Numeric.Histogram:binBounds from Chart-1.5.3

Percentage Accurate: 92.7% → 98.0%

Time: 8.5s

Alternatives: 18

Speedup: 1.0×

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - x) / (t / z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.4%

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

   1. associate-/l* 96.5%

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

3. Simplified 96.5%

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

4. Final simplification 96.5%

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

Alternative 2: 95.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq \infty\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) z) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 INFINITY)))
     (+ x (* z (/ (- y x) t)))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (((y - x) * z) / t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= ((double) INFINITY))) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (((y - x) * z) / t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= Double.POSITIVE_INFINITY)) {
		tmp = x + (z * ((y - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (((y - x) * z) / t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= math.inf):
		tmp = x + (z * ((y - x) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) * z) / t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= Inf))
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (((y - x) * z) / t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= Inf)))
		tmp = x + (z * ((y - x) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t)) < -inf.0 or +inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

   1. Initial program 85.0%

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

      1. associate-*l/ 94.8%

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

   3. Applied egg-rr 100.0%

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

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

   1. Initial program 93.7%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} \leq -\infty \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \leq \infty\right):\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]

Alternative 3: 53.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{-x}{t}\\ t_2 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{-38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.1 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+171}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ (- x) t))) (t_2 (/ y (/ t z))))
   (if (<= z -8.6e-38)
     t_2
     (if (<= z 4.9e-73)
       x
       (if (<= z 4.3e-6)
         t_1
         (if (<= z 8.1e+80) x (if (<= z 1.05e+171) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (-x / t);
	double t_2 = y / (t / z);
	double tmp;
	if (z <= -8.6e-38) {
		tmp = t_2;
	} else if (z <= 4.9e-73) {
		tmp = x;
	} else if (z <= 4.3e-6) {
		tmp = t_1;
	} else if (z <= 8.1e+80) {
		tmp = x;
	} else if (z <= 1.05e+171) {
		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 = z * (-x / t)
    t_2 = y / (t / z)
    if (z <= (-8.6d-38)) then
        tmp = t_2
    else if (z <= 4.9d-73) then
        tmp = x
    else if (z <= 4.3d-6) then
        tmp = t_1
    else if (z <= 8.1d+80) then
        tmp = x
    else if (z <= 1.05d+171) 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 = z * (-x / t);
	double t_2 = y / (t / z);
	double tmp;
	if (z <= -8.6e-38) {
		tmp = t_2;
	} else if (z <= 4.9e-73) {
		tmp = x;
	} else if (z <= 4.3e-6) {
		tmp = t_1;
	} else if (z <= 8.1e+80) {
		tmp = x;
	} else if (z <= 1.05e+171) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (-x / t)
	t_2 = y / (t / z)
	tmp = 0
	if z <= -8.6e-38:
		tmp = t_2
	elif z <= 4.9e-73:
		tmp = x
	elif z <= 4.3e-6:
		tmp = t_1
	elif z <= 8.1e+80:
		tmp = x
	elif z <= 1.05e+171:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(Float64(-x) / t))
	t_2 = Float64(y / Float64(t / z))
	tmp = 0.0
	if (z <= -8.6e-38)
		tmp = t_2;
	elseif (z <= 4.9e-73)
		tmp = x;
	elseif (z <= 4.3e-6)
		tmp = t_1;
	elseif (z <= 8.1e+80)
		tmp = x;
	elseif (z <= 1.05e+171)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (-x / t);
	t_2 = y / (t / z);
	tmp = 0.0;
	if (z <= -8.6e-38)
		tmp = t_2;
	elseif (z <= 4.9e-73)
		tmp = x;
	elseif (z <= 4.3e-6)
		tmp = t_1;
	elseif (z <= 8.1e+80)
		tmp = x;
	elseif (z <= 1.05e+171)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[((-x) / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.6e-38], t$95$2, If[LessEqual[z, 4.9e-73], x, If[LessEqual[z, 4.3e-6], t$95$1, If[LessEqual[z, 8.1e+80], x, If[LessEqual[z, 1.05e+171], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.6000000000000004e-38 or 1.0500000000000001e171 < z

   1. Initial program 87.5%

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

      1. +-commutative 87.5%

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

      2. *-commutative 87.5%

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

      3. associate-*l/ 95.5%

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

      4. fma-def 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around 0 82.4%

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

   5. Taylor expanded in y around inf 56.7%

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

      1. associate-*r/ 64.7%

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

   7. Simplified 64.7%

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

      1. clear-num 64.6%

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

      2. un-div-inv 64.7%

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

   9. Applied egg-rr 64.7%

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

   if -8.6000000000000004e-38 < z < 4.90000000000000028e-73 or 4.30000000000000033e-6 < z < 8.10000000000000002e80

   1. Initial program 97.4%

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

      1. +-commutative 97.4%

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

      2. *-commutative 97.4%

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

      3. associate-*l/ 99.1%

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

      4. fma-def 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 68.9%

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

   if 4.90000000000000028e-73 < z < 4.30000000000000033e-6 or 8.10000000000000002e80 < z < 1.0500000000000001e171

