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

Percentage Accurate: 97.1% → 96.6%

Time: 10.0s

Alternatives: 16

Speedup: 0.4×

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: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;t\_m \leq 2.6 \cdot 10^{+44}:\\ \;\;\;\;\frac{t\_m \cdot \left(x - y\right)}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_m}{\frac{z - y}{x - y}}\\ \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (<= t_m 2.6e+44)
    (/ (* t_m (- x y)) (- z y))
    (/ t_m (/ (- z y) (- x y))))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (t_m <= 2.6e+44) {
		tmp = (t_m * (x - y)) / (z - y);
	} else {
		tmp = t_m / ((z - y) / (x - y));
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if (t_m <= 2.6d+44) then
        tmp = (t_m * (x - y)) / (z - y)
    else
        tmp = t_m / ((z - y) / (x - y))
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (t_m <= 2.6e+44) {
		tmp = (t_m * (x - y)) / (z - y);
	} else {
		tmp = t_m / ((z - y) / (x - y));
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	tmp = 0
	if t_m <= 2.6e+44:
		tmp = (t_m * (x - y)) / (z - y)
	else:
		tmp = t_m / ((z - y) / (x - y))
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	tmp = 0.0
	if (t_m <= 2.6e+44)
		tmp = Float64(Float64(t_m * Float64(x - y)) / Float64(z - y));
	else
		tmp = Float64(t_m / Float64(Float64(z - y) / Float64(x - y)));
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	tmp = 0.0;
	if (t_m <= 2.6e+44)
		tmp = (t_m * (x - y)) / (z - y);
	else
		tmp = t_m / ((z - y) / (x - y));
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * If[LessEqual[t$95$m, 2.6e+44], N[(N[(t$95$m * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(t$95$m / N[(N[(z - y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < 2.5999999999999999e44

   1. Initial program 93.8%

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

      1. associate-*l/ 91.7%

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

      2. associate-/l* 82.7%

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

   3. Simplified 82.7%

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

      1. associate-*r/ 91.7%

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

   6. Applied egg-rr 91.7%

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

   if 2.5999999999999999e44 < t

   1. Initial program 96.2%

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

      1. associate-*l/ 50.7%

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

      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/ 50.7%

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

      2. associate-*l/ 96.2%

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

      3. *-commutative 96.2%

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

      4. clear-num 96.1%

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

      5. un-div-inv 96.2%

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

   6. Applied egg-rr 96.2%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.6 \cdot 10^{+44}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 68.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+79}:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+37}:\\ \;\;\;\;t\_m \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -950000:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-107}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t\_m}{z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \frac{t\_m}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_m\\ \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (<= y -5.3e+79)
    t_m
    (if (<= y -7e+37)
      (* t_m (/ x (- z y)))
      (if (<= y -950000.0)
        t_m
        (if (<= y -2.2e-107)
          (* (- x y) (/ t_m z))
          (if (<= y 4e+82) (* x (/ t_m (- z y))) t_m)))))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -5.3e+79) {
		tmp = t_m;
	} else if (y <= -7e+37) {
		tmp = t_m * (x / (z - y));
	} else if (y <= -950000.0) {
		tmp = t_m;
	} else if (y <= -2.2e-107) {
		tmp = (x - y) * (t_m / z);
	} else if (y <= 4e+82) {
		tmp = x * (t_m / (z - y));
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if (y <= (-5.3d+79)) then
        tmp = t_m
    else if (y <= (-7d+37)) then
        tmp = t_m * (x / (z - y))
    else if (y <= (-950000.0d0)) then
        tmp = t_m
    else if (y <= (-2.2d-107)) then
        tmp = (x - y) * (t_m / z)
    else if (y <= 4d+82) then
        tmp = x * (t_m / (z - y))
    else
        tmp = t_m
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -5.3e+79) {
		tmp = t_m;
	} else if (y <= -7e+37) {
		tmp = t_m * (x / (z - y));
	} else if (y <= -950000.0) {
		tmp = t_m;
	} else if (y <= -2.2e-107) {
		tmp = (x - y) * (t_m / z);
	} else if (y <= 4e+82) {
		tmp = x * (t_m / (z - y));
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	tmp = 0
	if y <= -5.3e+79:
		tmp = t_m
	elif y <= -7e+37:
		tmp = t_m * (x / (z - y))
	elif y <= -950000.0:
		tmp = t_m
	elif y <= -2.2e-107:
		tmp = (x - y) * (t_m / z)
	elif y <= 4e+82:
		tmp = x * (t_m / (z - y))
	else:
		tmp = t_m
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	tmp = 0.0
	if (y <= -5.3e+79)
		tmp = t_m;
	elseif (y <= -7e+37)
		tmp = Float64(t_m * Float64(x / Float64(z - y)));
	elseif (y <= -950000.0)
		tmp = t_m;
	elseif (y <= -2.2e-107)
		tmp = Float64(Float64(x - y) * Float64(t_m / z));
	elseif (y <= 4e+82)
		tmp = Float64(x * Float64(t_m / Float64(z - y)));
	else
		tmp = t_m;
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	tmp = 0.0;
	if (y <= -5.3e+79)
		tmp = t_m;
	elseif (y <= -7e+37)
		tmp = t_m * (x / (z - y));
	elseif (y <= -950000.0)
		tmp = t_m;
	elseif (y <= -2.2e-107)
		tmp = (x - y) * (t_m / z);
	elseif (y <= 4e+82)
		tmp = x * (t_m / (z - y));
	else
		tmp = t_m;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * If[LessEqual[y, -5.3e+79], t$95$m, If[LessEqual[y, -7e+37], N[(t$95$m * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -950000.0], t$95$m, If[LessEqual[y, -2.2e-107], N[(N[(x - y), $MachinePrecision] * N[(t$95$m / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+82], N[(x * N[(t$95$m / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$m]]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if y < -5.29999999999999978e79 or -7e37 < y < -9.5e5 or 3.9999999999999999e82 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 67.0%

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

      2. associate-/l* 75.2%

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

   3. Simplified 75.2%

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

   5. Taylor expanded in y around inf 73.3%

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

   if -5.29999999999999978e79 < y < -7e37

   1. Initial program 99.5%

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

   3. Taylor expanded in x around inf 78.9%

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

   if -9.5e5 < y < -2.20000000000000012e-107

   1. Initial program 93.0%

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

      1. associate-*l/ 94.9%

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

      2. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in z around inf 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-/l* 67.0%

