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

Percentage Accurate: 97.2% → 96.8%

Time: 9.7s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.2% 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: 96.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;t\_m \leq 7.5 \cdot 10^{-15}:\\ \;\;\;\;\frac{-1}{y - z} \cdot \frac{t\_m}{\frac{-1}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t\_m}}\\ \end{array} \end{array} \]

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 (<= t_m 7.5e-15)
    (* (/ -1.0 (- y z)) (/ t_m (/ -1.0 (- y x))))
    (/ (- x y) (/ (- 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 (t_m <= 7.5e-15) {
		tmp = (-1.0 / (y - z)) * (t_m / (-1.0 / (y - x)));
	} else {
		tmp = (x - y) / ((z - y) / 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 (t_m <= 7.5d-15) then
        tmp = ((-1.0d0) / (y - z)) * (t_m / ((-1.0d0) / (y - x)))
    else
        tmp = (x - y) / ((z - y) / 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 (t_m <= 7.5e-15) {
		tmp = (-1.0 / (y - z)) * (t_m / (-1.0 / (y - x)));
	} else {
		tmp = (x - y) / ((z - y) / 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 t_m <= 7.5e-15:
		tmp = (-1.0 / (y - z)) * (t_m / (-1.0 / (y - x)))
	else:
		tmp = (x - y) / ((z - y) / 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 (t_m <= 7.5e-15)
		tmp = Float64(Float64(-1.0 / Float64(y - z)) * Float64(t_m / Float64(-1.0 / Float64(y - x))));
	else
		tmp = Float64(Float64(x - y) / Float64(Float64(z - y) / 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 (t_m <= 7.5e-15)
		tmp = (-1.0 / (y - z)) * (t_m / (-1.0 / (y - x)));
	else
		tmp = (x - y) / ((z - y) / 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[t$95$m, 7.5e-15], N[(N[(-1.0 / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(t$95$m / N[(-1.0 / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(N[(z - y), $MachinePrecision] / t$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < 7.4999999999999996e-15

   1. Initial program 96.5%

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

      1. associate-*l/ 88.6%

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

      2. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

      1. associate-*r/ 88.6%

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

      2. associate-*l/ 96.5%

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

      3. *-commutative 96.5%

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

      4. clear-num 96.0%

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

      5. un-div-inv 96.5%

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

   6. Applied egg-rr 96.5%

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

      1. *-un-lft-identity 96.5%

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

      2. div-inv 96.4%

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

      3. times-frac 88.5%

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

   8. Applied egg-rr 88.5%

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

   if 7.4999999999999996e-15 < t

   1. Initial program 98.1%

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

      1. associate-*l/ 73.8%

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

      2. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

      1. clear-num 97.9%

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

      2. un-div-inv 98.1%

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

   6. Applied egg-rr 98.1%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7.5 \cdot 10^{-15}:\\ \;\;\;\;\frac{-1}{y - z} \cdot \frac{t}{\frac{-1}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+105}:\\ \;\;\;\;\frac{t\_m}{\frac{z - y}{x}}\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{+54}:\\ \;\;\;\;t\_m \cdot \frac{y - x}{y}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-25}:\\ \;\;\;\;\frac{t\_m \cdot x}{z - y}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+39}:\\ \;\;\;\;\frac{t\_m}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_m \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

