Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D

Percentage Accurate: 93.2% → 98.0%

Time: 9.4s

Alternatives: 12

Speedup: 1.0×

• 24.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.4%

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

   1. +-commutative 92.4%

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

   2. associate-/l* 96.3%

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

   3. fma-define 96.3%

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

3. Simplified 96.3%

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

   1. fma-undefine 96.3%

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

   2. associate-/l* 92.4%

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

   3. *-commutative 92.4%

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

   4. associate-/l* 96.6%

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

6. Applied egg-rr 96.6%

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

7. Final simplification 96.6%

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

Alternative 2: 49.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 125 \lor \neg \left(t \leq 1.3 \cdot 10^{+72}\right) \land t \leq 7.6 \cdot 10^{+189}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.6e-118)
   x
   (if (or (<= t 125.0) (and (not (<= t 1.3e+72)) (<= t 7.6e+189)))
     (* y (/ z t))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.6e-118) {
		tmp = x;
	} else if ((t <= 125.0) || (!(t <= 1.3e+72) && (t <= 7.6e+189))) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	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 <= (-1.6d-118)) then
        tmp = x
    else if ((t <= 125.0d0) .or. (.not. (t <= 1.3d+72)) .and. (t <= 7.6d+189)) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.6e-118) {
		tmp = x;
	} else if ((t <= 125.0) || (!(t <= 1.3e+72) && (t <= 7.6e+189))) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.6e-118:
		tmp = x
	elif (t <= 125.0) or (not (t <= 1.3e+72) and (t <= 7.6e+189)):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.6e-118)
		tmp = x;
	elseif ((t <= 125.0) || (!(t <= 1.3e+72) && (t <= 7.6e+189)))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.6e-118)
		tmp = x;
	elseif ((t <= 125.0) || (~((t <= 1.3e+72)) && (t <= 7.6e+189)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.6e-118], x, If[Or[LessEqual[t, 125.0], And[N[Not[LessEqual[t, 1.3e+72]], $MachinePrecision], LessEqual[t, 7.6e+189]]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.60000000000000002e-118 or 125 < t < 1.29999999999999991e72 or 7.5999999999999997e189 < t

   1. Initial program 87.1%

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

      1. +-commutative 87.1%

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

      2. associate-/l* 99.0%

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

      3. fma-define 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in y around 0 64.9%

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

   if -1.60000000000000002e-118 < t < 125 or 1.29999999999999991e72 < t < 7.5999999999999997e189

   1. Initial program 97.0%

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

      1. +-commutative 97.0%

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

      2. associate-/l* 94.0%

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

      3. fma-define 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in y around -inf 85.5%

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

   6. Taylor expanded in z around inf 52.7%

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

      1. associate-/l* 51.4%

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

   8. Simplified 51.4%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 125 \lor \neg \left(t \leq 1.3 \cdot 10^{+72}\right) \land t \leq 7.6 \cdot 10^{+189}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 220:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+190}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.7e-120)
   x
   (if (<= t 220.0)
     (/ y (/ t z))
     (if (<= t 2.4e+72) x (if (<= t 2.6e+190) (* y (/ z t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.7e-120) {
		tmp = x;
	} else if (t <= 220.0) {
		tmp = y / (t / z);
	} else if (t <= 2.4e+72) {
		tmp = x;
	} else if (t <= 2.6e+190) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	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 <= (-4.7d-120)) then
        tmp = x
    else if (t <= 220.0d0) then
        tmp = y / (t / z)
    else if (t <= 2.4d+72) then
        tmp = x
    else if (t <= 2.6d+190) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.7e-120) {
		tmp = x;
	} else if (t <= 220.0) {
		tmp = y / (t / z);
	} else if (t <= 2.4e+72) {
		tmp = x;
	} else if (t <= 2.6e+190) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.7e-120:
		tmp = x
	elif t <= 220.0:
		tmp = y / (t / z)
	elif t <= 2.4e+72:
		tmp = x
	elif t <= 2.6e+190:
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.7e-120)
		tmp = x;
	elseif (t <= 220.0)
		tmp = Float64(y / Float64(t / z));
	elseif (t <= 2.4e+72)
		tmp = x;
	elseif (t <= 2.6e+190)
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.7e-120)
		tmp = x;
	elseif (t <= 220.0)
		tmp = y / (t / z);
	elseif (t <= 2.4e+72)
		tmp = x;
	elseif (t <= 2.6e+190)
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.7e-120], x, If[LessEqual[t, 220.0], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+72], x, If[LessEqual[t, 2.6e+190], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.70000000000000016e-120 or 220 < t < 2.4000000000000001e72 or 2.60000000000000011e190 < t