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

   7. Simplified 67.0%

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

   if -2.20000000000000012e-107 < y < 3.9999999999999999e82

   1. Initial program 89.6%

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

      1. associate-*l/ 94.0%

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

      2. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

      1. clear-num 92.4%

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

      2. un-div-inv 92.6%

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

   6. Applied egg-rr 92.6%

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

   7. Taylor expanded in x around inf 79.2%

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

      1. *-commutative 79.2%

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

      2. associate-*r/ 79.4%

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

   9. Simplified 79.4%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+79}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -950000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-107}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := \frac{t\_m}{1 - \frac{z}{y}}\\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+58}:\\ \;\;\;\;\frac{t\_m}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-106} \lor \neg \left(y \leq 6.1 \cdot 10^{+38}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_m \cdot x}{z - y}\\ \end{array} \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (let* ((t_2 (/ t_m (- 1.0 (/ z y)))))
   (*
    t_s
    (if (<= y -3.4e+77)
      t_2
      (if (<= y -9e+58)
        (/ t_m (/ (- z y) x))
        (if (or (<= y -6.5e-106) (not (<= y 6.1e+38)))
          t_2
          (/ (* t_m x) (- z y))))))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double t_2 = t_m / (1.0 - (z / y));
	double tmp;
	if (y <= -3.4e+77) {
		tmp = t_2;
	} else if (y <= -9e+58) {
		tmp = t_m / ((z - y) / x);
	} else if ((y <= -6.5e-106) || !(y <= 6.1e+38)) {
		tmp = t_2;
	} else {
		tmp = (t_m * x) / (z - y);
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: t_2
    real(8) :: tmp
    t_2 = t_m / (1.0d0 - (z / y))
    if (y <= (-3.4d+77)) then
        tmp = t_2
    else if (y <= (-9d+58)) then
        tmp = t_m / ((z - y) / x)
    else if ((y <= (-6.5d-106)) .or. (.not. (y <= 6.1d+38))) then
        tmp = t_2
    else
        tmp = (t_m * x) / (z - y)
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double t_2 = t_m / (1.0 - (z / y));
	double tmp;
	if (y <= -3.4e+77) {
		tmp = t_2;
	} else if (y <= -9e+58) {
		tmp = t_m / ((z - y) / x);
	} else if ((y <= -6.5e-106) || !(y <= 6.1e+38)) {
		tmp = t_2;
	} else {
		tmp = (t_m * x) / (z - y);
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	t_2 = t_m / (1.0 - (z / y))
	tmp = 0
	if y <= -3.4e+77:
		tmp = t_2
	elif y <= -9e+58:
		tmp = t_m / ((z - y) / x)
	elif (y <= -6.5e-106) or not (y <= 6.1e+38):
		tmp = t_2
	else:
		tmp = (t_m * x) / (z - y)
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	t_2 = Float64(t_m / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -3.4e+77)
		tmp = t_2;
	elseif (y <= -9e+58)
		tmp = Float64(t_m / Float64(Float64(z - y) / x));
	elseif ((y <= -6.5e-106) || !(y <= 6.1e+38))
		tmp = t_2;
	else
		tmp = Float64(Float64(t_m * x) / Float64(z - y));
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	t_2 = t_m / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -3.4e+77)
		tmp = t_2;
	elseif (y <= -9e+58)
		tmp = t_m / ((z - y) / x);
	elseif ((y <= -6.5e-106) || ~((y <= 6.1e+38)))
		tmp = t_2;
	else
		tmp = (t_m * x) / (z - y);
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := Block[{t$95$2 = N[(t$95$m / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(t$95$s * If[LessEqual[y, -3.4e+77], t$95$2, If[LessEqual[y, -9e+58], N[(t$95$m / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -6.5e-106], N[Not[LessEqual[y, 6.1e+38]], $MachinePrecision]], t$95$2, N[(N[(t$95$m * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if y < -3.39999999999999997e77 or -8.9999999999999996e58 < y < -6.4999999999999997e-106 or 6.0999999999999999e38 < y

   1. Initial program 99.1%

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

      1. associate-*l/ 71.3%

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

      2. associate-/l* 77.9%

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

   3. Simplified 77.9%

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

      1. associate-*r/ 71.3%

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

      2. associate-*l/ 99.1%

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

      3. *-commutative 99.1%

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

      4. clear-num 99.0%

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

      5. un-div-inv 99.1%

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

   6. Applied egg-rr 99.1%

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

      1. div-sub 99.1%

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

   8. Applied egg-rr 99.1%

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

   9. Taylor expanded in x around 0 85.4%

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

       1. mul-1-neg 85.4%

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

       2. sub-neg 85.4%

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

   11. Simplified 85.4%

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

   if -3.39999999999999997e77 < y < -8.9999999999999996e58

   1. Initial program 99.7%

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

      1. associate-*l/ 99.7%

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

      2. associate-/l* 83.8%

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

   3. Simplified 83.8%

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

      1. associate-*r/ 99.7%

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

      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 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 100.0%

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

   if -6.4999999999999997e-106 < y < 6.0999999999999999e38

   1. Initial program 89.3%

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

      1. associate-*l/ 94.5%

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

      2. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around inf 81.5%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+77}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-106} \lor \neg \left(y \leq 6.1 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := \frac{t\_m}{1 - \frac{z}{y}}\\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{t\_m}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-106} \lor \neg \left(y \leq 5.6 \cdot 10^{+38}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t\_m}{z - y}\\ \end{array} \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (let* ((t_2 (/ t_m (- 1.0 (/ z y)))))
   (*
    t_s
    (if (<= y -3.5e+77)
      t_2
      (if (<= y -1.2e+58)
        (/ t_m (/ (- z y) x))
        (if (or (<= y -6.6e-106) (not (<= y 5.6e+38)))
          t_2
          (* x (/ t_m (- z y)))))))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double t_2 = t_m / (1.0 - (z / y));
	double tmp;
	if (y <= -3.5e+77) {
		tmp = t_2;
	} else if (y <= -1.2e+58) {
		tmp = t_m / ((z - y) / x);
	} else if ((y <= -6.6e-106) || !(y <= 5.6e+38)) {
		tmp = t_2;
	} else {
		tmp = x * (t_m / (z - y));
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: t_2
    real(8) :: tmp
    t_2 = t_m / (1.0d0 - (z / y))
    if (y <= (-3.5d+77)) then
        tmp = t_2
    else if (y <= (-1.2d+58)) then
        tmp = t_m / ((z - y) / x)
    else if ((y <= (-6.6d-106)) .or. (.not. (y <= 5.6d+38))) then
        tmp = t_2
    else
        tmp = x * (t_m / (z - y))
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double t_2 = t_m / (1.0 - (z / y));
	double tmp;
	if (y <= -3.5e+77) {
		tmp = t_2;
	} else if (y <= -1.2e+58) {
		tmp = t_m / ((z - y) / x);
	} else if ((y <= -6.6e-106) || !(y <= 5.6e+38)) {
		tmp = t_2;
	} else {
		tmp = x * (t_m / (z - y));
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	t_2 = t_m / (1.0 - (z / y))
	tmp = 0
	if y <= -3.5e+77:
		tmp = t_2
	elif y <= -1.2e+58:
		tmp = t_m / ((z - y) / x)
	elif (y <= -6.6e-106) or not (y <= 5.6e+38):
		tmp = t_2
	else:
		tmp = x * (t_m / (z - y))
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	t_2 = Float64(t_m / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -3.5e+77)
		tmp = t_2;
	elseif (y <= -1.2e+58)
		tmp = Float64(t_m / Float64(Float64(z - y) / x));
	elseif ((y <= -6.6e-106) || !(y <= 5.6e+38))
		tmp = t_2;
	else
		tmp = Float64(x * Float64(t_m / Float64(z - y)));
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	t_2 = t_m / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -3.5e+77)
		tmp = t_2;
	elseif (y <= -1.2e+58)
		tmp = t_m / ((z - y) / x);
	elseif ((y <= -6.6e-106) || ~((y <= 5.6e+38)))
		tmp = t_2;
	else
		tmp = x * (t_m / (z - y));
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := Block[{t$95$2 = N[(t$95$m / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(t$95$s * If[LessEqual[y, -3.5e+77], t$95$2, If[LessEqual[y, -1.2e+58], N[(t$95$m / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -6.6e-106], N[Not[LessEqual[y, 5.6e+38]], $MachinePrecision]], t$95$2, N[(x * N[(t$95$m / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000001e77 or -1.2e58 < y < -6.60000000000000031e-106 or 5.6e38 < y