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 (<= x -5.2e+105)
    (/ t_m (/ (- z y) x))
    (if (<= x -5.3e+54)
      (* t_m (/ (- y x) y))
      (if (<= x -2.4e-25)
        (/ (* t_m x) (- z y))
        (if (<= x 1.3e+39) (/ t_m (- 1.0 (/ z y))) (* 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 tmp;
	if (x <= -5.2e+105) {
		tmp = t_m / ((z - y) / x);
	} else if (x <= -5.3e+54) {
		tmp = t_m * ((y - x) / y);
	} else if (x <= -2.4e-25) {
		tmp = (t_m * x) / (z - y);
	} else if (x <= 1.3e+39) {
		tmp = t_m / (1.0 - (z / y));
	} 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) :: tmp
    if (x <= (-5.2d+105)) then
        tmp = t_m / ((z - y) / x)
    else if (x <= (-5.3d+54)) then
        tmp = t_m * ((y - x) / y)
    else if (x <= (-2.4d-25)) then
        tmp = (t_m * x) / (z - y)
    else if (x <= 1.3d+39) then
        tmp = t_m / (1.0d0 - (z / y))
    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 tmp;
	if (x <= -5.2e+105) {
		tmp = t_m / ((z - y) / x);
	} else if (x <= -5.3e+54) {
		tmp = t_m * ((y - x) / y);
	} else if (x <= -2.4e-25) {
		tmp = (t_m * x) / (z - y);
	} else if (x <= 1.3e+39) {
		tmp = t_m / (1.0 - (z / y));
	} 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):
	tmp = 0
	if x <= -5.2e+105:
		tmp = t_m / ((z - y) / x)
	elif x <= -5.3e+54:
		tmp = t_m * ((y - x) / y)
	elif x <= -2.4e-25:
		tmp = (t_m * x) / (z - y)
	elif x <= 1.3e+39:
		tmp = t_m / (1.0 - (z / y))
	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)
	tmp = 0.0
	if (x <= -5.2e+105)
		tmp = Float64(t_m / Float64(Float64(z - y) / x));
	elseif (x <= -5.3e+54)
		tmp = Float64(t_m * Float64(Float64(y - x) / y));
	elseif (x <= -2.4e-25)
		tmp = Float64(Float64(t_m * x) / Float64(z - y));
	elseif (x <= 1.3e+39)
		tmp = Float64(t_m / Float64(1.0 - Float64(z / y)));
	else
		tmp = Float64(t_m * Float64(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)
	tmp = 0.0;
	if (x <= -5.2e+105)
		tmp = t_m / ((z - y) / x);
	elseif (x <= -5.3e+54)
		tmp = t_m * ((y - x) / y);
	elseif (x <= -2.4e-25)
		tmp = (t_m * x) / (z - y);
	elseif (x <= 1.3e+39)
		tmp = t_m / (1.0 - (z / y));
	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_] := N[(t$95$s * If[LessEqual[x, -5.2e+105], N[(t$95$m / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.3e+54], N[(t$95$m * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.4e-25], N[(N[(t$95$m * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+39], N[(t$95$m / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$m * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if x < -5.2000000000000004e105

   1. Initial program 93.5%

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

      1. associate-*l/ 76.9%

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

      2. associate-/l* 83.6%

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

   3. Simplified 83.6%

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

      1. associate-*r/ 76.9%

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

      2. associate-*l/ 93.5%

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

      3. *-commutative 93.5%

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

      4. clear-num 93.5%

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

      5. un-div-inv 95.3%

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

   6. Applied egg-rr 95.3%

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

   7. Taylor expanded in x around inf 80.3%

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

   if -5.2000000000000004e105 < x < -5.30000000000000018e54

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   if -5.30000000000000018e54 < x < -2.40000000000000009e-25

   1. Initial program 99.3%

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

      1. associate-*l/ 99.9%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 83.7%

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

   if -2.40000000000000009e-25 < x < 1.3e39

   1. Initial program 97.6%

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

      1. associate-*l/ 88.6%

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

      2. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

      1. associate-*r/ 88.6%

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

      2. associate-*l/ 97.6%

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

      3. *-commutative 97.6%

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

      4. clear-num 97.0%

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

      5. un-div-inv 97.0%

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

   6. Applied egg-rr 97.0%

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

   7. Taylor expanded in x around 0 75.3%

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

      1. mul-1-neg 75.3%

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

      2. *-commutative 75.3%

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

      3. associate-*r/ 75.7%

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

      4. *-commutative 75.7%

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

      5. associate-/r/ 83.8%

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

      6. distribute-neg-frac2 83.8%

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

      7. div-sub 83.8%

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

      8. sub-neg 83.8%

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

      9. *-inverses 83.8%

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

      10. metadata-eval 83.8%

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

   9. Simplified 83.8%

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

   if 1.3e39 < x

   1. Initial program 96.5%

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

   3. Taylor expanded in x around inf 78.5%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+105}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-25}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+39}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+115}:\\ \;\;\;\;\frac{t\_m}{\frac{z - y}{x}}\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{+50}:\\ \;\;\;\;t\_m \cdot \frac{y - x}{y}\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-28}:\\ \;\;\;\;\frac{t\_m \cdot x}{z - y}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+37}:\\ \;\;\;\;t\_m \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\_m \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