   1. Initial program 91.2%

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

      1. +-commutative 91.2%

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

      2. *-commutative 91.2%

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

      3. associate-*l/ 89.1%

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

      4. fma-def 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in t around 0 78.6%

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

   5. Taylor expanded in y around 0 59.0%

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

      1. associate-*r/ 59.0%

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

      2. mul-1-neg 59.0%

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

      3. distribute-rgt-neg-out 59.0%

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

      4. associate-*l/ 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in z around 0 59.0%

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

      1. associate-*r/ 56.8%

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

      2. neg-mul-1 56.8%

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

      3. distribute-rgt-neg-in 56.8%

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

      4. distribute-neg-frac 56.8%

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

   10. Simplified 56.8%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{-38}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-6}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq 8.1 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+171}:\\ \;\;\;\;z \cdot \frac{-x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 4: 52.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{-z}{t}\\ t_2 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;z \leq -1.42 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+171}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z) t))) (t_2 (/ y (/ t z))))
   (if (<= z -1.42e-39)
     t_2
     (if (<= z 2.1e-118)
       x
       (if (<= z 5.5e-6)
         t_1
         (if (<= z 2.1e+80) x (if (<= z 6.5e+171) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (-z / t);
	double t_2 = y / (t / z);
	double tmp;
	if (z <= -1.42e-39) {
		tmp = t_2;
	} else if (z <= 2.1e-118) {
		tmp = x;
	} else if (z <= 5.5e-6) {
		tmp = t_1;
	} else if (z <= 2.1e+80) {
		tmp = x;
	} else if (z <= 6.5e+171) {
		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 = x * (-z / t)
    t_2 = y / (t / z)
    if (z <= (-1.42d-39)) then
        tmp = t_2
    else if (z <= 2.1d-118) then
        tmp = x
    else if (z <= 5.5d-6) then
        tmp = t_1
    else if (z <= 2.1d+80) then
        tmp = x
    else if (z <= 6.5d+171) 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 = x * (-z / t);
	double t_2 = y / (t / z);
	double tmp;
	if (z <= -1.42e-39) {
		tmp = t_2;
	} else if (z <= 2.1e-118) {
		tmp = x;
	} else if (z <= 5.5e-6) {
		tmp = t_1;
	} else if (z <= 2.1e+80) {
		tmp = x;
	} else if (z <= 6.5e+171) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (-z / t)
	t_2 = y / (t / z)
	tmp = 0
	if z <= -1.42e-39:
		tmp = t_2
	elif z <= 2.1e-118:
		tmp = x
	elif z <= 5.5e-6:
		tmp = t_1
	elif z <= 2.1e+80:
		tmp = x
	elif z <= 6.5e+171:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(-z) / t))
	t_2 = Float64(y / Float64(t / z))
	tmp = 0.0
	if (z <= -1.42e-39)
		tmp = t_2;
	elseif (z <= 2.1e-118)
		tmp = x;
	elseif (z <= 5.5e-6)
		tmp = t_1;
	elseif (z <= 2.1e+80)
		tmp = x;
	elseif (z <= 6.5e+171)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (-z / t);
	t_2 = y / (t / z);
	tmp = 0.0;
	if (z <= -1.42e-39)
		tmp = t_2;
	elseif (z <= 2.1e-118)
		tmp = x;
	elseif (z <= 5.5e-6)
		tmp = t_1;
	elseif (z <= 2.1e+80)
		tmp = x;
	elseif (z <= 6.5e+171)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.42e-39], t$95$2, If[LessEqual[z, 2.1e-118], x, If[LessEqual[z, 5.5e-6], t$95$1, If[LessEqual[z, 2.1e+80], x, If[LessEqual[z, 6.5e+171], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.42000000000000005e-39 or 6.5e171 < z

   1. Initial program 87.5%

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

      1. +-commutative 87.5%

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

      2. *-commutative 87.5%

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

      3. associate-*l/ 95.5%

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

      4. fma-def 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around 0 82.4%

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

   5. Taylor expanded in y around inf 56.7%

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

      1. associate-*r/ 64.7%

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

   7. Simplified 64.7%

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

      1. clear-num 64.6%

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

      2. un-div-inv 64.7%

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

   9. Applied egg-rr 64.7%

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

   if -1.42000000000000005e-39 < z < 2.1e-118 or 5.4999999999999999e-6 < z < 2.10000000000000001e80

   1. Initial program 97.1%

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

      1. +-commutative 97.1%

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

      2. *-commutative 97.1%

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

      3. associate-*l/ 99.0%

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

      4. fma-def 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in z around 0 72.3%

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

   if 2.1e-118 < z < 5.4999999999999999e-6 or 2.10000000000000001e80 < z < 6.5e171

   1. Initial program 93.1%

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

      1. +-commutative 93.1%

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

      2. *-commutative 93.1%

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

      3. associate-*l/ 91.5%

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

      4. fma-def 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in t around 0 76.5%