   1. Initial program 99.1%

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

      1. associate-*l/ 71.3%

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

      2. associate-/l* 77.9%

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

   3. Simplified 77.9%

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

      1. associate-*r/ 71.3%

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

      2. associate-*l/ 99.1%

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

      3. *-commutative 99.1%

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

      4. clear-num 99.0%

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

      5. un-div-inv 99.1%

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

   6. Applied egg-rr 99.1%

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

      1. div-sub 99.1%

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

   8. Applied egg-rr 99.1%

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

   9. Taylor expanded in x around 0 85.4%

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

       1. mul-1-neg 85.4%

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

       2. sub-neg 85.4%

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

   11. Simplified 85.4%

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

   if -3.5000000000000001e77 < y < -1.2e58

   1. Initial program 99.7%

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

      1. associate-*l/ 99.7%

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

      2. associate-/l* 83.8%

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

   3. Simplified 83.8%

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

      1. associate-*r/ 99.7%

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

      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 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 100.0%

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

   if -6.60000000000000031e-106 < y < 5.6e38

   1. Initial program 89.3%

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

      1. associate-*l/ 94.5%

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

      2. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

      1. clear-num 92.2%

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

      2. un-div-inv 92.4%

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

   6. Applied egg-rr 92.4%

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

   7. Taylor expanded in x around inf 81.5%

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

      1. *-commutative 81.5%

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

      2. associate-*r/ 81.1%

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

   9. Simplified 81.1%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+77}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-106} \lor \neg \left(y \leq 5.6 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := \frac{t\_m}{1 - \frac{z}{y}}\\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+58}:\\ \;\;\;\;t\_m \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-106} \lor \neg \left(y \leq 5.6 \cdot 10^{+38}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t\_m}{z - y}\\ \end{array} \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (let* ((t_2 (/ t_m (- 1.0 (/ z y)))))
   (*
    t_s
    (if (<= y -3.4e+77)
      t_2
      (if (<= y -9e+58)
        (* t_m (/ x (- z y)))
        (if (or (<= y -6.6e-106) (not (<= y 5.6e+38)))
          t_2
          (* x (/ t_m (- z y)))))))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double t_2 = t_m / (1.0 - (z / y));
	double tmp;
	if (y <= -3.4e+77) {
		tmp = t_2;
	} else if (y <= -9e+58) {
		tmp = t_m * (x / (z - y));
	} else if ((y <= -6.6e-106) || !(y <= 5.6e+38)) {
		tmp = t_2;
	} else {
		tmp = x * (t_m / (z - y));
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: t_2
    real(8) :: tmp
    t_2 = t_m / (1.0d0 - (z / y))
    if (y <= (-3.4d+77)) then
        tmp = t_2
    else if (y <= (-9d+58)) then
        tmp = t_m * (x / (z - y))
    else if ((y <= (-6.6d-106)) .or. (.not. (y <= 5.6d+38))) then
        tmp = t_2
    else
        tmp = x * (t_m / (z - y))
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double t_2 = t_m / (1.0 - (z / y));
	double tmp;
	if (y <= -3.4e+77) {
		tmp = t_2;
	} else if (y <= -9e+58) {
		tmp = t_m * (x / (z - y));
	} else if ((y <= -6.6e-106) || !(y <= 5.6e+38)) {
		tmp = t_2;
	} else {
		tmp = x * (t_m / (z - y));
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	t_2 = t_m / (1.0 - (z / y))
	tmp = 0
	if y <= -3.4e+77:
		tmp = t_2
	elif y <= -9e+58:
		tmp = t_m * (x / (z - y))
	elif (y <= -6.6e-106) or not (y <= 5.6e+38):
		tmp = t_2
	else:
		tmp = x * (t_m / (z - y))
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	t_2 = Float64(t_m / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -3.4e+77)
		tmp = t_2;
	elseif (y <= -9e+58)
		tmp = Float64(t_m * Float64(x / Float64(z - y)));
	elseif ((y <= -6.6e-106) || !(y <= 5.6e+38))
		tmp = t_2;
	else
		tmp = Float64(x * Float64(t_m / Float64(z - y)));
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	t_2 = t_m / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -3.4e+77)
		tmp = t_2;
	elseif (y <= -9e+58)
		tmp = t_m * (x / (z - y));
	elseif ((y <= -6.6e-106) || ~((y <= 5.6e+38)))
		tmp = t_2;
	else
		tmp = x * (t_m / (z - y));
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := Block[{t$95$2 = N[(t$95$m / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(t$95$s * If[LessEqual[y, -3.4e+77], t$95$2, If[LessEqual[y, -9e+58], N[(t$95$m * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -6.6e-106], N[Not[LessEqual[y, 5.6e+38]], $MachinePrecision]], t$95$2, N[(x * N[(t$95$m / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if y < -3.39999999999999997e77 or -8.9999999999999996e58 < y < -6.60000000000000031e-106 or 5.6e38 < y