   1. Initial program 87.1%

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

      1. +-commutative 87.1%

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

      2. associate-/l* 99.0%

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

      3. fma-define 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in y around 0 64.9%

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

   if -4.70000000000000016e-120 < t < 220

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate-/l* 93.8%

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

      3. fma-define 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in y around -inf 88.4%

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

   6. Taylor expanded in z around inf 52.9%

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

      1. associate-/l* 50.6%

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

   8. Simplified 50.6%

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

      1. clear-num 50.6%

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

      2. un-div-inv 50.8%

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

   10. Applied egg-rr 50.8%

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

   if 2.4000000000000001e72 < t < 2.60000000000000011e190

   1. Initial program 87.8%

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

      1. +-commutative 87.8%

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

      2. associate-/l* 95.8%

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

      3. fma-define 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in y around -inf 63.9%

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

   6. Taylor expanded in z around inf 51.6%

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

      1. associate-/l* 57.5%

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

   8. Simplified 57.5%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 220:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+190}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot y}{t}\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+51}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z y) t)))
   (if (<= z -2.35e-22)
     t_1
     (if (<= z 4.8e-295) x (if (<= z 6.8e+51) (* (/ y t) (- x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * y) / t;
	double tmp;
	if (z <= -2.35e-22) {
		tmp = t_1;
	} else if (z <= 4.8e-295) {
		tmp = x;
	} else if (z <= 6.8e+51) {
		tmp = (y / t) * -x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * y) / t
    if (z <= (-2.35d-22)) then
        tmp = t_1
    else if (z <= 4.8d-295) then
        tmp = x
    else if (z <= 6.8d+51) then
        tmp = (y / t) * -x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * y) / t;
	double tmp;
	if (z <= -2.35e-22) {
		tmp = t_1;
	} else if (z <= 4.8e-295) {
		tmp = x;
	} else if (z <= 6.8e+51) {
		tmp = (y / t) * -x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * y) / t
	tmp = 0
	if z <= -2.35e-22:
		tmp = t_1
	elif z <= 4.8e-295:
		tmp = x
	elif z <= 6.8e+51:
		tmp = (y / t) * -x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * y) / t)
	tmp = 0.0
	if (z <= -2.35e-22)
		tmp = t_1;
	elseif (z <= 4.8e-295)
		tmp = x;
	elseif (z <= 6.8e+51)
		tmp = Float64(Float64(y / t) * Float64(-x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * y) / t;
	tmp = 0.0;
	if (z <= -2.35e-22)
		tmp = t_1;
	elseif (z <= 4.8e-295)
		tmp = x;
	elseif (z <= 6.8e+51)
		tmp = (y / t) * -x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -2.35e-22], t$95$1, If[LessEqual[z, 4.8e-295], x, If[LessEqual[z, 6.8e+51], N[(N[(y / t), $MachinePrecision] * (-x)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3500000000000001e-22 or 6.79999999999999969e51 < z

   1. Initial program 93.0%

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

      1. +-commutative 93.0%

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

      2. associate-/l* 95.6%

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

      3. fma-define 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in y around -inf 71.5%

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

   6. Taylor expanded in z around inf 65.3%

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

   if -2.3500000000000001e-22 < z < 4.7999999999999996e-295

   1. Initial program 88.4%

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

      1. +-commutative 88.4%

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

      2. associate-/l* 96.2%

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

      3. fma-define 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around 0 56.1%

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

   if 4.7999999999999996e-295 < z < 6.79999999999999969e51

   1. Initial program 95.1%

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

      1. +-commutative 95.1%

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

      2. associate-/l* 97.4%

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

      3. fma-define 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in y around -inf 61.8%