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

   5. Taylor expanded in y around 0 54.7%

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

      1. associate-*r/ 54.7%

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

      2. mul-1-neg 54.7%

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

      3. distribute-rgt-neg-out 54.7%

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

      4. associate-*l/ 55.2%

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

   7. Simplified 55.2%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{-39}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 5: 51.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.76 \cdot 10^{-6}:\\ \;\;\;\;\frac{x \cdot z}{-t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (/ t z))))
   (if (<= z -1.15e-37)
     t_1
     (if (<= z 2.8e-119)
       x
       (if (<= z 1.76e-6)
         (/ (* x z) (- t))
         (if (<= z 1.6e+79) x (if (<= z 1.2e+171) (* x (/ (- z) t)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (t / z);
	double tmp;
	if (z <= -1.15e-37) {
		tmp = t_1;
	} else if (z <= 2.8e-119) {
		tmp = x;
	} else if (z <= 1.76e-6) {
		tmp = (x * z) / -t;
	} else if (z <= 1.6e+79) {
		tmp = x;
	} else if (z <= 1.2e+171) {
		tmp = x * (-z / 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 = y / (t / z)
    if (z <= (-1.15d-37)) then
        tmp = t_1
    else if (z <= 2.8d-119) then
        tmp = x
    else if (z <= 1.76d-6) then
        tmp = (x * z) / -t
    else if (z <= 1.6d+79) then
        tmp = x
    else if (z <= 1.2d+171) then
        tmp = x * (-z / 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 = y / (t / z);
	double tmp;
	if (z <= -1.15e-37) {
		tmp = t_1;
	} else if (z <= 2.8e-119) {
		tmp = x;
	} else if (z <= 1.76e-6) {
		tmp = (x * z) / -t;
	} else if (z <= 1.6e+79) {
		tmp = x;
	} else if (z <= 1.2e+171) {
		tmp = x * (-z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (t / z)
	tmp = 0
	if z <= -1.15e-37:
		tmp = t_1
	elif z <= 2.8e-119:
		tmp = x
	elif z <= 1.76e-6:
		tmp = (x * z) / -t
	elif z <= 1.6e+79:
		tmp = x
	elif z <= 1.2e+171:
		tmp = x * (-z / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(t / z))
	tmp = 0.0
	if (z <= -1.15e-37)
		tmp = t_1;
	elseif (z <= 2.8e-119)
		tmp = x;
	elseif (z <= 1.76e-6)
		tmp = Float64(Float64(x * z) / Float64(-t));
	elseif (z <= 1.6e+79)
		tmp = x;
	elseif (z <= 1.2e+171)
		tmp = Float64(x * Float64(Float64(-z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (t / z);
	tmp = 0.0;
	if (z <= -1.15e-37)
		tmp = t_1;
	elseif (z <= 2.8e-119)
		tmp = x;
	elseif (z <= 1.76e-6)
		tmp = (x * z) / -t;
	elseif (z <= 1.6e+79)
		tmp = x;
	elseif (z <= 1.2e+171)
		tmp = x * (-z / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e-37], t$95$1, If[LessEqual[z, 2.8e-119], x, If[LessEqual[z, 1.76e-6], N[(N[(x * z), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[z, 1.6e+79], x, If[LessEqual[z, 1.2e+171], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.15e-37 or 1.19999999999999999e171 < z

   1. Initial program 87.5%

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

      1. +-commutative 87.5%

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

      2. *-commutative 87.5%

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

      3. associate-*l/ 95.5%

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

      4. fma-def 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around 0 82.4%

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

   5. Taylor expanded in y around inf 56.7%

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

      1. associate-*r/ 64.7%

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

   7. Simplified 64.7%

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

      1. clear-num 64.6%

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

      2. un-div-inv 64.7%

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

   9. Applied egg-rr 64.7%

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

   if -1.15e-37 < z < 2.8e-119 or 1.7600000000000001e-6 < z < 1.60000000000000001e79

   1. Initial program 97.1%

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

      1. +-commutative 97.1%

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

      2. *-commutative 97.1%

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

      3. associate-*l/ 99.0%

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

      4. fma-def 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in z around 0 72.3%

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

   if 2.8e-119 < z < 1.7600000000000001e-6

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*l/ 99.7%

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

      4. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around 0 73.1%

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

   5. Taylor expanded in y around 0 53.1%

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

      1. associate-*r/ 53.1%

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

      2. mul-1-neg 53.1%

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

      3. distribute-rgt-neg-out 53.1%

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

      4. associate-*l/ 53.1%

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

   7. Simplified 53.1%

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

      1. associate-*l/ 53.1%

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

      2. frac-2neg 53.1%

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

      3. add-sqr-sqrt 19.7%

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

      4. sqrt-unprod 13.9%

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

      5. sqr-neg 13.9%

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

      6. sqrt-unprod 1.0%

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

      7. add-sqr-sqrt 1.7%

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

      8. distribute-rgt-neg-out 1.7%

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

      9. add-sqr-sqrt 0.7%

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

      10. sqrt-unprod 26.5%

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

      11. sqr-neg 26.5%

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

      12. sqrt-unprod 33.4%

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

      13. add-sqr-sqrt 53.1%

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

   9. Applied egg-rr 53.1%

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

   if 1.60000000000000001e79 < z < 1.19999999999999999e171

   1. Initial program 85.2%

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

      1. +-commutative 85.2%

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

      2. *-commutative 85.2%

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

      3. associate-*l/ 81.8%

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

      4. fma-def 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in t around 0 80.5%