   1. Initial program 99.1%

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

      1. associate-*l/ 71.3%

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

      2. associate-/l* 77.9%

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

   3. Simplified 77.9%

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

      1. associate-*r/ 71.3%

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

      2. associate-*l/ 99.1%

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

      3. *-commutative 99.1%

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

      4. clear-num 99.0%

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

      5. un-div-inv 99.1%

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

   6. Applied egg-rr 99.1%

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

      1. div-sub 99.1%

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

   8. Applied egg-rr 99.1%

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

   9. Taylor expanded in x around 0 85.4%

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

       1. mul-1-neg 85.4%

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

       2. sub-neg 85.4%

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

   11. Simplified 85.4%

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

   if -3.39999999999999997e77 < y < -8.9999999999999996e58

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 99.7%

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

   if -6.60000000000000031e-106 < y < 5.6e38

   1. Initial program 89.3%

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

      1. associate-*l/ 94.5%

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

      2. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

      1. clear-num 92.2%

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

      2. un-div-inv 92.4%

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

   6. Applied egg-rr 92.4%

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

   7. Taylor expanded in x around inf 81.5%

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

      1. *-commutative 81.5%

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

      2. associate-*r/ 81.1%

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

   9. Simplified 81.1%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+77}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-106} \lor \neg \left(y \leq 5.6 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := t\_m \cdot \frac{y}{y - z}\\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+73}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{t\_m}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-106}:\\ \;\;\;\;\frac{t\_m \cdot y}{y - z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+38}:\\ \;\;\;\;\frac{t\_m \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (let* ((t_2 (* t_m (/ y (- y z)))))
   (*
    t_s
    (if (<= y -3.7e+73)
      t_2
      (if (<= y -9.5e+57)
        (/ t_m (/ (- z y) x))
        (if (<= y -6.6e-106)
          (/ (* t_m y) (- y z))
          (if (<= y 7e+38) (/ (* t_m x) (- z y)) t_2)))))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double t_2 = t_m * (y / (y - z));
	double tmp;
	if (y <= -3.7e+73) {
		tmp = t_2;
	} else if (y <= -9.5e+57) {
		tmp = t_m / ((z - y) / x);
	} else if (y <= -6.6e-106) {
		tmp = (t_m * y) / (y - z);
	} else if (y <= 7e+38) {
		tmp = (t_m * x) / (z - y);
	} else {
		tmp = t_2;
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: t_2
    real(8) :: tmp
    t_2 = t_m * (y / (y - z))
    if (y <= (-3.7d+73)) then
        tmp = t_2
    else if (y <= (-9.5d+57)) then
        tmp = t_m / ((z - y) / x)
    else if (y <= (-6.6d-106)) then
        tmp = (t_m * y) / (y - z)
    else if (y <= 7d+38) then
        tmp = (t_m * x) / (z - y)
    else
        tmp = t_2
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double t_2 = t_m * (y / (y - z));
	double tmp;
	if (y <= -3.7e+73) {
		tmp = t_2;
	} else if (y <= -9.5e+57) {
		tmp = t_m / ((z - y) / x);
	} else if (y <= -6.6e-106) {
		tmp = (t_m * y) / (y - z);
	} else if (y <= 7e+38) {
		tmp = (t_m * x) / (z - y);
	} else {
		tmp = t_2;
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	t_2 = t_m * (y / (y - z))
	tmp = 0
	if y <= -3.7e+73:
		tmp = t_2
	elif y <= -9.5e+57:
		tmp = t_m / ((z - y) / x)
	elif y <= -6.6e-106:
		tmp = (t_m * y) / (y - z)
	elif y <= 7e+38:
		tmp = (t_m * x) / (z - y)
	else:
		tmp = t_2
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	t_2 = Float64(t_m * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -3.7e+73)
		tmp = t_2;
	elseif (y <= -9.5e+57)
		tmp = Float64(t_m / Float64(Float64(z - y) / x));
	elseif (y <= -6.6e-106)
		tmp = Float64(Float64(t_m * y) / Float64(y - z));
	elseif (y <= 7e+38)
		tmp = Float64(Float64(t_m * x) / Float64(z - y));
	else
		tmp = t_2;
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	t_2 = t_m * (y / (y - z));
	tmp = 0.0;
	if (y <= -3.7e+73)
		tmp = t_2;
	elseif (y <= -9.5e+57)
		tmp = t_m / ((z - y) / x);
	elseif (y <= -6.6e-106)
		tmp = (t_m * y) / (y - z);
	elseif (y <= 7e+38)
		tmp = (t_m * x) / (z - y);
	else
		tmp = t_2;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := Block[{t$95$2 = N[(t$95$m * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(t$95$s * If[LessEqual[y, -3.7e+73], t$95$2, If[LessEqual[y, -9.5e+57], N[(t$95$m / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.6e-106], N[(N[(t$95$m * y), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+38], N[(N[(t$95$m * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if y < -3.69999999999999973e73 or 7.00000000000000003e38 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 88.9%

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

      1. neg-mul-1 88.9%

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

      2. distribute-neg-frac2 88.9%

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

   5. Simplified 88.9%

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

   if -3.69999999999999973e73 < y < -9.4999999999999997e57

   1. Initial program 99.7%

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

      1. associate-*l/ 99.7%

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

      2. associate-/l* 83.8%

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

   3. Simplified 83.8%

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

      1. associate-*r/ 99.7%

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

      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 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 100.0%

