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

Percentage Accurate: 98.0% → 97.8%

Time: 6.8s

Alternatives: 9

Speedup: 1.0×

• 25.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x}{y} \cdot \left(z - t\right) + t \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return ((x / y) * (z - t)) + 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 - t)) + t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \cdot \left(z - t\right) + t \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return ((x / y) * (z - t)) + 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 - t)) + t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.1 \cdot 10^{-152} \lor \neg \left(t \leq 1.5 \cdot 10^{-172}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{z - t}{y}, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -7.1e-152) (not (<= t 1.5e-172)))
   (+ t (* (/ x y) (- z t)))
   (fma x (/ (- z t) y) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7.1e-152) || !(t <= 1.5e-172)) {
		tmp = t + ((x / y) * (z - t));
	} else {
		tmp = fma(x, ((z - t) / y), t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -7.1e-152) || !(t <= 1.5e-172))
		tmp = Float64(t + Float64(Float64(x / y) * Float64(z - t)));
	else
		tmp = fma(x, Float64(Float64(z - t) / y), t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -7.1e-152], N[Not[LessEqual[t, 1.5e-172]], $MachinePrecision]], N[(t + N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] + t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.10000000000000011e-152 or 1.49999999999999992e-172 < t

   1. Initial program 99.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   if -7.10000000000000011e-152 < t < 1.49999999999999992e-172

   1. Initial program 82.4%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Step-by-step derivation

      1. associate-*l/ 90.4%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.1 \cdot 10^{-152} \lor \neg \left(t \leq 1.5 \cdot 10^{-172}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{z - t}{y}, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{+99} \lor \neg \left(t \leq -1.05 \cdot 10^{-13} \lor \neg \left(t \leq -1.9 \cdot 10^{-60}\right) \land t \leq 1.1 \cdot 10^{-55}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.08e+99)
         (not
          (or (<= t -1.05e-13) (and (not (<= t -1.9e-60)) (<= t 1.1e-55)))))
   (* t (- 1.0 (/ x y)))
   (+ t (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.08e+99) || !((t <= -1.05e-13) || (!(t <= -1.9e-60) && (t <= 1.1e-55)))) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.08d+99)) .or. (.not. (t <= (-1.05d-13)) .or. (.not. (t <= (-1.9d-60))) .and. (t <= 1.1d-55))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t + (x * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.08e+99) || !((t <= -1.05e-13) || (!(t <= -1.9e-60) && (t <= 1.1e-55)))) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.08e+99) or not ((t <= -1.05e-13) or (not (t <= -1.9e-60) and (t <= 1.1e-55))):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + (x * (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.08e+99) || !((t <= -1.05e-13) || (!(t <= -1.9e-60) && (t <= 1.1e-55))))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t + Float64(x * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.08e+99) || ~(((t <= -1.05e-13) || (~((t <= -1.9e-60)) && (t <= 1.1e-55)))))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.08e+99], N[Not[Or[LessEqual[t, -1.05e-13], And[N[Not[LessEqual[t, -1.9e-60]], $MachinePrecision], LessEqual[t, 1.1e-55]]]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.08e99 or -1.04999999999999994e-13 < t < -1.89999999999999997e-60 or 1.1e-55 < t

   1. Initial program 99.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 88.2%

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

      1. mul-1-neg 88.2%

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

      2. unsub-neg 88.2%

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

      3. *-rgt-identity 88.2%

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

      4. associate-/l* 93.2%

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

      5. distribute-lft-out-- 93.2%

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

   5. Simplified 93.2%

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

   if -1.08e99 < t < -1.04999999999999994e-13 or -1.89999999999999997e-60 < t < 1.1e-55