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

   5. Taylor expanded in y around 0 56.7%

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

      1. associate-*r/ 56.7%

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

      2. mul-1-neg 56.7%

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

      3. distribute-rgt-neg-out 56.7%

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

      4. associate-*l/ 57.6%

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

   7. Simplified 57.6%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-37}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.76 \cdot 10^{-6}:\\ \;\;\;\;\frac{x \cdot z}{-t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 6: 70.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-90} \lor \neg \left(z \leq 1.55 \cdot 10^{-120}\right) \land \left(z \leq 0.07 \lor \neg \left(z \leq 5.4 \cdot 10^{+76}\right)\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.8e-90)
         (and (not (<= z 1.55e-120)) (or (<= z 0.07) (not (<= z 5.4e+76)))))
   (* z (/ (- y x) t))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e-90) || (!(z <= 1.55e-120) && ((z <= 0.07) || !(z <= 5.4e+76)))) {
		tmp = z * ((y - x) / 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 <= (-2.8d-90)) .or. (.not. (z <= 1.55d-120)) .and. (z <= 0.07d0) .or. (.not. (z <= 5.4d+76))) then
        tmp = z * ((y - x) / 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 <= -2.8e-90) || (!(z <= 1.55e-120) && ((z <= 0.07) || !(z <= 5.4e+76)))) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.8e-90) or (not (z <= 1.55e-120) and ((z <= 0.07) or not (z <= 5.4e+76))):
		tmp = z * ((y - x) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.8e-90) || (!(z <= 1.55e-120) && ((z <= 0.07) || !(z <= 5.4e+76))))
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.8e-90) || (~((z <= 1.55e-120)) && ((z <= 0.07) || ~((z <= 5.4e+76)))))
		tmp = z * ((y - x) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.8e-90], And[N[Not[LessEqual[z, 1.55e-120]], $MachinePrecision], Or[LessEqual[z, 0.07], N[Not[LessEqual[z, 5.4e+76]], $MachinePrecision]]]], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.7999999999999999e-90 or 1.5500000000000001e-120 < z < 0.070000000000000007 or 5.3999999999999998e76 < z

   1. Initial program 89.7%

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

      1. +-commutative 89.7%

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

      2. *-commutative 89.7%

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

      3. associate-*l/ 94.6%

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

      4. fma-def 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in t around 0 79.8%

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

      1. associate-*l/ 83.6%

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

   6. Applied egg-rr 83.6%

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

   if -2.7999999999999999e-90 < z < 1.5500000000000001e-120 or 0.070000000000000007 < z < 5.3999999999999998e76

   1. Initial program 96.9%

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

      1. +-commutative 96.9%

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

      2. *-commutative 96.9%

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

      3. associate-*l/ 99.0%

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

      4. fma-def 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in z around 0 75.1%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-90} \lor \neg \left(z \leq 1.55 \cdot 10^{-120}\right) \land \left(z \leq 0.07 \lor \neg \left(z \leq 5.4 \cdot 10^{+76}\right)\right):\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 83.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y - x}{t}\\ \mathbf{if}\;z \leq -4 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-9}:\\ \;\;\;\;x - z \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+77}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ (- y x) t))))
   (if (<= z -4e-14)
     t_1
     (if (<= z 4.9e-80)
       (+ x (/ y (/ t z)))
       (if (<= z 3.1e-9)
         (- x (* z (/ x t)))
         (if (<= z 1.02e+77) (+ x (* y (/ z t))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * ((y - x) / t);
	double tmp;
	if (z <= -4e-14) {
		tmp = t_1;
	} else if (z <= 4.9e-80) {
		tmp = x + (y / (t / z));
	} else if (z <= 3.1e-9) {
		tmp = x - (z * (x / t));
	} else if (z <= 1.02e+77) {
		tmp = x + (y * (z / 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 - x) / t)
    if (z <= (-4d-14)) then
        tmp = t_1
    else if (z <= 4.9d-80) then
        tmp = x + (y / (t / z))
    else if (z <= 3.1d-9) then
        tmp = x - (z * (x / t))
    else if (z <= 1.02d+77) then
        tmp = x + (y * (z / 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 - x) / t);
	double tmp;
	if (z <= -4e-14) {
		tmp = t_1;
	} else if (z <= 4.9e-80) {
		tmp = x + (y / (t / z));
	} else if (z <= 3.1e-9) {
		tmp = x - (z * (x / t));
	} else if (z <= 1.02e+77) {
		tmp = x + (y * (z / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * ((y - x) / t)
	tmp = 0
	if z <= -4e-14:
		tmp = t_1
	elif z <= 4.9e-80:
		tmp = x + (y / (t / z))
	elif z <= 3.1e-9:
		tmp = x - (z * (x / t))
	elif z <= 1.02e+77:
		tmp = x + (y * (z / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(Float64(y - x) / t))
	tmp = 0.0
	if (z <= -4e-14)
		tmp = t_1;
	elseif (z <= 4.9e-80)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (z <= 3.1e-9)
		tmp = Float64(x - Float64(z * Float64(x / t)));
	elseif (z <= 1.02e+77)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * ((y - x) / t);
	tmp = 0.0;
	if (z <= -4e-14)
		tmp = t_1;
	elseif (z <= 4.9e-80)
		tmp = x + (y / (t / z));
	elseif (z <= 3.1e-9)
		tmp = x - (z * (x / t));
	elseif (z <= 1.02e+77)
		tmp = x + (y * (z / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e-14], t$95$1, If[LessEqual[z, 4.9e-80], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e-9], N[(x - N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+77], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4e-14 or 1.02e77 < z