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

   if -9.4999999999999997e57 < y < -6.60000000000000031e-106

   1. Initial program 95.4%

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

      1. associate-*l/ 96.7%

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

      2. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

      1. associate-*r/ 96.7%

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

      2. associate-*l/ 95.4%

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

      3. *-commutative 95.4%

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

      4. clear-num 95.3%

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

      5. un-div-inv 95.5%

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

   6. Applied egg-rr 95.5%

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

   7. Taylor expanded in x around 0 70.6%

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

      1. associate-*r/ 70.6%

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

      2. mul-1-neg 70.6%

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

      3. distribute-rgt-neg-out 70.6%

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

   9. Simplified 70.6%

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

   if -6.60000000000000031e-106 < y < 7.00000000000000003e38

   1. Initial program 89.3%

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

      1. associate-*l/ 94.5%

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

      2. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around inf 81.5%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-106}:\\ \;\;\;\;\frac{t \cdot y}{y - z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+38}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := t\_m \cdot \frac{y}{y - z}\\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+73}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{t\_m}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-106}:\\ \;\;\;\;\frac{t\_m}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+38}:\\ \;\;\;\;\frac{t\_m \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (let* ((t_2 (* t_m (/ y (- y z)))))
   (*
    t_s
    (if (<= y -1.4e+73)
      t_2
      (if (<= y -4.5e+58)
        (/ t_m (/ (- z y) x))
        (if (<= y -6.6e-106)
          (/ t_m (- 1.0 (/ z y)))
          (if (<= y 8e+38) (/ (* t_m x) (- z y)) t_2)))))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double t_2 = t_m * (y / (y - z));
	double tmp;
	if (y <= -1.4e+73) {
		tmp = t_2;
	} else if (y <= -4.5e+58) {
		tmp = t_m / ((z - y) / x);
	} else if (y <= -6.6e-106) {
		tmp = t_m / (1.0 - (z / y));
	} else if (y <= 8e+38) {
		tmp = (t_m * x) / (z - y);
	} else {
		tmp = t_2;
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: t_2
    real(8) :: tmp
    t_2 = t_m * (y / (y - z))
    if (y <= (-1.4d+73)) then
        tmp = t_2
    else if (y <= (-4.5d+58)) then
        tmp = t_m / ((z - y) / x)
    else if (y <= (-6.6d-106)) then
        tmp = t_m / (1.0d0 - (z / y))
    else if (y <= 8d+38) then
        tmp = (t_m * x) / (z - y)
    else
        tmp = t_2
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double t_2 = t_m * (y / (y - z));
	double tmp;
	if (y <= -1.4e+73) {
		tmp = t_2;
	} else if (y <= -4.5e+58) {
		tmp = t_m / ((z - y) / x);
	} else if (y <= -6.6e-106) {
		tmp = t_m / (1.0 - (z / y));
	} else if (y <= 8e+38) {
		tmp = (t_m * x) / (z - y);
	} else {
		tmp = t_2;
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	t_2 = t_m * (y / (y - z))
	tmp = 0
	if y <= -1.4e+73:
		tmp = t_2
	elif y <= -4.5e+58:
		tmp = t_m / ((z - y) / x)
	elif y <= -6.6e-106:
		tmp = t_m / (1.0 - (z / y))
	elif y <= 8e+38:
		tmp = (t_m * x) / (z - y)
	else:
		tmp = t_2
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	t_2 = Float64(t_m * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -1.4e+73)
		tmp = t_2;
	elseif (y <= -4.5e+58)
		tmp = Float64(t_m / Float64(Float64(z - y) / x));
	elseif (y <= -6.6e-106)
		tmp = Float64(t_m / Float64(1.0 - Float64(z / y)));
	elseif (y <= 8e+38)
		tmp = Float64(Float64(t_m * x) / Float64(z - y));
	else
		tmp = t_2;
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	t_2 = t_m * (y / (y - z));
	tmp = 0.0;
	if (y <= -1.4e+73)
		tmp = t_2;
	elseif (y <= -4.5e+58)
		tmp = t_m / ((z - y) / x);
	elseif (y <= -6.6e-106)
		tmp = t_m / (1.0 - (z / y));
	elseif (y <= 8e+38)
		tmp = (t_m * x) / (z - y);
	else
		tmp = t_2;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := Block[{t$95$2 = N[(t$95$m * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(t$95$s * If[LessEqual[y, -1.4e+73], t$95$2, If[LessEqual[y, -4.5e+58], N[(t$95$m / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.6e-106], N[(t$95$m / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+38], N[(N[(t$95$m * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if y < -1.40000000000000004e73 or 7.99999999999999982e38 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 88.9%

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

      1. neg-mul-1 88.9%

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

      2. distribute-neg-frac2 88.9%

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

   5. Simplified 88.9%

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

   if -1.40000000000000004e73 < y < -4.4999999999999998e58

   1. Initial program 99.7%

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

      1. associate-*l/ 99.7%

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

      2. associate-/l* 83.8%

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

   3. Simplified 83.8%

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

      1. associate-*r/ 99.7%

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

      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 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 100.0%

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

   if -4.4999999999999998e58 < y < -6.60000000000000031e-106

   1. Initial program 95.4%

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

      1. associate-*l/ 96.7%

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

      2. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

      1. associate-*r/ 96.7%

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

      2. associate-*l/ 95.4%

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

      3. *-commutative 95.4%

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

      4. clear-num 95.3%

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

      5. un-div-inv 95.5%

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

   6. Applied egg-rr 95.5%

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

      1. div-sub 95.5%

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

   8. Applied egg-rr 95.5%

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

   9. Taylor expanded in x around 0 69.5%

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

       1. mul-1-neg 69.5%

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

       2. sub-neg 69.5%

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

   11. Simplified 69.5%

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

   if -6.60000000000000031e-106 < y < 7.99999999999999982e38

   1. Initial program 89.3%

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

      1. associate-*l/ 94.5%

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

      2. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around inf 81.5%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-106}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+38}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-43}:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-109}:\\ \;\;\;\;\frac{t\_m \cdot x}{z}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{t\_m \cdot \left(-x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_m\\ \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (<= y -2.15e-43)
    t_m
    (if (<= y 2.1e-109)
      (/ (* t_m x) z)
      (if (<= y 6.5e+44) (/ (* t_m (- x)) y) t_m)))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -2.15e-43) {
		tmp = t_m;
	} else if (y <= 2.1e-109) {
		tmp = (t_m * x) / z;
	} else if (y <= 6.5e+44) {
		tmp = (t_m * -x) / y;
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if (y <= (-2.15d-43)) then
        tmp = t_m
    else if (y <= 2.1d-109) then
        tmp = (t_m * x) / z
    else if (y <= 6.5d+44) then
        tmp = (t_m * -x) / y
    else
        tmp = t_m
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -2.15e-43) {
		tmp = t_m;
	} else if (y <= 2.1e-109) {
		tmp = (t_m * x) / z;
	} else if (y <= 6.5e+44) {
		tmp = (t_m * -x) / y;
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	tmp = 0
	if y <= -2.15e-43:
		tmp = t_m
	elif y <= 2.1e-109:
		tmp = (t_m * x) / z
	elif y <= 6.5e+44:
		tmp = (t_m * -x) / y
	else:
		tmp = t_m
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	tmp = 0.0
	if (y <= -2.15e-43)
		tmp = t_m;
	elseif (y <= 2.1e-109)
		tmp = Float64(Float64(t_m * x) / z);
	elseif (y <= 6.5e+44)
		tmp = Float64(Float64(t_m * Float64(-x)) / y);
	else
		tmp = t_m;
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	tmp = 0.0;
	if (y <= -2.15e-43)
		tmp = t_m;
	elseif (y <= 2.1e-109)
		tmp = (t_m * x) / z;
	elseif (y <= 6.5e+44)
		tmp = (t_m * -x) / y;
	else
		tmp = t_m;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * If[LessEqual[y, -2.15e-43], t$95$m, If[LessEqual[y, 2.1e-109], N[(N[(t$95$m * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 6.5e+44], N[(N[(t$95$m * (-x)), $MachinePrecision] / y), $MachinePrecision], t$95$m]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -2.14999999999999982e-43 or 6.50000000000000018e44 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 71.4%