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

   6. Taylor expanded in z around 0 50.8%

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

      1. mul-1-neg 50.8%

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

      2. associate-/l* 50.7%

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

      3. distribute-rgt-neg-in 50.7%

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

      4. mul-1-neg 50.7%

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

      5. associate-*r/ 50.7%

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

      6. mul-1-neg 50.7%

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

   8. Simplified 50.7%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-22}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+51}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 48.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot y}{t}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-294}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z y) t)))
   (if (<= z -2.25e-24)
     t_1
     (if (<= z 1.02e-294) x (if (<= z 9e+43) (* y (/ (- x) t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * y) / t;
	double tmp;
	if (z <= -2.25e-24) {
		tmp = t_1;
	} else if (z <= 1.02e-294) {
		tmp = x;
	} else if (z <= 9e+43) {
		tmp = y * (-x / 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 = (z * y) / t
    if (z <= (-2.25d-24)) then
        tmp = t_1
    else if (z <= 1.02d-294) then
        tmp = x
    else if (z <= 9d+43) then
        tmp = y * (-x / 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 = (z * y) / t;
	double tmp;
	if (z <= -2.25e-24) {
		tmp = t_1;
	} else if (z <= 1.02e-294) {
		tmp = x;
	} else if (z <= 9e+43) {
		tmp = y * (-x / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * y) / t
	tmp = 0
	if z <= -2.25e-24:
		tmp = t_1
	elif z <= 1.02e-294:
		tmp = x
	elif z <= 9e+43:
		tmp = y * (-x / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * y) / t)
	tmp = 0.0
	if (z <= -2.25e-24)
		tmp = t_1;
	elseif (z <= 1.02e-294)
		tmp = x;
	elseif (z <= 9e+43)
		tmp = Float64(y * Float64(Float64(-x) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * y) / t;
	tmp = 0.0;
	if (z <= -2.25e-24)
		tmp = t_1;
	elseif (z <= 1.02e-294)
		tmp = x;
	elseif (z <= 9e+43)
		tmp = y * (-x / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -2.25e-24], t$95$1, If[LessEqual[z, 1.02e-294], x, If[LessEqual[z, 9e+43], N[(y * N[((-x) / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2499999999999999e-24 or 9e43 < z

   1. Initial program 93.2%

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

      1. +-commutative 93.2%

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

      2. associate-/l* 95.0%

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

      3. fma-define 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around -inf 71.4%

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

   6. Taylor expanded in z around inf 64.5%

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

   if -2.2499999999999999e-24 < z < 1.01999999999999998e-294

   1. Initial program 88.4%

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

      1. +-commutative 88.4%

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

      2. associate-/l* 96.2%

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

      3. fma-define 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around 0 56.1%

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

   if 1.01999999999999998e-294 < z < 9e43

   1. Initial program 94.9%

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

      1. +-commutative 94.9%

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

      2. associate-/l* 98.5%

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

      3. fma-define 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in y around -inf 61.5%

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

      1. associate-/l* 64.8%

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

      2. *-commutative 64.8%

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

   7. Applied egg-rr 64.8%

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

   8. Taylor expanded in z around 0 53.5%

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

      1. neg-mul-1 53.5%

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

      2. distribute-neg-frac2 53.5%

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

   10. Simplified 53.5%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-24}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-294}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+62} \lor \neg \left(z \leq 2.2 \cdot 10^{+58}\right):\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.1e+62) (not (<= z 2.2e+58)))
   (/ (* z y) t)
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.1e+62) || !(z <= 2.2e+58)) {
		tmp = (z * y) / t;
	} else {
		tmp = x * (1.0 - (y / 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 ((z <= (-5.1d+62)) .or. (.not. (z <= 2.2d+58))) then
        tmp = (z * y) / t
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.1e+62) || !(z <= 2.2e+58)) {
		tmp = (z * y) / t;
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.1e+62) or not (z <= 2.2e+58):
		tmp = (z * y) / t
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.1e+62) || !(z <= 2.2e+58))
		tmp = Float64(Float64(z * y) / t);
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.1e+62) || ~((z <= 2.2e+58)))
		tmp = (z * y) / t;
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.1e+62], N[Not[LessEqual[z, 2.2e+58]], $MachinePrecision]], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.09999999999999998e62 or 2.2000000000000001e58 < z