   1. Initial program 86.5%

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

      1. +-commutative 86.5%

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

      2. *-commutative 86.5%

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

      3. associate-*l/ 93.0%

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

      4. fma-def 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in t around 0 82.0%

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

      1. associate-*l/ 90.5%

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

   6. Applied egg-rr 90.5%

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

   if -4e-14 < z < 4.8999999999999999e-80

   1. Initial program 98.8%

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

   2. Taylor expanded in y around inf 88.3%

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

      1. associate-*r/ 24.3%

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

   4. Simplified 87.4%

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

      1. clear-num 24.3%

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

      2. un-div-inv 24.4%

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

   6. Applied egg-rr 87.4%

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

   if 4.8999999999999999e-80 < z < 3.10000000000000005e-9

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*l/ 99.7%

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

      4. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 93.0%

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

      1. fma-def 93.0%

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

      2. *-commutative 93.0%

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

      3. associate-*r/ 92.7%

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

      4. fma-def 92.7%

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

      5. neg-mul-1 92.7%

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

      6. +-commutative 92.7%

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

      7. unsub-neg 92.7%

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

      8. *-commutative 92.7%

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

      9. associate-/r/ 87.5%

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

   6. Simplified 87.5%

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

      1. clear-num 87.3%

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

      2. associate-/r/ 87.3%

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

      3. clear-num 87.3%

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

   8. Applied egg-rr 87.3%

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

   if 3.10000000000000005e-9 < z < 1.02e77

   1. Initial program 91.7%

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

   2. Taylor expanded in y around inf 91.0%

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

      1. associate-*r/ 32.1%

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

   4. Simplified 91.1%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-80}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-9}:\\ \;\;\;\;x - z \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+77}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 8: 82.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-116} \lor \neg \left(x \leq 1.55 \cdot 10^{-27}\right):\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \frac{1}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.6e-116) (not (<= x 1.55e-27)))
   (- x (* x (/ z t)))
   (+ x (* (* y z) (/ 1.0 t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.6e-116) || !(x <= 1.55e-27)) {
		tmp = x - (x * (z / t));
	} else {
		tmp = x + ((y * z) * (1.0 / 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 <= (-7.6d-116)) .or. (.not. (x <= 1.55d-27))) then
        tmp = x - (x * (z / t))
    else
        tmp = x + ((y * z) * (1.0d0 / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.6e-116) || !(x <= 1.55e-27)) {
		tmp = x - (x * (z / t));
	} else {
		tmp = x + ((y * z) * (1.0 / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.6e-116) or not (x <= 1.55e-27):
		tmp = x - (x * (z / t))
	else:
		tmp = x + ((y * z) * (1.0 / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.6e-116) || !(x <= 1.55e-27))
		tmp = Float64(x - Float64(x * Float64(z / t)));
	else
		tmp = Float64(x + Float64(Float64(y * z) * Float64(1.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.6e-116) || ~((x <= 1.55e-27)))
		tmp = x - (x * (z / t));
	else
		tmp = x + ((y * z) * (1.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.6e-116], N[Not[LessEqual[x, 1.55e-27]], $MachinePrecision]], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.6000000000000003e-116 or 1.5499999999999999e-27 < x

   1. Initial program 90.9%

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

   2. Taylor expanded in y around 0 84.9%

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

      1. associate-*r/ 42.9%

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

      2. mul-1-neg 42.9%

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

      3. distribute-rgt-neg-out 42.9%

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

      4. associate-*l/ 44.8%

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

   4. Simplified 90.7%

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

   if -7.6000000000000003e-116 < x < 1.5499999999999999e-27

   1. Initial program 94.5%

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

   2. Taylor expanded in y around inf 87.0%

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

      1. associate-*r/ 65.2%

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

   4. Simplified 85.5%

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

      1. clear-num 65.1%

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

      2. un-div-inv 65.5%

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

   6. Applied egg-rr 85.8%

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

      1. div-inv 85.5%

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

      2. clear-num 85.5%

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

      3. div-inv 85.5%

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

      4. associate-*r* 87.0%

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

   8. Applied egg-rr 87.0%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-116} \lor \neg \left(x \leq 1.55 \cdot 10^{-27}\right):\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot z\right) \cdot \frac{1}{t}\\ \end{array} \]