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

      2. associate-/l* 76.8%

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

   3. Simplified 76.8%

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

   5. Taylor expanded in y around inf 65.6%

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

   if -2.14999999999999982e-43 < y < 2.09999999999999996e-109

   1. Initial program 88.2%

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

      1. associate-*l/ 95.6%

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

      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. Taylor expanded in y around 0 70.2%

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

   if 2.09999999999999996e-109 < y < 6.50000000000000018e44

   1. Initial program 93.1%

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

      1. associate-*l/ 89.7%

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

      2. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in z around 0 62.4%

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

      1. associate-*r/ 62.4%

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

      2. mul-1-neg 62.4%

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

      3. distribute-lft-neg-out 62.4%

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

      4. *-commutative 62.4%

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

   7. Simplified 62.4%

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

   8. Taylor expanded in x around inf 59.2%

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

      1. associate-*r/ 59.2%

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

      2. associate-*r* 59.2%

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

      3. mul-1-neg 59.2%

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

   10. Simplified 59.2%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-43}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-109}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-44}:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-109}:\\ \;\;\;\;\frac{t\_m \cdot x}{z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+79}:\\ \;\;\;\;t\_m \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_m\\ \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (<= y -8.5e-44)
    t_m
    (if (<= y 2.8e-109)
      (/ (* t_m x) z)
      (if (<= y 1.7e+79) (* t_m (/ (- x) y)) t_m)))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -8.5e-44) {
		tmp = t_m;
	} else if (y <= 2.8e-109) {
		tmp = (t_m * x) / z;
	} else if (y <= 1.7e+79) {
		tmp = t_m * (-x / y);
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if (y <= (-8.5d-44)) then
        tmp = t_m
    else if (y <= 2.8d-109) then
        tmp = (t_m * x) / z
    else if (y <= 1.7d+79) then
        tmp = t_m * (-x / y)
    else
        tmp = t_m
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -8.5e-44) {
		tmp = t_m;
	} else if (y <= 2.8e-109) {
		tmp = (t_m * x) / z;
	} else if (y <= 1.7e+79) {
		tmp = t_m * (-x / y);
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	tmp = 0
	if y <= -8.5e-44:
		tmp = t_m
	elif y <= 2.8e-109:
		tmp = (t_m * x) / z
	elif y <= 1.7e+79:
		tmp = t_m * (-x / y)
	else:
		tmp = t_m
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	tmp = 0.0
	if (y <= -8.5e-44)
		tmp = t_m;
	elseif (y <= 2.8e-109)
		tmp = Float64(Float64(t_m * x) / z);
	elseif (y <= 1.7e+79)
		tmp = Float64(t_m * Float64(Float64(-x) / y));
	else
		tmp = t_m;
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	tmp = 0.0;
	if (y <= -8.5e-44)
		tmp = t_m;
	elseif (y <= 2.8e-109)
		tmp = (t_m * x) / z;
	elseif (y <= 1.7e+79)
		tmp = t_m * (-x / y);
	else
		tmp = t_m;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * If[LessEqual[y, -8.5e-44], t$95$m, If[LessEqual[y, 2.8e-109], N[(N[(t$95$m * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.7e+79], N[(t$95$m * N[((-x) / y), $MachinePrecision]), $MachinePrecision], t$95$m]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -8.5000000000000002e-44 or 1.70000000000000016e79 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 71.2%

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

      2. associate-/l* 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in y around inf 66.9%

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

   if -8.5000000000000002e-44 < y < 2.79999999999999979e-109

   1. Initial program 88.2%

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

      1. associate-*l/ 95.6%

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

      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. Taylor expanded in y around 0 70.2%

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

   if 2.79999999999999979e-109 < y < 1.70000000000000016e79

   1. Initial program 93.9%

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

      1. associate-*l/ 88.1%

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

      2. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in z around 0 58.3%

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

      1. associate-*r/ 58.3%

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

      2. mul-1-neg 58.3%

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

      3. distribute-lft-neg-out 58.3%

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

      4. *-commutative 58.3%

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

   7. Simplified 58.3%

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

   8. Taylor expanded in x around inf 52.5%

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

      1. mul-1-neg 52.5%

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

      2. associate-/l* 49.6%

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

      3. distribute-rgt-neg-in 49.6%

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

      4. distribute-neg-frac2 49.6%

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

   10. Simplified 49.6%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-44}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-109}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -5 \cdot 10^{+302}:\\ \;\;\;\;x \cdot \frac{t\_m}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_m}{\frac{z - y}{x - y}}\\ \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (<= (/ (- x y) (- z y)) -5e+302)
    (* x (/ t_m (- z y)))
    (/ t_m (/ (- z y) (- x y))))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (((x - y) / (z - y)) <= -5e+302) {
		tmp = x * (t_m / (z - y));
	} else {
		tmp = t_m / ((z - y) / (x - y));
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if (((x - y) / (z - y)) <= (-5d+302)) then
        tmp = x * (t_m / (z - y))
    else
        tmp = t_m / ((z - y) / (x - y))
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (((x - y) / (z - y)) <= -5e+302) {
		tmp = x * (t_m / (z - y));
	} else {
		tmp = t_m / ((z - y) / (x - y));
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	tmp = 0
	if ((x - y) / (z - y)) <= -5e+302:
		tmp = x * (t_m / (z - y))
	else:
		tmp = t_m / ((z - y) / (x - y))
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	tmp = 0.0
	if (Float64(Float64(x - y) / Float64(z - y)) <= -5e+302)
		tmp = Float64(x * Float64(t_m / Float64(z - y)));
	else
		tmp = Float64(t_m / Float64(Float64(z - y) / Float64(x - y)));
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	tmp = 0.0;
	if (((x - y) / (z - y)) <= -5e+302)
		tmp = x * (t_m / (z - y));
	else
		tmp = t_m / ((z - y) / (x - y));
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], -5e+302], N[(x * N[(t$95$m / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$m / N[(N[(z - y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -5e302

   1. Initial program 40.2%

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

      1. associate-*l/ 99.7%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*r/ 99.9%

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

   9. Simplified 99.9%

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

   if -5e302 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.7%

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

      1. associate-*l/ 82.8%

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

      2. associate-/l* 84.7%

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

   3. Simplified 84.7%

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

      1. associate-*r/ 82.8%

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

      2. associate-*l/ 96.7%

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

      3. *-commutative 96.7%

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

      4. clear-num 96.6%

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

      5. un-div-inv 96.8%

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

   6. Applied egg-rr 96.8%

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

Alternative 11: 97.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := \frac{x - y}{z - y}\\ t\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;x \cdot \frac{t\_m}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_m \cdot t\_2\\ \end{array} \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (let* ((t_2 (/ (- x y) (- z y))))
   (* t_s (if (<= t_2 (- INFINITY)) (* x (/ t_m (- z y))) (* t_m t_2)))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double t_2 = (x - y) / (z - y);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = x * (t_m / (z - y));
	} else {
		tmp = t_m * t_2;
	}
	return t_s * tmp;
}