   1. Initial program 91.3%

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

      1. +-commutative 91.3%

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

      2. associate-/l* 94.6%

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

      3. fma-define 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in y around -inf 72.7%

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

   6. Taylor expanded in z around inf 69.4%

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

   if -5.09999999999999998e62 < z < 2.2000000000000001e58

   1. Initial program 93.1%

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

      1. +-commutative 93.1%

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

      2. associate-/l* 97.2%

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

      3. fma-define 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in z around 0 80.4%

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

      1. *-rgt-identity 80.4%

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

      2. mul-1-neg 80.4%

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

      3. associate-/l* 84.4%

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

      4. distribute-rgt-neg-in 84.4%

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

      5. mul-1-neg 84.4%

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

      6. distribute-lft-in 84.4%

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

      7. mul-1-neg 84.4%

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

      8. unsub-neg 84.4%

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

   7. Simplified 84.4%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+62} \lor \neg \left(z \leq 2.2 \cdot 10^{+58}\right):\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-16} \lor \neg \left(x \leq 4.3 \cdot 10^{-93}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.25e-16) (not (<= x 4.3e-93)))
   (* x (- 1.0 (/ y t)))
   (* y (/ (- z x) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.25e-16) || !(x <= 4.3e-93)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = y * ((z - x) / 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 <= (-1.25d-16)) .or. (.not. (x <= 4.3d-93))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = y * ((z - x) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.25e-16) || !(x <= 4.3e-93)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = y * ((z - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.25e-16) or not (x <= 4.3e-93):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = y * ((z - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.25e-16) || !(x <= 4.3e-93))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(y * Float64(Float64(z - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.25e-16) || ~((x <= 4.3e-93)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = y * ((z - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.25e-16], N[Not[LessEqual[x, 4.3e-93]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2500000000000001e-16 or 4.29999999999999963e-93 < x

   1. Initial program 90.0%

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

      1. +-commutative 90.0%

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

      2. associate-/l* 96.2%

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

      3. fma-define 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in z around 0 82.0%

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

      1. *-rgt-identity 82.0%

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

      2. mul-1-neg 82.0%

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

      3. associate-/l* 88.8%

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

      4. distribute-rgt-neg-in 88.8%

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

      5. mul-1-neg 88.8%

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

      6. distribute-lft-in 88.8%

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

      7. mul-1-neg 88.8%

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

      8. unsub-neg 88.8%

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

   7. Simplified 88.8%

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

   if -1.2500000000000001e-16 < x < 4.29999999999999963e-93

   1. Initial program 96.1%

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

      1. +-commutative 96.1%

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

      2. associate-/l* 96.5%

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

      3. fma-define 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in y around -inf 70.4%

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

      1. associate-/l* 70.7%

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

      2. *-commutative 70.7%

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

   7. Applied egg-rr 70.7%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-16} \lor \neg \left(x \leq 4.3 \cdot 10^{-93}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{-20} \lor \neg \left(x \leq 1.8 \cdot 10^{-43}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9.8e-20) (not (<= x 1.8e-43)))
   (* x (- 1.0 (/ y t)))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9.8e-20) || !(x <= 1.8e-43)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (y * (z / 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 <= (-9.8d-20)) .or. (.not. (x <= 1.8d-43))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9.8e-20) || !(x <= 1.8e-43)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -9.8e-20) or not (x <= 1.8e-43):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -9.8e-20) || !(x <= 1.8e-43))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -9.8e-20) || ~((x <= 1.8e-43)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -9.8e-20], N[Not[LessEqual[x, 1.8e-43]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.8000000000000003e-20 or 1.7999999999999999e-43 < x

   1. Initial program 89.0%

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

      1. +-commutative 89.0%

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

      2. associate-/l* 96.6%

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

      3. fma-define 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in z around 0 83.4%