Alternative 9: 79.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+57} \lor \neg \left(t \leq 8 \cdot 10^{+36}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.4e+57) (not (<= t 8e+36)))
   (+ x (* y (/ z t)))
   (* z (/ (- y x) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.4e+57) || !(t <= 8e+36)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y - 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 ((t <= (-1.4d+57)) .or. (.not. (t <= 8d+36))) then
        tmp = x + (y * (z / t))
    else
        tmp = z * ((y - x) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.4e+57) || !(t <= 8e+36)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = z * ((y - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.4e+57) or not (t <= 8e+36):
		tmp = x + (y * (z / t))
	else:
		tmp = z * ((y - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.4e+57) || !(t <= 8e+36))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(z * Float64(Float64(y - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.4e+57) || ~((t <= 8e+36)))
		tmp = x + (y * (z / t));
	else
		tmp = z * ((y - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.4e+57], N[Not[LessEqual[t, 8e+36]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4e57 or 8.00000000000000034e36 < t

   1. Initial program 83.5%

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

   2. Taylor expanded in y around inf 82.6%

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

      1. associate-*r/ 28.5%

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

   4. Simplified 92.6%

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

   if -1.4e57 < t < 8.00000000000000034e36

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. *-commutative 99.1%

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

      3. associate-*l/ 94.2%

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

      4. fma-def 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in t around 0 85.4%

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

      1. associate-*l/ 80.6%

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

   6. Applied egg-rr 80.6%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+57} \lor \neg \left(t \leq 8 \cdot 10^{+36}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \end{array} \]

Alternative 10: 82.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+57} \lor \neg \left(t \leq 5.8 \cdot 10^{+37}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.4e+57) (not (<= t 5.8e+37)))
   (+ x (* y (/ z t)))
   (/ (* (- y x) z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.4e+57) || !(t <= 5.8e+37)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = ((y - x) * 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 ((t <= (-1.4d+57)) .or. (.not. (t <= 5.8d+37))) then
        tmp = x + (y * (z / t))
    else
        tmp = ((y - x) * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.4e+57) || !(t <= 5.8e+37)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = ((y - x) * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.4e+57) or not (t <= 5.8e+37):
		tmp = x + (y * (z / t))
	else:
		tmp = ((y - x) * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.4e+57) || !(t <= 5.8e+37))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(Float64(Float64(y - x) * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.4e+57) || ~((t <= 5.8e+37)))
		tmp = x + (y * (z / t));
	else
		tmp = ((y - x) * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.4e+57], N[Not[LessEqual[t, 5.8e+37]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.4e57 or 5.79999999999999957e37 < t

   1. Initial program 83.4%

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

   2. Taylor expanded in y around inf 82.4%

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

      1. associate-*r/ 27.9%

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

   4. Simplified 92.5%

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

   if -1.4e57 < t < 5.79999999999999957e37

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. *-commutative 99.1%

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

      3. associate-*l/ 94.2%

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

      4. fma-def 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in t around 0 85.5%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+57} \lor \neg \left(t \leq 5.8 \cdot 10^{+37}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot z}{t}\\ \end{array} \]

Alternative 11: 83.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-116} \lor \neg \left(x \leq 1.05 \cdot 10^{-27}\right):\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.6e-116) (not (<= x 1.05e-27)))
   (- x (* x (/ z t)))
   (+ x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.6e-116) || !(x <= 1.05e-27)) {
		tmp = x - (x * (z / t));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-7.6d-116)) .or. (.not. (x <= 1.05d-27))) then
        tmp = x - (x * (z / t))
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.6e-116) || !(x <= 1.05e-27)) {
		tmp = x - (x * (z / t));
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.6e-116) or not (x <= 1.05e-27):
		tmp = x - (x * (z / t))
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.6e-116) || !(x <= 1.05e-27))
		tmp = Float64(x - Float64(x * Float64(z / t)));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.6e-116) || ~((x <= 1.05e-27)))
		tmp = x - (x * (z / t));
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.6e-116], N[Not[LessEqual[x, 1.05e-27]], $MachinePrecision]], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.6000000000000003e-116 or 1.05000000000000008e-27 < x