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 (<= x -2.9e+115)
    (/ t_m (/ (- z y) x))
    (if (<= x -8.8e+50)
      (* t_m (/ (- y x) y))
      (if (<= x -2.7e-28)
        (/ (* t_m x) (- z y))
        (if (<= x 3.9e+37) (* t_m (/ y (- y z))) (* 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 tmp;
	if (x <= -2.9e+115) {
		tmp = t_m / ((z - y) / x);
	} else if (x <= -8.8e+50) {
		tmp = t_m * ((y - x) / y);
	} else if (x <= -2.7e-28) {
		tmp = (t_m * x) / (z - y);
	} else if (x <= 3.9e+37) {
		tmp = t_m * (y / (y - z));
	} 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) :: tmp
    if (x <= (-2.9d+115)) then
        tmp = t_m / ((z - y) / x)
    else if (x <= (-8.8d+50)) then
        tmp = t_m * ((y - x) / y)
    else if (x <= (-2.7d-28)) then
        tmp = (t_m * x) / (z - y)
    else if (x <= 3.9d+37) then
        tmp = t_m * (y / (y - z))
    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 tmp;
	if (x <= -2.9e+115) {
		tmp = t_m / ((z - y) / x);
	} else if (x <= -8.8e+50) {
		tmp = t_m * ((y - x) / y);
	} else if (x <= -2.7e-28) {
		tmp = (t_m * x) / (z - y);
	} else if (x <= 3.9e+37) {
		tmp = t_m * (y / (y - z));
	} 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):
	tmp = 0
	if x <= -2.9e+115:
		tmp = t_m / ((z - y) / x)
	elif x <= -8.8e+50:
		tmp = t_m * ((y - x) / y)
	elif x <= -2.7e-28:
		tmp = (t_m * x) / (z - y)
	elif x <= 3.9e+37:
		tmp = t_m * (y / (y - z))
	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)
	tmp = 0.0
	if (x <= -2.9e+115)
		tmp = Float64(t_m / Float64(Float64(z - y) / x));
	elseif (x <= -8.8e+50)
		tmp = Float64(t_m * Float64(Float64(y - x) / y));
	elseif (x <= -2.7e-28)
		tmp = Float64(Float64(t_m * x) / Float64(z - y));
	elseif (x <= 3.9e+37)
		tmp = Float64(t_m * Float64(y / Float64(y - z)));
	else
		tmp = Float64(t_m * Float64(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)
	tmp = 0.0;
	if (x <= -2.9e+115)
		tmp = t_m / ((z - y) / x);
	elseif (x <= -8.8e+50)
		tmp = t_m * ((y - x) / y);
	elseif (x <= -2.7e-28)
		tmp = (t_m * x) / (z - y);
	elseif (x <= 3.9e+37)
		tmp = t_m * (y / (y - z));
	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_] := N[(t$95$s * If[LessEqual[x, -2.9e+115], N[(t$95$m / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.8e+50], N[(t$95$m * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.7e-28], N[(N[(t$95$m * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.9e+37], N[(t$95$m * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$m * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if x < -2.90000000000000005e115

   1. Initial program 93.5%

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

      1. associate-*l/ 76.9%

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

      2. associate-/l* 83.6%

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

   3. Simplified 83.6%

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

      1. associate-*r/ 76.9%

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

      2. associate-*l/ 93.5%

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

      3. *-commutative 93.5%

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

      4. clear-num 93.5%

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

      5. un-div-inv 95.3%

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

   6. Applied egg-rr 95.3%

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

   7. Taylor expanded in x around inf 80.3%

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

   if -2.90000000000000005e115 < x < -8.80000000000000067e50

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   if -8.80000000000000067e50 < x < -2.6999999999999999e-28

   1. Initial program 99.3%

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

      1. associate-*l/ 99.9%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 83.7%

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

   if -2.6999999999999999e-28 < x < 3.8999999999999999e37

   1. Initial program 97.6%

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

   3. Taylor expanded in x around 0 83.8%

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

      1. neg-mul-1 83.8%

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

      2. distribute-neg-frac2 83.8%

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

   5. Simplified 83.8%

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

   if 3.8999999999999999e37 < x

   1. Initial program 96.5%

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

   3. Taylor expanded in x around inf 78.5%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+115}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-28}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+182}:\\ \;\;\;\;t\_m \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+184}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t\_m}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_m \cdot \frac{y - x}{y}\\ \end{array} \end{array} \]

