -2e12

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 49.2%

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

   if -1.02e-15 < y < 6.2e6

   1. Initial program 95.7%

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

   3. Taylor expanded in y around 0 65.5%

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

      1. *-commutative 65.5%

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

      2. clear-num 65.4%

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

      3. un-div-inv 65.5%

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

   5. Applied egg-rr 65.5%

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

      1. associate-/r/ 65.8%

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

   7. Simplified 65.8%

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

   if 6.2e6 < y < 1.0499999999999999e86

   1. Initial program 99.5%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 96.1%

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

   3. Simplified 96.1%

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

      1. associate-*r/ 89.8%

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

      2. associate-*l/ 99.5%

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

      3. *-commutative 99.5%

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

      4. clear-num 99.5%

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

      5. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 65.5%

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

   8. Taylor expanded in z around 0 55.1%

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

      1. neg-mul-1 55.1%

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

      2. distribute-neg-frac2 55.1%

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

   10. Simplified 55.1%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+114}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2000000000000:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-15}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6200000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+86}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+129}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{+90}:\\ \;\;\;\;\left(\frac{x}{y} + -1\right) \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-30} \lor \neg \left(x \leq 4.7 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.3e+129)
   (* t (/ x (- z y)))
   (if (<= x -3.9e+90)
     (* (+ (/ x y) -1.0) (- t))
     (if (or (<= x -1.3e-30) (not (<= x 4.7e+30)))
       (/ t (/ (- z y) x))
       (* t (/ y (- y z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.3e+129) {
		tmp = t * (x / (z - y));
	} else if (x <= -3.9e+90) {
		tmp = ((x / y) + -1.0) * -t;
	} else if ((x <= -1.3e-30) || !(x <= 4.7e+30)) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.3d+129)) then
        tmp = t * (x / (z - y))
    else if (x <= (-3.9d+90)) then
        tmp = ((x / y) + (-1.0d0)) * -t
    else if ((x <= (-1.3d-30)) .or. (.not. (x <= 4.7d+30))) then
        tmp = t / ((z - y) / x)
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.3e+129) {
		tmp = t * (x / (z - y));
	} else if (x <= -3.9e+90) {
		tmp = ((x / y) + -1.0) * -t;
	} else if ((x <= -1.3e-30) || !(x <= 4.7e+30)) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.3e+129:
		tmp = t * (x / (z - y))
	elif x <= -3.9e+90:
		tmp = ((x / y) + -1.0) * -t
	elif (x <= -1.3e-30) or not (x <= 4.7e+30):
		tmp = t / ((z - y) / x)
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.3e+129)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (x <= -3.9e+90)
		tmp = Float64(Float64(Float64(x / y) + -1.0) * Float64(-t));
	elseif ((x <= -1.3e-30) || !(x <= 4.7e+30))
		tmp = Float64(t / Float64(Float64(z - y) / x));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.3e+129)
		tmp = t * (x / (z - y));
	elseif (x <= -3.9e+90)
		tmp = ((x / y) + -1.0) * -t;
	elseif ((x <= -1.3e-30) || ~((x <= 4.7e+30)))
		tmp = t / ((z - y) / x);
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.3e+129], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.9e+90], N[(N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision] * (-t)), $MachinePrecision], If[Or[LessEqual[x, -1.3e-30], N[Not[LessEqual[x, 4.7e+30]], $MachinePrecision]], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.30000000000000006e129

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 88.3%

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

   if -1.30000000000000006e129 < x < -3.9000000000000002e90

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 99.8%

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

      1. mul-1-neg 99.8%

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

      2. div-sub 100.0%

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

      3. sub-neg 100.0%

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

      4. *-inverses 100.0%

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

      5. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   if -3.9000000000000002e90 < x < -1.29999999999999993e-30 or 4.6999999999999999e30 < x