   1. Initial program 90.9%

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

   2. Taylor expanded in y around 0 84.9%

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

      1. associate-*r/ 42.9%

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

      2. mul-1-neg 42.9%

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

      3. distribute-rgt-neg-out 42.9%

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

      4. associate-*l/ 44.8%

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

   4. Simplified 90.7%

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

   if -7.6000000000000003e-116 < x < 1.05000000000000008e-27

   1. Initial program 94.5%

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

   2. Taylor expanded in y around inf 87.0%

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

      1. associate-*r/ 65.2%

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

   4. Simplified 85.5%

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

      1. clear-num 65.1%

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

      2. un-div-inv 65.5%

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

   6. Applied egg-rr 85.8%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-116} \lor \neg \left(x \leq 1.05 \cdot 10^{-27}\right):\\ \;\;\;\;x - x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 12: 79.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{+57}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.52e+57)
   (+ x (* y (/ z t)))
   (if (<= t 9.5e+36) (* z (/ (- y x) t)) (+ x (/ y (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.52e+57) {
		tmp = x + (y * (z / t));
	} else if (t <= 9.5e+36) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.52d+57)) then
        tmp = x + (y * (z / t))
    else if (t <= 9.5d+36) then
        tmp = z * ((y - x) / t)
    else
        tmp = x + (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.52e+57) {
		tmp = x + (y * (z / t));
	} else if (t <= 9.5e+36) {
		tmp = z * ((y - x) / t);
	} else {
		tmp = x + (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.52e+57:
		tmp = x + (y * (z / t))
	elif t <= 9.5e+36:
		tmp = z * ((y - x) / t)
	else:
		tmp = x + (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.52e+57)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (t <= 9.5e+36)
		tmp = Float64(z * Float64(Float64(y - x) / t));
	else
		tmp = Float64(x + Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.52e+57)
		tmp = x + (y * (z / t));
	elseif (t <= 9.5e+36)
		tmp = z * ((y - x) / t);
	else
		tmp = x + (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.52e+57], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+36], N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.51999999999999998e57

   1. Initial program 83.6%

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

   2. Taylor expanded in y around inf 81.9%

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

      1. associate-*r/ 24.6%

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

   4. Simplified 93.0%

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

   if -1.51999999999999998e57 < t < 9.49999999999999974e36

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. *-commutative 99.1%

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

      3. associate-*l/ 94.2%

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

      4. fma-def 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in t around 0 85.4%

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

      1. associate-*l/ 80.6%

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

   6. Applied egg-rr 80.6%

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

   if 9.49999999999999974e36 < t

   1. Initial program 83.5%

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

   2. Taylor expanded in y around inf 83.3%

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

      1. associate-*r/ 33.0%

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

   4. Simplified 92.0%

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

      1. clear-num 32.9%

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

      2. un-div-inv 33.0%

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

   6. Applied egg-rr 92.0%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{+57}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 13: 80.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-116}:\\ \;\;\;\;x - z \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7.6e-116)
   (- x (* z (/ x t)))
   (if (<= x 2.8e-27) (+ x (/ y (/ t z))) (- x (/ z (/ t x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.6e-116) {
		tmp = x - (z * (x / t));
	} else if (x <= 2.8e-27) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (z / (t / 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 (x <= (-7.6d-116)) then
        tmp = x - (z * (x / t))
    else if (x <= 2.8d-27) then
        tmp = x + (y / (t / z))
    else
        tmp = x - (z / (t / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.6e-116) {
		tmp = x - (z * (x / t));
	} else if (x <= 2.8e-27) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x - (z / (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7.6e-116:
		tmp = x - (z * (x / t))
	elif x <= 2.8e-27:
		tmp = x + (y / (t / z))
	else:
		tmp = x - (z / (t / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7.6e-116)
		tmp = Float64(x - Float64(z * Float64(x / t)));
	elseif (x <= 2.8e-27)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(x - Float64(z / Float64(t / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7.6e-116)
		tmp = x - (z * (x / t));
	elseif (x <= 2.8e-27)
		tmp = x + (y / (t / z));
	else
		tmp = x - (z / (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7.6e-116], N[(x - N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e-27], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.6000000000000003e-116

   1. Initial program 88.4%

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

      1. +-commutative 88.4%

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

      2. *-commutative 88.4%

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

      3. associate-*l/ 99.9%

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

      4. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 81.8%

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

      1. fma-def 81.8%

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

      2. *-commutative 81.8%

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

      3. associate-*r/ 88.2%

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

      4. fma-def 88.2%

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

      5. neg-mul-1 88.2%

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

      6. +-commutative 88.2%

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

      7. unsub-neg 88.2%

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

      8. *-commutative 88.2%

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

      9. associate-/r/ 83.7%

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

   6. Simplified 83.7%

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

      1. clear-num 83.7%

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

      2. associate-/r/ 83.7%

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

      3. clear-num 83.7%

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

   8. Applied egg-rr 83.7%

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

   if -7.6000000000000003e-116 < x < 2.8e-27

   1. Initial program 94.5%

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

   2. Taylor expanded in y around inf 87.0%

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

      1. associate-*r/ 65.2%

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

   4. Simplified 85.5%

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

      1. clear-num 65.1%

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

      2. un-div-inv 65.5%

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

   6. Applied egg-rr 85.8%

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

   if 2.8e-27 < x

   1. Initial program 93.4%

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

      1. +-commutative 93.4%

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

      2. *-commutative 93.4%

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

      3. associate-*l/ 100.0%

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

      4. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 88.1%

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

      1. fma-def 88.1%

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

      2. *-commutative 88.1%

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

      3. associate-*r/ 93.3%

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

      4. fma-def 93.3%

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

      5. neg-mul-1 93.3%

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

      6. +-commutative 93.3%

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

      7. unsub-neg 93.3%

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

      8. *-commutative 93.3%

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

      9. associate-/r/ 89.3%

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

   6. Simplified 89.3%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-116}:\\ \;\;\;\;x - z \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{t}{x}}\\ \end{array} \]