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 (<= y -2e+182)
    (* t_m (/ y (- y z)))
    (if (<= y 7e+184) (* (- x y) (/ t_m (- z y))) (* t_m (/ (- 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 (y <= -2e+182) {
		tmp = t_m * (y / (y - z));
	} else if (y <= 7e+184) {
		tmp = (x - y) * (t_m / (z - y));
	} else {
		tmp = t_m * ((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 (y <= (-2d+182)) then
        tmp = t_m * (y / (y - z))
    else if (y <= 7d+184) then
        tmp = (x - y) * (t_m / (z - y))
    else
        tmp = t_m * ((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 (y <= -2e+182) {
		tmp = t_m * (y / (y - z));
	} else if (y <= 7e+184) {
		tmp = (x - y) * (t_m / (z - y));
	} else {
		tmp = t_m * ((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 y <= -2e+182:
		tmp = t_m * (y / (y - z))
	elif y <= 7e+184:
		tmp = (x - y) * (t_m / (z - y))
	else:
		tmp = t_m * ((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 (y <= -2e+182)
		tmp = Float64(t_m * Float64(y / Float64(y - z)));
	elseif (y <= 7e+184)
		tmp = Float64(Float64(x - y) * Float64(t_m / Float64(z - y)));
	else
		tmp = Float64(t_m * Float64(Float64(y - 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 (y <= -2e+182)
		tmp = t_m * (y / (y - z));
	elseif (y <= 7e+184)
		tmp = (x - y) * (t_m / (z - y));
	else
		tmp = t_m * ((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[y, -2e+182], N[(t$95$m * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+184], N[(N[(x - y), $MachinePrecision] * N[(t$95$m / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$m * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -2.0000000000000001e182

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 89.7%

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

      1. neg-mul-1 89.7%

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

      2. distribute-neg-frac2 89.7%

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

   5. Simplified 89.7%

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

   if -2.0000000000000001e182 < y < 6.99999999999999956e184

   1. Initial program 96.0%

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

      1. associate-*l/ 91.3%

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

      2. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

   if 6.99999999999999956e184 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 98.3%

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

      1. mul-1-neg 98.3%

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

   5. Simplified 98.3%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+182}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+184}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+23} \lor \neg \left(y \leq 1.9 \cdot 10^{-59}\right):\\ \;\;\;\;t\_m - t\_m \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_m}{\frac{z - y}{x}}\\ \end{array} \end{array} \]

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 (or (<= y -6.2e+23) (not (<= y 1.9e-59)))
    (- t_m (* t_m (/ x y)))
    (/ t_m (/ (- z y) x)))))

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 <= -6.2e+23) || !(y <= 1.9e-59)) {
		tmp = t_m - (t_m * (x / y));
	} else {
		tmp = t_m / ((z - y) / x);
	}
	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 <= (-6.2d+23)) .or. (.not. (y <= 1.9d-59))) then
        tmp = t_m - (t_m * (x / y))
    else
        tmp = t_m / ((z - y) / x)
    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 <= -6.2e+23) || !(y <= 1.9e-59)) {
		tmp = t_m - (t_m * (x / y));
	} else {
		tmp = t_m / ((z - y) / x);
	}
	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 <= -6.2e+23) or not (y <= 1.9e-59):
		tmp = t_m - (t_m * (x / y))
	else:
		tmp = t_m / ((z - y) / x)
	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 <= -6.2e+23) || !(y <= 1.9e-59))
		tmp = Float64(t_m - Float64(t_m * Float64(x / y)));
	else
		tmp = Float64(t_m / Float64(Float64(z - y) / x));
	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 <= -6.2e+23) || ~((y <= 1.9e-59)))
		tmp = t_m - (t_m * (x / y));
	else
		tmp = t_m / ((z - y) / x);
	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[Or[LessEqual[y, -6.2e+23], N[Not[LessEqual[y, 1.9e-59]], $MachinePrecision]], N[(t$95$m - N[(t$95$m * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$m / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -6.19999999999999941e23 or 1.89999999999999992e-59 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 80.2%

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

      2. associate-/l* 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in z around 0 60.9%