   1. Initial program 91.4%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 77.2%

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

      1. associate-/l* 86.6%

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

   5. Simplified 86.6%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{+99} \lor \neg \left(t \leq -1.05 \cdot 10^{-13} \lor \neg \left(t \leq -1.9 \cdot 10^{-60}\right) \land t \leq 1.1 \cdot 10^{-55}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + x \cdot \frac{z}{y}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+98}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-58}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* x (/ z y)))) (t_2 (* t (- 1.0 (/ x y)))))
   (if (<= t -5.5e+98)
     t_2
     (if (<= t -2.3e-13)
       t_1
       (if (<= t -9.6e-58) (- t (* x (/ t y))) (if (<= t 8.5e-56) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t + (x * (z / y));
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -5.5e+98) {
		tmp = t_2;
	} else if (t <= -2.3e-13) {
		tmp = t_1;
	} else if (t <= -9.6e-58) {
		tmp = t - (x * (t / y));
	} else if (t <= 8.5e-56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (x * (z / y))
    t_2 = t * (1.0d0 - (x / y))
    if (t <= (-5.5d+98)) then
        tmp = t_2
    else if (t <= (-2.3d-13)) then
        tmp = t_1
    else if (t <= (-9.6d-58)) then
        tmp = t - (x * (t / y))
    else if (t <= 8.5d-56) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t + (x * (z / y));
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -5.5e+98) {
		tmp = t_2;
	} else if (t <= -2.3e-13) {
		tmp = t_1;
	} else if (t <= -9.6e-58) {
		tmp = t - (x * (t / y));
	} else if (t <= 8.5e-56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t + (x * (z / y))
	t_2 = t * (1.0 - (x / y))
	tmp = 0
	if t <= -5.5e+98:
		tmp = t_2
	elif t <= -2.3e-13:
		tmp = t_1
	elif t <= -9.6e-58:
		tmp = t - (x * (t / y))
	elif t <= 8.5e-56:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t + Float64(x * Float64(z / y)))
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (t <= -5.5e+98)
		tmp = t_2;
	elseif (t <= -2.3e-13)
		tmp = t_1;
	elseif (t <= -9.6e-58)
		tmp = Float64(t - Float64(x * Float64(t / y)));
	elseif (t <= 8.5e-56)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t + (x * (z / y));
	t_2 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (t <= -5.5e+98)
		tmp = t_2;
	elseif (t <= -2.3e-13)
		tmp = t_1;
	elseif (t <= -9.6e-58)
		tmp = t - (x * (t / y));
	elseif (t <= 8.5e-56)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e+98], t$95$2, If[LessEqual[t, -2.3e-13], t$95$1, If[LessEqual[t, -9.6e-58], N[(t - N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-56], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.49999999999999946e98 or 8.49999999999999932e-56 < t

   1. Initial program 99.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 87.4%

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

      1. mul-1-neg 87.4%

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

      2. unsub-neg 87.4%

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

      3. *-rgt-identity 87.4%

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

      4. associate-/l* 92.8%

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

      5. distribute-lft-out-- 92.8%

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

   5. Simplified 92.8%

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

   if -5.49999999999999946e98 < t < -2.29999999999999979e-13 or -9.6000000000000002e-58 < t < 8.49999999999999932e-56

   1. Initial program 91.4%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 77.2%

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

      1. associate-/l* 86.6%

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

   5. Simplified 86.6%

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

   if -2.29999999999999979e-13 < t < -9.6000000000000002e-58

   1. Initial program 99.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

      1. div-inv 99.8%

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

      2. clear-num 99.8%

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

      3. div-inv 99.8%

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

      4. associate-*r* 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-*r/ 99.8%

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

      3. *-commutative 99.8%

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

      4. distribute-lft-neg-in 99.8%

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

      5. cancel-sign-sub-inv 99.8%

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

      6. associate-*l/ 100.0%

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

      7. associate-/l* 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-13}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-58}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-56}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -2.5 \cdot 10^{+305}:\\ \;\;\;\;t + \left(x \cdot \left(z - t\right)\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* (/ x y) (- z t)))))
   (if (<= t_1 -2.5e+305) (+ t (* (* x (- z t)) (/ 1.0 y))) t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = t + ((x / y) * (z - t));
	double tmp;
	if (t_1 <= -2.5e+305) {
		tmp = t + ((x * (z - t)) * (1.0 / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((x / y) * (z - t))
    if (t_1 <= (-2.5d+305)) then
        tmp = t + ((x * (z - t)) * (1.0d0 / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t + ((x / y) * (z - t));
	double tmp;
	if (t_1 <= -2.5e+305) {
		tmp = t + ((x * (z - t)) * (1.0 / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t + ((x / y) * (z - t))
	tmp = 0
	if t_1 <= -2.5e+305:
		tmp = t + ((x * (z - t)) * (1.0 / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t + Float64(Float64(x / y) * Float64(z - t)))
	tmp = 0.0
	if (t_1 <= -2.5e+305)
		tmp = Float64(t + Float64(Float64(x * Float64(z - t)) * Float64(1.0 / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t + ((x / y) * (z - t));
	tmp = 0.0;
	if (t_1 <= -2.5e+305)
		tmp = t + ((x * (z - t)) * (1.0 / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t + N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2.5e+305], N[(t + N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t) < -2.50000000000000004e305