   1. Initial program 97.7%

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

      1. associate-*l/ 88.2%

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

      2. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

      1. associate-*r/ 88.2%

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

      2. associate-*l/ 97.7%

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

      3. *-commutative 97.7%

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

      4. clear-num 97.6%

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

      5. un-div-inv 97.8%

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

   6. Applied egg-rr 97.8%

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

   7. Taylor expanded in x around inf 84.0%

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

   if -1.29999999999999993e-30 < x < 4.6999999999999999e30

   1. Initial program 97.1%

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

   3. Taylor expanded in x around 0 81.0%

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

      1. neg-mul-1 81.0%

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

      2. distribute-neg-frac 81.0%

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

   5. Simplified 81.0%

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

      1. *-commutative 81.0%

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

      2. distribute-frac-neg 81.0%

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

      3. distribute-frac-neg2 81.0%

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

      4. associate-*r/ 67.9%

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

      5. sub-neg 67.9%

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

      6. distribute-neg-in 67.9%

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

      7. remove-double-neg 67.9%

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

   7. Applied egg-rr 67.9%

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

      1. associate-/l* 81.0%

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

      2. +-commutative 81.0%

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

      3. unsub-neg 81.0%

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

   9. Simplified 81.0%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+129}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{+90}:\\ \;\;\;\;\left(\frac{x}{y} + -1\right) \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-30} \lor \neg \left(x \leq 4.7 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.56 \cdot 10^{+102}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1700000000000 \lor \neg \left(y \leq -1.75 \cdot 10^{-14}\right) \land y \leq 2000000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.56e+102)
   t
   (if (or (<= y -1700000000000.0)
           (and (not (<= y -1.75e-14)) (<= y 2000000.0)))
     (* x (/ t z))
     t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.56e+102) {
		tmp = t;
	} else if ((y <= -1700000000000.0) || (!(y <= -1.75e-14) && (y <= 2000000.0))) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.56d+102)) then
        tmp = t
    else if ((y <= (-1700000000000.0d0)) .or. (.not. (y <= (-1.75d-14))) .and. (y <= 2000000.0d0)) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.56e+102) {
		tmp = t;
	} else if ((y <= -1700000000000.0) || (!(y <= -1.75e-14) && (y <= 2000000.0))) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.56e+102:
		tmp = t
	elif (y <= -1700000000000.0) or (not (y <= -1.75e-14) and (y <= 2000000.0)):
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.56e+102)
		tmp = t;
	elseif ((y <= -1700000000000.0) || (!(y <= -1.75e-14) && (y <= 2000000.0)))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.56e+102)
		tmp = t;
	elseif ((y <= -1700000000000.0) || (~((y <= -1.75e-14)) && (y <= 2000000.0)))
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.56e+102], t, If[Or[LessEqual[y, -1700000000000.0], And[N[Not[LessEqual[y, -1.75e-14]], $MachinePrecision], LessEqual[y, 2000000.0]]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.56e102 or -1.7e12 < y < -1.7500000000000001e-14 or 2e6 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 76.5%

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

      2. associate-/l* 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in y around inf 58.5%

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

   if -1.56e102 < y < -1.7e12 or -1.7500000000000001e-14 < y < 2e6

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0 64.0%

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

      1. *-commutative 64.0%

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

      2. clear-num 64.0%

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

      3. un-div-inv 64.0%

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

   5. Applied egg-rr 64.0%

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

      1. associate-/r/ 63.6%

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

   7. Simplified 63.6%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.56 \cdot 10^{+102}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1700000000000 \lor \neg \left(y \leq -1.75 \cdot 10^{-14}\right) \land y \leq 2000000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1900000000000:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1300000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.85e+112)
   t
   (if (<= y -1900000000000.0)
     (* t (/ x z))
     (if (<= y -2.1e-14) t (if (<= y 1300000.0) (* x (/ t z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.85e+112) {
		tmp = t;
	} else if (y <= -1900000000000.0) {
		tmp = t * (x / z);
	} else if (y <= -2.1e-14) {
		tmp = t;
	} else if (y <= 1300000.0) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.85d+112)) then
        tmp = t
    else if (y <= (-1900000000000.0d0)) then
        tmp = t * (x / z)
    else if (y <= (-2.1d-14)) then
        tmp = t
    else if (y <= 1300000.0d0) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.85e+112) {
		tmp = t;
	} else if (y <= -1900000000000.0) {
		tmp = t * (x / z);
	} else if (y <= -2.1e-14) {
		tmp = t;
	} else if (y <= 1300000.0) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.85e+112:
		tmp = t
	elif y <= -1900000000000.0:
		tmp = t * (x / z)
	elif y <= -2.1e-14:
		tmp = t
	elif y <= 1300000.0:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.85e+112)
		tmp = t;
	elseif (y <= -1900000000000.0)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= -2.1e-14)
		tmp = t;
	elseif (y <= 1300000.0)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.85e+112)
		tmp = t;
	elseif (y <= -1900000000000.0)
		tmp = t * (x / z);
	elseif (y <= -2.1e-14)
		tmp = t;
	elseif (y <= 1300000.0)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.85e+112], t, If[LessEqual[y, -1900000000000.0], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.1e-14], t, If[LessEqual[y, 1300000.0], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.85000000000000002e112 or -1.9e12 < y < -2.0999999999999999e-14 or 1.3e6 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 76.3%

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

      2. associate-/l* 77.6%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in y around inf 60.2%