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

      1. associate-*r/ 60.9%

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

      2. neg-mul-1 60.9%

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

   7. Simplified 60.9%

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

   8. Taylor expanded in x around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. unsub-neg 71.2%

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

      3. associate-/l* 78.2%

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

   10. Simplified 78.2%

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

   if -6.19999999999999941e23 < y < 1.89999999999999992e-59

   1. Initial program 93.2%

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

      1. associate-*l/ 91.6%

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

      2. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

      1. associate-*r/ 91.6%

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

      2. associate-*l/ 93.2%

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

      3. *-commutative 93.2%

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

      4. clear-num 92.5%

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

      5. un-div-inv 93.2%

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

   6. Applied egg-rr 93.2%

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

   7. Taylor expanded in x around inf 77.5%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+23} \lor \neg \left(y \leq 1.9 \cdot 10^{-59}\right):\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -4100000000000 \lor \neg \left(y \leq 1.4 \cdot 10^{-62}\right):\\ \;\;\;\;t\_m - t\_m \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_m \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

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 (or (<= y -4100000000000.0) (not (<= y 1.4e-62)))
    (- t_m (* t_m (/ x y)))
    (* 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 tmp;
	if ((y <= -4100000000000.0) || !(y <= 1.4e-62)) {
		tmp = t_m - (t_m * (x / y));
	} 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) :: tmp
    if ((y <= (-4100000000000.0d0)) .or. (.not. (y <= 1.4d-62))) then
        tmp = t_m - (t_m * (x / y))
    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 tmp;
	if ((y <= -4100000000000.0) || !(y <= 1.4e-62)) {
		tmp = t_m - (t_m * (x / y));
	} 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):
	tmp = 0
	if (y <= -4100000000000.0) or not (y <= 1.4e-62):
		tmp = t_m - (t_m * (x / y))
	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)
	tmp = 0.0
	if ((y <= -4100000000000.0) || !(y <= 1.4e-62))
		tmp = Float64(t_m - Float64(t_m * Float64(x / y)));
	else
		tmp = Float64(t_m * Float64(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)
	tmp = 0.0;
	if ((y <= -4100000000000.0) || ~((y <= 1.4e-62)))
		tmp = t_m - (t_m * (x / y));
	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_] := N[(t$95$s * If[Or[LessEqual[y, -4100000000000.0], N[Not[LessEqual[y, 1.4e-62]], $MachinePrecision]], N[(t$95$m - N[(t$95$m * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$m * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -4.1e12 or 1.40000000000000001e-62 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 80.2%

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

      2. associate-/l* 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in z around 0 60.9%

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

      1. associate-*r/ 60.9%

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

      2. neg-mul-1 60.9%

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

   7. Simplified 60.9%

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

   8. Taylor expanded in x around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. unsub-neg 71.2%

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

      3. associate-/l* 78.2%

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

   10. Simplified 78.2%

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

   if -4.1e12 < y < 1.40000000000000001e-62

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf 77.4%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4100000000000 \lor \neg \left(y \leq 1.4 \cdot 10^{-62}\right):\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+18} \lor \neg \left(y \leq 1.35 \cdot 10^{-58}\right):\\ \;\;\;\;t\_m \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_m \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

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 (or (<= y -9.6e+18) (not (<= y 1.35e-58)))
    (* t_m (/ (- y x) y))
    (* 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 tmp;
	if ((y <= -9.6e+18) || !(y <= 1.35e-58)) {
		tmp = t_m * ((y - x) / y);
	} 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) :: tmp
    if ((y <= (-9.6d+18)) .or. (.not. (y <= 1.35d-58))) then
        tmp = t_m * ((y - x) / y)
    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 tmp;
	if ((y <= -9.6e+18) || !(y <= 1.35e-58)) {
		tmp = t_m * ((y - x) / y);
	} 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):
	tmp = 0
	if (y <= -9.6e+18) or not (y <= 1.35e-58):
		tmp = t_m * ((y - x) / y)
	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)
	tmp = 0.0
	if ((y <= -9.6e+18) || !(y <= 1.35e-58))
		tmp = Float64(t_m * Float64(Float64(y - x) / y));
	else
		tmp = Float64(t_m * Float64(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)
	tmp = 0.0;
	if ((y <= -9.6e+18) || ~((y <= 1.35e-58)))
		tmp = t_m * ((y - x) / y);
	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_] := N[(t$95$s * If[Or[LessEqual[y, -9.6e+18], N[Not[LessEqual[y, 1.35e-58]], $MachinePrecision]], N[(t$95$m * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t$95$m * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -9.6e18 or 1.3499999999999999e-58 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 78.2%

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

      1. mul-1-neg 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in y around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. distribute-rgt-neg-in 61.7%