   1. Initial program 84.3%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 84.3%

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

      2. clear-num 84.4%

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

      3. un-div-inv 84.4%

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

   4. Applied egg-rr 84.4%

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

      1. div-inv 84.4%

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

      2. clear-num 84.3%

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

      3. div-inv 84.4%

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

      4. associate-*r* 100.0%

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

   6. Applied egg-rr 100.0%

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

   if -2.50000000000000004e305 < (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

   1. Initial program 97.7%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + \frac{x}{y} \cdot \left(z - t\right) \leq -2.5 \cdot 10^{+305}:\\ \;\;\;\;t + \left(x \cdot \left(z - t\right)\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+37} \lor \neg \left(x \leq 4 \cdot 10^{+29}\right):\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.9e+37) (not (<= x 4e+29))) (* t (/ x (- y))) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.9e+37) || !(x <= 4e+29)) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.9d+37)) .or. (.not. (x <= 4d+29))) then
        tmp = t * (x / -y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.9e+37) || !(x <= 4e+29)) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.9e+37) or not (x <= 4e+29):
		tmp = t * (x / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.9e+37) || !(x <= 4e+29))
		tmp = Float64(t * Float64(x / Float64(-y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.9e+37) || ~((x <= 4e+29)))
		tmp = t * (x / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.9e+37], N[Not[LessEqual[x, 4e+29]], $MachinePrecision]], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -1.89999999999999995e37 or 3.99999999999999966e29 < x

   1. Initial program 93.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 93.8%

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

      2. clear-num 93.8%

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

      3. un-div-inv 93.8%

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

   4. Applied egg-rr 93.8%

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

      1. div-inv 93.8%

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

      2. clear-num 93.8%

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

      3. div-inv 93.8%

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

      4. associate-*r* 85.7%

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

   6. Applied egg-rr 85.7%

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

   7. Taylor expanded in z around 0 54.2%

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

      1. mul-1-neg 54.2%

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

      2. associate-*r/ 56.5%

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

      3. *-commutative 56.5%

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

      4. distribute-lft-neg-in 56.5%

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

      5. cancel-sign-sub-inv 56.5%

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

      6. associate-*l/ 54.2%

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

      7. associate-/l* 58.8%

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

   9. Simplified 58.8%

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

   10. Taylor expanded in x around inf 46.5%

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

       1. mul-1-neg 46.5%

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

       2. associate-*l/ 48.8%

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

       3. distribute-rgt-neg-in 48.8%

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

       4. associate-*l/ 46.5%

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

       5. associate-*r/ 46.5%

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

   12. Simplified 46.5%

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

   if -1.89999999999999995e37 < x < 3.99999999999999966e29

   1. Initial program 97.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 64.2%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+37} \lor \neg \left(x \leq 4 \cdot 10^{+29}\right):\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;x \leq 1.52 \cdot 10^{+18}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.5e+37)
   (* t (/ x (- y)))
   (if (<= x 1.52e+18) t (* x (/ t (- y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.5e+37) {
		tmp = t * (x / -y);
	} else if (x <= 1.52e+18) {
		tmp = t;
	} else {
		tmp = x * (t / -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-6.5d+37)) then
        tmp = t * (x / -y)
    else if (x <= 1.52d+18) then
        tmp = t
    else
        tmp = x * (t / -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.5e+37) {
		tmp = t * (x / -y);
	} else if (x <= 1.52e+18) {
		tmp = t;
	} else {
		tmp = x * (t / -y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.5e+37:
		tmp = t * (x / -y)
	elif x <= 1.52e+18:
		tmp = t
	else:
		tmp = x * (t / -y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.5e+37)
		tmp = Float64(t * Float64(x / Float64(-y)));
	elseif (x <= 1.52e+18)
		tmp = t;
	else
		tmp = Float64(x * Float64(t / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.5e+37)
		tmp = t * (x / -y);
	elseif (x <= 1.52e+18)
		tmp = t;
	else
		tmp = x * (t / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.5e+37], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.52e+18], t, N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.4999999999999998e37