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double t_2 = (x - y) / (z - y);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = x * (t_m / (z - y));
	} else {
		tmp = t_m * t_2;
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	t_2 = (x - y) / (z - y)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = x * (t_m / (z - y))
	else:
		tmp = t_m * t_2
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	t_2 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(x * Float64(t_m / Float64(z - y)));
	else
		tmp = Float64(t_m * t_2);
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	t_2 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = x * (t_m / (z - y));
	else
		tmp = t_m * t_2;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := Block[{t$95$2 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, N[(t$95$s * If[LessEqual[t$95$2, (-Infinity)], N[(x * N[(t$95$m / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$m * t$95$2), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -inf.0

   1. Initial program 34.2%

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

      1. associate-*l/ 99.7%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*r/ 99.8%

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

   9. Simplified 99.8%

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

   if -inf.0 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.7%

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

4. Final simplification 96.8%

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

Alternative 12: 90.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+157}:\\ \;\;\;\;\frac{t\_m}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+161}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t\_m}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_m}{1 - \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (<= y -1.65e+157)
    (/ t_m (/ y (- y x)))
    (if (<= y 2.8e+161) (* (- x y) (/ t_m (- z y))) (/ t_m (- 1.0 (/ z y)))))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -1.65e+157) {
		tmp = t_m / (y / (y - x));
	} else if (y <= 2.8e+161) {
		tmp = (x - y) * (t_m / (z - y));
	} else {
		tmp = t_m / (1.0 - (z / y));
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if (y <= (-1.65d+157)) then
        tmp = t_m / (y / (y - x))
    else if (y <= 2.8d+161) then
        tmp = (x - y) * (t_m / (z - y))
    else
        tmp = t_m / (1.0d0 - (z / y))
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -1.65e+157) {
		tmp = t_m / (y / (y - x));
	} else if (y <= 2.8e+161) {
		tmp = (x - y) * (t_m / (z - y));
	} else {
		tmp = t_m / (1.0 - (z / y));
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	tmp = 0
	if y <= -1.65e+157:
		tmp = t_m / (y / (y - x))
	elif y <= 2.8e+161:
		tmp = (x - y) * (t_m / (z - y))
	else:
		tmp = t_m / (1.0 - (z / y))
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	tmp = 0.0
	if (y <= -1.65e+157)
		tmp = Float64(t_m / Float64(y / Float64(y - x)));
	elseif (y <= 2.8e+161)
		tmp = Float64(Float64(x - y) * Float64(t_m / Float64(z - y)));
	else
		tmp = Float64(t_m / Float64(1.0 - Float64(z / y)));
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	tmp = 0.0;
	if (y <= -1.65e+157)
		tmp = t_m / (y / (y - x));
	elseif (y <= 2.8e+161)
		tmp = (x - y) * (t_m / (z - y));
	else
		tmp = t_m / (1.0 - (z / y));
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * If[LessEqual[y, -1.65e+157], N[(t$95$m / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+161], N[(N[(x - y), $MachinePrecision] * N[(t$95$m / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$m / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -1.6500000000000001e157

   1. Initial program 100.0%

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

      1. associate-*l/ 61.8%

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

      2. associate-/l* 64.7%

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

   3. Simplified 64.7%

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

      1. associate-*r/ 61.8%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

      4. clear-num 100.0%

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

      5. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around 0 97.1%

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

      1. neg-mul-1 97.1%

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

      2. distribute-neg-frac 97.1%

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

   9. Simplified 97.1%

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

   if -1.6500000000000001e157 < y < 2.80000000000000021e161

   1. Initial program 92.5%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 91.0%

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

   3. Simplified 91.0%

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

   if 2.80000000000000021e161 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 55.1%

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

      2. associate-/l* 69.1%

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

   3. Simplified 69.1%

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

      1. associate-*r/ 55.1%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. div-sub 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in x around 0 95.4%

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

       1. mul-1-neg 95.4%

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

       2. sub-neg 95.4%

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

   11. Simplified 95.4%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+157}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+161}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 70.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-29}:\\ \;\;\;\;t\_m - \frac{t\_m \cdot x}{y}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \frac{t\_m}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_m\\ \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (*
  t_s
  (if (<= y -2.1e-29)
    (- t_m (/ (* t_m x) y))
    (if (<= y 3.6e+80) (* x (/ t_m (- z y))) t_m))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -2.1e-29) {
		tmp = t_m - ((t_m * x) / y);
	} else if (y <= 3.6e+80) {
		tmp = x * (t_m / (z - y));
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if (y <= (-2.1d-29)) then
        tmp = t_m - ((t_m * x) / y)
    else if (y <= 3.6d+80) then
        tmp = x * (t_m / (z - y))
    else
        tmp = t_m
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -2.1e-29) {
		tmp = t_m - ((t_m * x) / y);
	} else if (y <= 3.6e+80) {
		tmp = x * (t_m / (z - y));
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	tmp = 0
	if y <= -2.1e-29:
		tmp = t_m - ((t_m * x) / y)
	elif y <= 3.6e+80:
		tmp = x * (t_m / (z - y))
	else:
		tmp = t_m
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	tmp = 0.0
	if (y <= -2.1e-29)
		tmp = Float64(t_m - Float64(Float64(t_m * x) / y));
	elseif (y <= 3.6e+80)
		tmp = Float64(x * Float64(t_m / Float64(z - y)));
	else
		tmp = t_m;
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	tmp = 0.0;
	if (y <= -2.1e-29)
		tmp = t_m - ((t_m * x) / y);
	elseif (y <= 3.6e+80)
		tmp = x * (t_m / (z - y));
	else
		tmp = t_m;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * If[LessEqual[y, -2.1e-29], N[(t$95$m - N[(N[(t$95$m * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+80], N[(x * N[(t$95$m / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$m]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -2.09999999999999989e-29

   1. Initial program 99.9%

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

      1. associate-*l/ 76.2%

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

      2. associate-/l* 77.5%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in z around 0 57.6%