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

      3. distribute-lft-in 62.6%

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

      4. associate-/l* 78.2%

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

      5. +-commutative 78.2%

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

      6. unsub-neg 78.2%

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

   8. Simplified 78.2%

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

   if -9.6e18 < y < 1.3499999999999999e-58

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf 77.4%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+18} \lor \neg \left(y \leq 1.35 \cdot 10^{-58}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+38} \lor \neg \left(y \leq 2.4 \cdot 10^{-63}\right):\\ \;\;\;\;t\_m \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t\_m}{z}\\ \end{array} \end{array} \]

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 (or (<= y -1.85e+38) (not (<= y 2.4e-63)))
    (* t_m (/ (- y x) y))
    (* (- x y) (/ t_m z)))))

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 <= -1.85e+38) || !(y <= 2.4e-63)) {
		tmp = t_m * ((y - x) / y);
	} else {
		tmp = (x - y) * (t_m / z);
	}
	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 <= (-1.85d+38)) .or. (.not. (y <= 2.4d-63))) then
        tmp = t_m * ((y - x) / y)
    else
        tmp = (x - y) * (t_m / z)
    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 <= -1.85e+38) || !(y <= 2.4e-63)) {
		tmp = t_m * ((y - x) / y);
	} else {
		tmp = (x - y) * (t_m / z);
	}
	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 <= -1.85e+38) or not (y <= 2.4e-63):
		tmp = t_m * ((y - x) / y)
	else:
		tmp = (x - y) * (t_m / z)
	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 <= -1.85e+38) || !(y <= 2.4e-63))
		tmp = Float64(t_m * Float64(Float64(y - x) / y));
	else
		tmp = Float64(Float64(x - y) * Float64(t_m / z));
	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 <= -1.85e+38) || ~((y <= 2.4e-63)))
		tmp = t_m * ((y - x) / y);
	else
		tmp = (x - y) * (t_m / z);
	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[Or[LessEqual[y, -1.85e+38], N[Not[LessEqual[y, 2.4e-63]], $MachinePrecision]], N[(t$95$m * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t$95$m / z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -1.8500000000000001e38 or 2.4000000000000001e-63 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 78.7%

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

      1. mul-1-neg 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in y around 0 62.1%

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

      1. mul-1-neg 62.1%

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

      2. distribute-rgt-neg-in 62.1%

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

      3. distribute-lft-in 63.0%

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

      4. associate-/l* 78.7%

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

      5. +-commutative 78.7%

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

      6. unsub-neg 78.7%

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

   8. Simplified 78.7%

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

   if -1.8500000000000001e38 < y < 2.4000000000000001e-63

   1. Initial program 93.2%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in z around inf 73.2%

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

      1. *-commutative 73.2%

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

      2. associate-/l* 75.7%

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

   7. Simplified 75.7%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+38} \lor \neg \left(y \leq 2.4 \cdot 10^{-63}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-70} \lor \neg \left(y \leq 1.02 \cdot 10^{-58}\right):\\ \;\;\;\;t\_m \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_m \cdot \frac{x}{z}\\ \end{array} \end{array} \]

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 (or (<= y -1.9e-70) (not (<= y 1.02e-58)))
    (* t_m (/ (- y x) y))
    (* t_m (/ x z)))))

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 <= -1.9e-70) || !(y <= 1.02e-58)) {
		tmp = t_m * ((y - x) / y);
	} else {
		tmp = t_m * (x / z);
	}
	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 <= (-1.9d-70)) .or. (.not. (y <= 1.02d-58))) then
        tmp = t_m * ((y - x) / y)
    else
        tmp = t_m * (x / z)
    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 <= -1.9e-70) || !(y <= 1.02e-58)) {
		tmp = t_m * ((y - x) / y);
	} else {
		tmp = t_m * (x / z);
	}
	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 <= -1.9e-70) or not (y <= 1.02e-58):
		tmp = t_m * ((y - x) / y)
	else:
		tmp = t_m * (x / z)
	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 <= -1.9e-70) || !(y <= 1.02e-58))
		tmp = Float64(t_m * Float64(Float64(y - x) / y));
	else
		tmp = Float64(t_m * Float64(x / z));
	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 <= -1.9e-70) || ~((y <= 1.02e-58)))
		tmp = t_m * ((y - x) / y);
	else
		tmp = t_m * (x / z);
	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[Or[LessEqual[y, -1.9e-70], N[Not[LessEqual[y, 1.02e-58]], $MachinePrecision]], N[(t$95$m * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t$95$m * N[(x / z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -1.8999999999999999e-70 or 1.0199999999999999e-58 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 74.0%