   1. Initial program 95.1%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 95.1%

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

      2. clear-num 95.1%

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

      3. un-div-inv 95.0%

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

   4. Applied egg-rr 95.0%

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

      1. div-inv 95.1%

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

      2. clear-num 95.1%

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

      3. div-inv 95.1%

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

      4. associate-*r* 88.5%

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

   6. Applied egg-rr 88.5%

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

   7. Taylor expanded in z around 0 51.2%

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

      1. mul-1-neg 51.2%

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

      2. associate-*r/ 54.7%

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

      3. *-commutative 54.7%

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

      4. distribute-lft-neg-in 54.7%

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

      5. cancel-sign-sub-inv 54.7%

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

      6. associate-*l/ 51.2%

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

      7. associate-/l* 54.6%

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

   9. Simplified 54.6%

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

   10. Taylor expanded in x around inf 42.8%

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

       1. mul-1-neg 42.8%

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

       2. associate-*l/ 42.8%

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

       3. distribute-rgt-neg-in 42.8%

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

       4. associate-*l/ 42.8%

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

       5. associate-*r/ 42.9%

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

   12. Simplified 42.9%

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

   if -6.4999999999999998e37 < x < 1.52e18

   1. Initial program 97.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 64.2%

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

   if 1.52e18 < x

   1. Initial program 92.7%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 92.7%

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

      2. clear-num 92.6%

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

      3. un-div-inv 92.8%

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

   4. Applied egg-rr 92.8%

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

      1. div-inv 92.6%

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

      2. clear-num 92.7%

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

      3. div-inv 92.7%

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

      4. associate-*r* 83.2%

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

   6. Applied egg-rr 83.2%

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

   7. Taylor expanded in z around 0 56.8%

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

      1. mul-1-neg 56.8%

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

      2. associate-*r/ 58.0%

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

      3. *-commutative 58.0%

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

      4. distribute-lft-neg-in 58.0%

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

      5. cancel-sign-sub-inv 58.0%

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

      6. associate-*l/ 56.8%

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

      7. associate-/l* 62.4%

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

   9. Simplified 62.4%

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

   10. Taylor expanded in x around inf 49.7%

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

       1. mul-1-neg 49.7%

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

       2. associate-*l/ 53.9%

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

       3. distribute-rgt-neg-in 53.9%

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

   12. Simplified 53.9%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+37}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;x \leq 1.52 \cdot 10^{+18}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ t + \frac{x}{y} \cdot \left(z - t\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.8%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
2. Add Preprocessing

3. Final simplification 95.8%

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

Alternative 8: 65.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ t \cdot \left(1 - \frac{x}{y}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* t (- 1.0 (/ x y))))

C

double code(double x, double y, double z, double t) {
	return t * (1.0 - (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 * (1.0d0 - (x / y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return t * (1.0 - (x / y));
}

Python

def code(x, y, z, t):
	return t * (1.0 - (x / y))

Julia

function code(x, y, z, t)
	return Float64(t * Float64(1.0 - Float64(x / y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t * (1.0 - (x / y));
end

Wolfram

code[x_, y_, z_, t_] := N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.8%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
2. Add Preprocessing

3. Taylor expanded in z around 0 66.0%

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

   1. mul-1-neg 66.0%

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

   2. unsub-neg 66.0%

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

   3. *-rgt-identity 66.0%

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

   4. associate-/l* 67.7%

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

   5. distribute-lft-out-- 67.7%

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

5. Simplified 67.7%

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

6. Final simplification 67.7%

   \[\leadsto t \cdot \left(1 - \frac{x}{y}\right) \]
7. Add Preprocessing

Alternative 9: 38.0% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.8%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
2. Add Preprocessing

3. Taylor expanded in x around 0 38.8%

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

4. Final simplification 38.8%

   \[\leadsto t \]
5. Add Preprocessing

Developer target: 97.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* (/ x y) (- z t)) t)))
   (if (< z 2.759456554562692e-282)
     t_1
     (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x / y) * (z - t)) + t
    if (z < 2.759456554562692d-282) then
        tmp = t_1
    else if (z < 2.326994450874436d-110) then
        tmp = (x * ((z - t) / y)) + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x / y) * (z - t)) + t
	tmp = 0
	if z < 2.759456554562692e-282:
		tmp = t_1
	elif z < 2.326994450874436e-110:
		tmp = (x * ((z - t) / y)) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x / y) * Float64(z - t)) + t)
	tmp = 0.0
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = Float64(Float64(x * Float64(Float64(z - t) / y)) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x / y) * (z - t)) + t;
	tmp = 0.0;
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = (x * ((z - t) / y)) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[Less[z, 2.759456554562692e-282], t$95$1, If[Less[z, 2.326994450874436e-110], N[(N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024130 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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