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

   if -1.85000000000000002e112 < y < -1.9e12

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 49.2%

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

   if -2.0999999999999999e-14 < y < 1.3e6

   1. Initial program 95.7%

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

   3. Taylor expanded in y around 0 65.5%

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

      1. *-commutative 65.5%

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

      2. clear-num 65.4%

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

      3. un-div-inv 65.5%

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

   5. Applied egg-rr 65.5%

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

      1. associate-/r/ 65.8%

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

   7. Simplified 65.8%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1900000000000:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1300000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -1.08 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5000000:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+82}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -1.08e-16)
     t_1
     (if (<= y 5000000.0)
       (* (- x y) (/ t z))
       (if (<= y 2.2e+82) (/ t (/ y (- x))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -1.08e-16) {
		tmp = t_1;
	} else if (y <= 5000000.0) {
		tmp = (x - y) * (t / z);
	} else if (y <= 2.2e+82) {
		tmp = t / (y / -x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    if (y <= (-1.08d-16)) then
        tmp = t_1
    else if (y <= 5000000.0d0) then
        tmp = (x - y) * (t / z)
    else if (y <= 2.2d+82) then
        tmp = t / (y / -x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -1.08e-16) {
		tmp = t_1;
	} else if (y <= 5000000.0) {
		tmp = (x - y) * (t / z);
	} else if (y <= 2.2e+82) {
		tmp = t / (y / -x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -1.08e-16:
		tmp = t_1
	elif y <= 5000000.0:
		tmp = (x - y) * (t / z)
	elif y <= 2.2e+82:
		tmp = t / (y / -x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -1.08e-16)
		tmp = t_1;
	elseif (y <= 5000000.0)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 2.2e+82)
		tmp = Float64(t / Float64(y / Float64(-x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -1.08e-16)
		tmp = t_1;
	elseif (y <= 5000000.0)
		tmp = (x - y) * (t / z);
	elseif (y <= 2.2e+82)
		tmp = t / (y / -x);
	else
		tmp = t_1;
	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]}, If[LessEqual[y, -1.08e-16], t$95$1, If[LessEqual[y, 5000000.0], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+82], N[(t / N[(y / (-x)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.08e-16 or 2.2000000000000001e82 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 69.8%

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

      1. neg-mul-1 69.8%

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

      2. distribute-neg-frac 69.8%

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

   5. Simplified 69.8%

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

      1. *-commutative 69.8%

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

      2. distribute-frac-neg 69.8%

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

      3. distribute-frac-neg2 69.8%

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

      4. associate-*r/ 55.7%

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

      5. sub-neg 55.7%

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

      6. distribute-neg-in 55.7%

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

      7. remove-double-neg 55.7%

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

   7. Applied egg-rr 55.7%

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

      1. associate-/l* 69.8%

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

      2. +-commutative 69.8%

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

      3. unsub-neg 69.8%

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

   9. Simplified 69.8%

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

   if -1.08e-16 < y < 5e6

   1. Initial program 95.7%

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

      1. associate-*l/ 90.5%

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

      2. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in z around inf 77.8%

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

   if 5e6 < y < 2.2000000000000001e82

   1. Initial program 99.5%

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

      1. associate-*l/ 89.2%

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

      2. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

      1. associate-*r/ 89.2%

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

      2. associate-*l/ 99.5%

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

      3. *-commutative 99.5%

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

      4. clear-num 99.5%

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

      5. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 66.3%

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

   8. Taylor expanded in z around 0 57.9%

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

      1. neg-mul-1 57.9%

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

      2. distribute-neg-frac2 57.9%

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

   10. Simplified 57.9%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 5000000:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+82}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+115} \lor \neg \left(y \leq 1.55 \cdot 10^{+182}\right):\\ \;\;\;\;\left(\frac{x}{y} + -1\right) \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9.5e+115) (not (<= y 1.55e+182)))
   (* (+ (/ x y) -1.0) (- t))
   (* (- x y) (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.5e+115) || !(y <= 1.55e+182)) {
		tmp = ((x / y) + -1.0) * -t;
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-9.5d+115)) .or. (.not. (y <= 1.55d+182))) then
        tmp = ((x / y) + (-1.0d0)) * -t
    else
        tmp = (x - y) * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.5e+115) || !(y <= 1.55e+182)) {
		tmp = ((x / y) + -1.0) * -t;
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9.5e+115) or not (y <= 1.55e+182):
		tmp = ((x / y) + -1.0) * -t
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9.5e+115) || !(y <= 1.55e+182))
		tmp = Float64(Float64(Float64(x / y) + -1.0) * Float64(-t));
	else
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9.5e+115) || ~((y <= 1.55e+182)))
		tmp = ((x / y) + -1.0) * -t;
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9.5e+115], N[Not[LessEqual[y, 1.55e+182]], $MachinePrecision]], N[(N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision] * (-t)), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.4999999999999997e115 or 1.54999999999999998e182 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 97.1%