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

      1. mul-1-neg 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in y around 0 59.5%

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

      1. mul-1-neg 59.5%

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

      2. distribute-rgt-neg-in 59.5%

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

      3. distribute-lft-in 60.3%

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

      4. associate-/l* 74.0%

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

      5. +-commutative 74.0%

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

      6. unsub-neg 74.0%

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

   8. Simplified 74.0%

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

   if -1.8999999999999999e-70 < y < 1.0199999999999999e-58

   1. Initial program 91.9%

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

   3. Taylor expanded in y around 0 72.4%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-70} \lor \neg \left(y \leq 1.02 \cdot 10^{-58}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+20}:\\ \;\;\;\;t\_m - t\_m \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-58}:\\ \;\;\;\;\frac{t\_m}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_m \cdot \frac{y - x}{y}\\ \end{array} \end{array} \]

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 (<= y -4e+20)
    (- t_m (* t_m (/ x y)))
    (if (<= y 1.75e-58) (/ t_m (/ (- z y) x)) (* t_m (/ (- 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 (y <= -4e+20) {
		tmp = t_m - (t_m * (x / y));
	} else if (y <= 1.75e-58) {
		tmp = t_m / ((z - y) / x);
	} else {
		tmp = t_m * ((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 (y <= (-4d+20)) then
        tmp = t_m - (t_m * (x / y))
    else if (y <= 1.75d-58) then
        tmp = t_m / ((z - y) / x)
    else
        tmp = t_m * ((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 (y <= -4e+20) {
		tmp = t_m - (t_m * (x / y));
	} else if (y <= 1.75e-58) {
		tmp = t_m / ((z - y) / x);
	} else {
		tmp = t_m * ((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 y <= -4e+20:
		tmp = t_m - (t_m * (x / y))
	elif y <= 1.75e-58:
		tmp = t_m / ((z - y) / x)
	else:
		tmp = t_m * ((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 (y <= -4e+20)
		tmp = Float64(t_m - Float64(t_m * Float64(x / y)));
	elseif (y <= 1.75e-58)
		tmp = Float64(t_m / Float64(Float64(z - y) / x));
	else
		tmp = Float64(t_m * Float64(Float64(y - 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 (y <= -4e+20)
		tmp = t_m - (t_m * (x / y));
	elseif (y <= 1.75e-58)
		tmp = t_m / ((z - y) / x);
	else
		tmp = t_m * ((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[y, -4e+20], N[(t$95$m - N[(t$95$m * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e-58], N[(t$95$m / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t$95$m * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -4e20

   1. Initial program 99.8%

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

      1. associate-*l/ 83.6%

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

      2. associate-/l* 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in z around 0 58.0%

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

      1. associate-*r/ 58.0%

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

      2. neg-mul-1 58.0%

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

   7. Simplified 58.0%

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

   8. Taylor expanded in x around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. unsub-neg 75.1%

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

      3. associate-/l* 78.3%

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

   10. Simplified 78.3%

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

   if -4e20 < y < 1.75e-58

   1. Initial program 93.2%

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

      1. associate-*l/ 91.6%

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

      2. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

      1. associate-*r/ 91.6%

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

      2. associate-*l/ 93.2%

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

      3. *-commutative 93.2%

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

      4. clear-num 92.5%

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

      5. un-div-inv 93.2%

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

   6. Applied egg-rr 93.2%

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

   7. Taylor expanded in x around inf 77.5%

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

   if 1.75e-58 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 78.1%

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

      1. mul-1-neg 78.1%

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

   5. Simplified 78.1%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+20}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-58}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -66000000000000:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-59}:\\ \;\;\;\;t\_m \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_m\\ \end{array} \end{array} \]