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

      1. *-rgt-identity 83.4%

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

      2. mul-1-neg 83.4%

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

      3. associate-/l* 91.6%

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

      4. distribute-rgt-neg-in 91.6%

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

      5. mul-1-neg 91.6%

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

      6. distribute-lft-in 91.6%

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

      7. mul-1-neg 91.6%

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

      8. unsub-neg 91.6%

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

   7. Simplified 91.6%

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

   if -9.8000000000000003e-20 < x < 1.7999999999999999e-43

   1. Initial program 96.5%

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

   3. Taylor expanded in z around inf 82.4%

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

      1. associate-/l* 54.9%

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

   5. Simplified 82.4%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{-20} \lor \neg \left(x \leq 1.8 \cdot 10^{-43}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+23} \lor \neg \left(x \leq 6 \cdot 10^{-41}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.8e+23) (not (<= x 6e-41)))
   (* x (- 1.0 (/ y t)))
   (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.8e+23) || !(x <= 6e-41)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z * (y / 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 <= (-1.8d+23)) .or. (.not. (x <= 6d-41))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.8e+23) || !(x <= 6e-41)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.8e+23) or not (x <= 6e-41):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.8e+23) || !(x <= 6e-41))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.8e+23) || ~((x <= 6e-41)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.8e+23], N[Not[LessEqual[x, 6e-41]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7999999999999999e23 or 5.99999999999999978e-41 < x

   1. Initial program 88.5%

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

      1. +-commutative 88.5%

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

      2. associate-/l* 97.1%

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

      3. fma-define 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around 0 84.1%

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

      1. *-rgt-identity 84.1%

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

      2. mul-1-neg 84.1%

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

      3. associate-/l* 92.6%

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

      4. distribute-rgt-neg-in 92.6%

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

      5. mul-1-neg 92.6%

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

      6. distribute-lft-in 92.6%

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

      7. mul-1-neg 92.6%

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

      8. unsub-neg 92.6%

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

   7. Simplified 92.6%

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

   if -1.7999999999999999e23 < x < 5.99999999999999978e-41

   1. Initial program 96.7%

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

   3. Taylor expanded in z around inf 81.9%

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

      1. associate-/l* 52.9%

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

   5. Simplified 81.1%

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

      1. clear-num 52.8%

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

      2. un-div-inv 53.1%

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

   7. Applied egg-rr 80.9%

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

      1. associate-/r/ 83.5%

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

   9. Applied egg-rr 83.5%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+23} \lor \neg \left(x \leq 6 \cdot 10^{-41}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-33} \lor \neg \left(z \leq 2.65 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.05e-33) (not (<= z 2.65e+54))) (/ (* z y) t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.05e-33) || !(z <= 2.65e+54)) {
		tmp = (z * y) / t;
	} else {
		tmp = x;
	}
	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 ((z <= (-2.05d-33)) .or. (.not. (z <= 2.65d+54))) then
        tmp = (z * y) / t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.05e-33) || !(z <= 2.65e+54)) {
		tmp = (z * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.05e-33) or not (z <= 2.65e+54):
		tmp = (z * y) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.05e-33) || !(z <= 2.65e+54))
		tmp = Float64(Float64(z * y) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.05e-33) || ~((z <= 2.65e+54)))
		tmp = (z * y) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.05e-33], N[Not[LessEqual[z, 2.65e+54]], $MachinePrecision]], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.05e-33 or 2.65000000000000009e54 < z

   1. Initial program 93.0%

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

      1. +-commutative 93.0%

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

      2. associate-/l* 95.6%

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

      3. fma-define 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in y around -inf 71.5%

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

   6. Taylor expanded in z around inf 65.3%

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

   if -2.05e-33 < z < 2.65000000000000009e54

   1. Initial program 92.0%

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

      1. +-commutative 92.0%

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

      2. associate-/l* 96.8%

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

      3. fma-define 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in y around 0 45.7%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-33} \lor \neg \left(z \leq 2.65 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 92.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.4%

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

   1. associate-/l* 61.5%

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

   2. *-commutative 61.5%

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

4. Applied egg-rr 96.3%

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

5. Final simplification 96.3%

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

Alternative 12: 39.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.4%

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

   1. +-commutative 92.4%

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

   2. associate-/l* 96.3%

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

   3. fma-define 96.3%

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

3. Simplified 96.3%

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

5. Taylor expanded in y around 0 37.5%

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

6. Final simplification 37.5%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 91.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024053 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

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

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