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

      1. mul-1-neg 97.1%

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

      2. div-sub 97.1%

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

      3. sub-neg 97.1%

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

      4. *-inverses 97.1%

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

      5. metadata-eval 97.1%

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

   5. Simplified 97.1%

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

   if -9.4999999999999997e115 < y < 1.54999999999999998e182

   1. Initial program 97.2%

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

      1. associate-*l/ 88.9%

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

      2. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+115} \lor \neg \left(y \leq 1.55 \cdot 10^{+182}\right):\\ \;\;\;\;\left(\frac{x}{y} + -1\right) \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-31} \lor \neg \left(x \leq 2.45 \cdot 10^{+30}\right):\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -6.2e-31) (not (<= x 2.45e+30)))
   (* t (/ x (- z y)))
   (* t (/ y (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6.2e-31) || !(x <= 2.45e+30)) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-6.2d-31)) .or. (.not. (x <= 2.45d+30))) then
        tmp = t * (x / (z - y))
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6.2e-31) || !(x <= 2.45e+30)) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -6.2e-31) or not (x <= 2.45e+30):
		tmp = t * (x / (z - y))
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -6.2e-31) || !(x <= 2.45e+30))
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -6.2e-31) || ~((x <= 2.45e+30)))
		tmp = t * (x / (z - y));
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -6.2e-31], N[Not[LessEqual[x, 2.45e+30]], $MachinePrecision]], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.19999999999999999e-31 or 2.44999999999999992e30 < x

   1. Initial program 98.3%

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

   3. Taylor expanded in x around inf 82.5%

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

   if -6.19999999999999999e-31 < x < 2.44999999999999992e30

   1. Initial program 97.1%

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

   3. Taylor expanded in x around 0 81.0%

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

      1. neg-mul-1 81.0%

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

      2. distribute-neg-frac 81.0%

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

   5. Simplified 81.0%

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

      1. *-commutative 81.0%

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

      2. distribute-frac-neg 81.0%

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

      3. distribute-frac-neg2 81.0%

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

      4. associate-*r/ 67.9%

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

      5. sub-neg 67.9%

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

      6. distribute-neg-in 67.9%

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

      7. remove-double-neg 67.9%

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

   7. Applied egg-rr 67.9%

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

      1. associate-/l* 81.0%

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

      2. +-commutative 81.0%

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

      3. unsub-neg 81.0%

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

   9. Simplified 81.0%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-31} \lor \neg \left(x \leq 2.45 \cdot 10^{+30}\right):\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-30} \lor \neg \left(x \leq 1.3 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.45e-30) (not (<= x 1.3e+33)))
   (/ t (/ (- z y) x))
   (* t (/ y (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.45e-30) || !(x <= 1.3e+33)) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.45d-30)) .or. (.not. (x <= 1.3d+33))) then
        tmp = t / ((z - y) / x)
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.45e-30) || !(x <= 1.3e+33)) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.45e-30) or not (x <= 1.3e+33):
		tmp = t / ((z - y) / x)
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.45e-30) || !(x <= 1.3e+33))
		tmp = Float64(t / Float64(Float64(z - y) / x));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.45e-30) || ~((x <= 1.3e+33)))
		tmp = t / ((z - y) / x);
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.45e-30], N[Not[LessEqual[x, 1.3e+33]], $MachinePrecision]], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.44999999999999995e-30 or 1.2999999999999999e33 < x

   1. Initial program 98.3%

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

      1. associate-*l/ 86.7%

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

      2. associate-/l* 87.6%

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

   3. Simplified 87.6%

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

      1. associate-*r/ 86.7%

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

      2. associate-*l/ 98.3%

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

      3. *-commutative 98.3%

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

      4. clear-num 98.3%

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

      5. un-div-inv 98.4%

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

   6. Applied egg-rr 98.4%

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

   7. Taylor expanded in x around inf 82.5%

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

   if -1.44999999999999995e-30 < x < 1.2999999999999999e33

   1. Initial program 97.1%

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

   3. Taylor expanded in x around 0 81.0%

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

      1. neg-mul-1 81.0%

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

      2. distribute-neg-frac 81.0%

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

   5. Simplified 81.0%

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

      1. *-commutative 81.0%

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

      2. distribute-frac-neg 81.0%

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

      3. distribute-frac-neg2 81.0%

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

      4. associate-*r/ 67.9%

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

      5. sub-neg 67.9%

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

      6. distribute-neg-in 67.9%

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

      7. remove-double-neg 67.9%

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

   7. Applied egg-rr 67.9%

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

      1. associate-/l* 81.0%

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

      2. +-commutative 81.0%

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

      3. unsub-neg 81.0%

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

   9. Simplified 81.0%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-30} \lor \neg \left(x \leq 1.3 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. associate-*l/ 85.1%

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

   2. associate-/l* 87.8%

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

3. Simplified 87.8%

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

5. Taylor expanded in y around inf 31.4%

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

6. Final simplification 31.4%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 97.0% 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 2024055 
(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))