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 -66000000000000.0) t_m (if (<= y 1.85e-59) (* t_m (/ x 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 <= -66000000000000.0) {
		tmp = t_m;
	} else if (y <= 1.85e-59) {
		tmp = t_m * (x / 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 <= (-66000000000000.0d0)) then
        tmp = t_m
    else if (y <= 1.85d-59) then
        tmp = t_m * (x / 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 <= -66000000000000.0) {
		tmp = t_m;
	} else if (y <= 1.85e-59) {
		tmp = t_m * (x / 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 <= -66000000000000.0:
		tmp = t_m
	elif y <= 1.85e-59:
		tmp = t_m * (x / 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 <= -66000000000000.0)
		tmp = t_m;
	elseif (y <= 1.85e-59)
		tmp = Float64(t_m * Float64(x / 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 <= -66000000000000.0)
		tmp = t_m;
	elseif (y <= 1.85e-59)
		tmp = t_m * (x / 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, -66000000000000.0], t$95$m, If[LessEqual[y, 1.85e-59], N[(t$95$m * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -6.6e13 or 1.85e-59 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 80.2%

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

      2. associate-/l* 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in y around inf 59.2%

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

   if -6.6e13 < y < 1.85e-59

   1. Initial program 93.2%

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

   3. Taylor expanded in y around 0 67.4%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -66000000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} t\_m = \left|t\right| \\ t\_s = \mathsf{copysign}\left(1, t\right) \\ t\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -10500000000000:\\ \;\;\;\;t\_m\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{t\_m}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_m\\ \end{array} \end{array} \]

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 -10500000000000.0) t_m (if (<= y 1.75e-58) (* 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 <= -10500000000000.0) {
		tmp = t_m;
	} else if (y <= 1.75e-58) {
		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 <= (-10500000000000.0d0)) then
        tmp = t_m
    else if (y <= 1.75d-58) 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 <= -10500000000000.0) {
		tmp = t_m;
	} else if (y <= 1.75e-58) {
		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 <= -10500000000000.0:
		tmp = t_m
	elif y <= 1.75e-58:
		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 <= -10500000000000.0)
		tmp = t_m;
	elseif (y <= 1.75e-58)
		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 <= -10500000000000.0)
		tmp = t_m;
	elseif (y <= 1.75e-58)
		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, -10500000000000.0], t$95$m, If[LessEqual[y, 1.75e-58], N[(x * N[(t$95$m / z), $MachinePrecision]), $MachinePrecision], t$95$m]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e13 or 1.75e-58 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 80.2%

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

      2. associate-/l* 78.9%

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

   3. Simplified 78.9%

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

   5. Taylor expanded in y around inf 59.2%

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

   if -1.05e13 < y < 1.75e-58

   1. Initial program 93.2%

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

      1. associate-*l/ 91.6%

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

      2. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in y around 0 62.8%

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

      1. *-commutative 62.8%

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

      2. associate-/l* 65.3%

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

   7. Simplified 65.3%

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

Alternative 13: 97.0% accurate, 1.0× speedup

Math

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

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 (/ (- 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) {
	return t_s * (t_m / ((z - y) / (x - y)));
}

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 / ((z - y) / (x - y)))
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 / ((z - y) / (x - y)));
}

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 / ((z - y) / (x - y)))

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	return Float64(t_s * Float64(t_m / Float64(Float64(z - y) / Float64(x - y))))
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 / ((z - y) / (x - y)));
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 * N[(t$95$m / N[(N[(z - y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.8%

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

   1. associate-*l/ 85.5%

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

   2. associate-/l* 85.9%

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

3. Simplified 85.9%

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

   1. associate-*r/ 85.5%

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

   2. associate-*l/ 96.8%

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

   3. *-commutative 96.8%

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

   4. clear-num 96.5%

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

   5. un-div-inv 96.8%

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

6. Applied egg-rr 96.8%

   \[\leadsto \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]
7. Add Preprocessing

Alternative 14: 97.2% accurate, 1.0× speedup

Math

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

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 (/ (- x y) (- 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) {
	return t_s * (t_m * ((x - y) / (z - y)));
}

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 * ((x - y) / (z - y)))
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 * ((x - y) / (z - y)));
}

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

Julia

t\_m = abs(t)
t\_s = copysign(1.0, t)
function code(t_s, x, y, z, t_m)
	return Float64(t_s * Float64(t_m * Float64(Float64(x - y) / Float64(z - y))))
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 * ((x - y) / (z - y)));
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 * N[(t$95$m * N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.8%

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

3. Final simplification 96.8%

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

Alternative 15: 35.9% 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 96.8%

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

   1. associate-*l/ 85.5%

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

   2. associate-/l* 85.9%

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

3. Simplified 85.9%

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

5. Taylor expanded in y around inf 36.7%

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

Developer target: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024103 
(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))