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

      1. associate-*r/ 57.6%

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

      2. mul-1-neg 57.6%

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

      3. distribute-lft-neg-out 57.6%

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

      4. *-commutative 57.6%

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

   7. Simplified 57.6%

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

   8. Taylor expanded in x around 0 75.9%

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

      1. mul-1-neg 75.9%

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

      2. unsub-neg 75.9%

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

   10. Simplified 75.9%

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

   if -2.09999999999999989e-29 < y < 3.59999999999999995e80

   1. Initial program 89.7%

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

      1. associate-*l/ 94.0%

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

      2. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

      1. clear-num 92.4%

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

      2. un-div-inv 92.5%

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

   6. Applied egg-rr 92.5%

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

   7. Taylor expanded in x around inf 77.5%

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

      1. *-commutative 77.5%

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

      2. associate-*r/ 77.8%

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

   9. Simplified 77.8%

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

   if 3.59999999999999995e80 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 62.3%

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

      2. associate-/l* 74.3%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in y around inf 72.7%

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

Alternative 14: 68.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+81}:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{t\_m}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_m\\ \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (* t_s (if (<= y -3e+81) t_m (if (<= y 2.2e+81) (* x (/ t_m (- z y))) t_m))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -3e+81) {
		tmp = t_m;
	} else if (y <= 2.2e+81) {
		tmp = x * (t_m / (z - y));
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if (y <= (-3d+81)) then
        tmp = t_m
    else if (y <= 2.2d+81) then
        tmp = x * (t_m / (z - y))
    else
        tmp = t_m
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -3e+81) {
		tmp = t_m;
	} else if (y <= 2.2e+81) {
		tmp = x * (t_m / (z - y));
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	tmp = 0
	if y <= -3e+81:
		tmp = t_m
	elif y <= 2.2e+81:
		tmp = x * (t_m / (z - y))
	else:
		tmp = t_m
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	tmp = 0.0
	if (y <= -3e+81)
		tmp = t_m;
	elseif (y <= 2.2e+81)
		tmp = Float64(x * Float64(t_m / Float64(z - y)));
	else
		tmp = t_m;
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	tmp = 0.0;
	if (y <= -3e+81)
		tmp = t_m;
	elseif (y <= 2.2e+81)
		tmp = x * (t_m / (z - y));
	else
		tmp = t_m;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * If[LessEqual[y, -3e+81], t$95$m, If[LessEqual[y, 2.2e+81], N[(x * N[(t$95$m / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -2.99999999999999997e81 or 2.19999999999999987e81 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 65.0%

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

      2. associate-/l* 73.7%

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

   3. Simplified 73.7%

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

   5. Taylor expanded in y around inf 73.6%

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

   if -2.99999999999999997e81 < y < 2.19999999999999987e81

   1. Initial program 90.8%

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

      1. associate-*l/ 94.6%

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

      2. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

      1. clear-num 92.0%

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

      2. un-div-inv 92.2%

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

   6. Applied egg-rr 92.2%

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

   7. Taylor expanded in x around inf 75.2%

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

      1. *-commutative 75.2%

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

      2. associate-*r/ 74.9%

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

   9. Simplified 74.9%

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

Alternative 15: 60.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-29}:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \frac{t\_m}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_m\\ \end{array} \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m)
 :precision binary64
 (* t_s (if (<= y -2.05e-29) t_m (if (<= y 6.5e+46) (* x (/ t_m z)) t_m))))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -2.05e-29) {
		tmp = t_m;
	} else if (y <= 6.5e+46) {
		tmp = x * (t_m / z);
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    real(8) :: tmp
    if (y <= (-2.05d-29)) then
        tmp = t_m
    else if (y <= 6.5d+46) then
        tmp = x * (t_m / z)
    else
        tmp = t_m
    end if
    code = t_s * tmp
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	double tmp;
	if (y <= -2.05e-29) {
		tmp = t_m;
	} else if (y <= 6.5e+46) {
		tmp = x * (t_m / z);
	} else {
		tmp = t_m;
	}
	return t_s * tmp;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	tmp = 0
	if y <= -2.05e-29:
		tmp = t_m
	elif y <= 6.5e+46:
		tmp = x * (t_m / z)
	else:
		tmp = t_m
	return t_s * tmp

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	tmp = 0.0
	if (y <= -2.05e-29)
		tmp = t_m;
	elseif (y <= 6.5e+46)
		tmp = Float64(x * Float64(t_m / z));
	else
		tmp = t_m;
	end
	return Float64(t_s * tmp)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, x, y, z, t_m)
	tmp = 0.0;
	if (y <= -2.05e-29)
		tmp = t_m;
	elseif (y <= 6.5e+46)
		tmp = x * (t_m / z);
	else
		tmp = t_m;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * If[LessEqual[y, -2.05e-29], t$95$m, If[LessEqual[y, 6.5e+46], N[(x * N[(t$95$m / z), $MachinePrecision]), $MachinePrecision], t$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -2.0499999999999999e-29 or 6.50000000000000008e46 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 70.7%

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

      2. associate-/l* 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in y around inf 66.3%

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

   if -2.0499999999999999e-29 < y < 6.50000000000000008e46

   1. Initial program 89.4%

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

      1. associate-*l/ 94.5%

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

      2. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in y around 0 59.5%

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

      1. *-commutative 59.5%

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

      2. associate-/l* 59.8%

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

   7. Simplified 59.8%

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

Alternative 16: 36.2% accurate, 9.0× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot t\_m \end{array} \]

FPCore

t\_m = (fabs.f64 t)
t\_s = (copysign.f64 #s(literal 1 binary64) t)
(FPCore (t_s x y z t_m) :precision binary64 (* t_s t_m))

C

t\_m = fabs(t);
t\_s = copysign(1.0, t);
double code(double t_s, double x, double y, double z, double t_m) {
	return t_s * t_m;
}

Fortran

t\_m = abs(t)
t\_s = copysign(1.0d0, t)
real(8) function code(t_s, x, y, z, t_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t_m
    code = t_s * t_m
end function

Java

t\_m = Math.abs(t);
t\_s = Math.copySign(1.0, t);
public static double code(double t_s, double x, double y, double z, double t_m) {
	return t_s * t_m;
}

Python

t\_m = math.fabs(t)
t\_s = math.copysign(1.0, t)
def code(t_s, x, y, z, t_m):
	return t_s * t_m

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	return Float64(t_s * t_m)
end

MATLAB

t\_m = abs(t);
t\_s = sign(t) * abs(1.0);
function tmp = code(t_s, x, y, z, t_m)
	tmp = t_s * t_m;
end

Wolfram

t\_m = N[Abs[t], $MachinePrecision]
t\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, x_, y_, z_, t$95$m_] := N[(t$95$s * t$95$m), $MachinePrecision]

Derivation

1. Initial program 94.2%

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

   1. associate-*l/ 83.5%

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

   2. associate-/l* 85.4%

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

3. Simplified 85.4%

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

5. Taylor expanded in y around inf 35.4%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Developer target: 97.1% 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 2024086 
(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))