Alternative 14: 53.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-39} \lor \neg \left(z \leq 1.35 \cdot 10^{+141}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8e-39) (not (<= z 1.35e+141))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8e-39) || !(z <= 1.35e+141)) {
		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 ((z <= (-8d-39)) .or. (.not. (z <= 1.35d+141))) 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 ((z <= -8e-39) || !(z <= 1.35e+141)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8e-39) or not (z <= 1.35e+141):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8e-39) || !(z <= 1.35e+141))
		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 ((z <= -8e-39) || ~((z <= 1.35e+141)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8e-39], N[Not[LessEqual[z, 1.35e+141]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.99999999999999943e-39 or 1.35e141 < z

   1. Initial program 87.2%

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

      1. +-commutative 87.2%

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

      2. *-commutative 87.2%

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

      3. associate-*l/ 94.1%

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

      4. fma-def 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in t around 0 82.4%

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

   5. Taylor expanded in y around inf 56.4%

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

      1. associate-*r/ 62.4%

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

   7. Simplified 62.4%

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

   if -7.99999999999999943e-39 < z < 1.35e141

   1. Initial program 96.5%

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

      1. +-commutative 96.5%

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

      2. *-commutative 96.5%

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

      3. associate-*l/ 97.9%

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

      4. fma-def 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in z around 0 59.3%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-39} \lor \neg \left(z \leq 1.35 \cdot 10^{+141}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 54.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.5e-39) (* y (/ z t)) (if (<= z 5.4e+76) x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.5e-39) {
		tmp = y * (z / t);
	} else if (z <= 5.4e+76) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-3.5d-39)) then
        tmp = y * (z / t)
    else if (z <= 5.4d+76) then
        tmp = x
    else
        tmp = 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 (z <= -3.5e-39) {
		tmp = y * (z / t);
	} else if (z <= 5.4e+76) {
		tmp = x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.5e-39:
		tmp = y * (z / t)
	elif z <= 5.4e+76:
		tmp = x
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.5e-39)
		tmp = Float64(y * Float64(z / t));
	elseif (z <= 5.4e+76)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.5e-39)
		tmp = y * (z / t);
	elseif (z <= 5.4e+76)
		tmp = x;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.5e-39], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+76], x, N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5e-39

   1. Initial program 91.8%

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

      1. +-commutative 91.8%

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

      2. *-commutative 91.8%

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

      3. associate-*l/ 95.9%

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

      4. fma-def 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in t around 0 85.4%

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

   5. Taylor expanded in y around inf 57.7%

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

      1. associate-*r/ 61.8%

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

   7. Simplified 61.8%

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

   if -3.5e-39 < z < 5.3999999999999998e76

   1. Initial program 97.6%

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

      1. +-commutative 97.6%

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

      2. *-commutative 97.6%

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

      3. associate-*l/ 99.1%

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

      4. fma-def 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 64.0%

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

   if 5.3999999999999998e76 < z

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. *-commutative 81.2%

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

      3. associate-*l/ 90.0%

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

      4. fma-def 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in t around 0 77.9%

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

   5. Taylor expanded in y around inf 44.8%

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

      1. associate-*r/ 49.9%

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

   7. Simplified 49.9%

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

      1. clear-num 49.9%

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

      2. un-div-inv 50.6%

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

   9. Applied egg-rr 50.6%

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

       1. associate-/r/ 53.2%

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

   11. Applied egg-rr 53.2%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 16: 54.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-38}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.8e-38) (/ y (/ t z)) (if (<= z 5.4e+76) x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.8e-38) {
		tmp = y / (t / z);
	} else if (z <= 5.4e+76) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-6.8d-38)) then
        tmp = y / (t / z)
    else if (z <= 5.4d+76) then
        tmp = x
    else
        tmp = 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 (z <= -6.8e-38) {
		tmp = y / (t / z);
	} else if (z <= 5.4e+76) {
		tmp = x;
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.8e-38:
		tmp = y / (t / z)
	elif z <= 5.4e+76:
		tmp = x
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.8e-38)
		tmp = Float64(y / Float64(t / z));
	elseif (z <= 5.4e+76)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.8e-38)
		tmp = y / (t / z);
	elseif (z <= 5.4e+76)
		tmp = x;
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.8e-38], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+76], x, N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8000000000000004e-38

   1. Initial program 91.8%

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

      1. +-commutative 91.8%

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

      2. *-commutative 91.8%

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

      3. associate-*l/ 95.9%

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

      4. fma-def 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in t around 0 85.4%

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

   5. Taylor expanded in y around inf 57.7%

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

      1. associate-*r/ 61.8%

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

   7. Simplified 61.8%

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

      1. clear-num 61.7%

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

      2. un-div-inv 61.8%

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

   9. Applied egg-rr 61.8%

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

   if -6.8000000000000004e-38 < z < 5.3999999999999998e76

   1. Initial program 97.6%

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

      1. +-commutative 97.6%

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

      2. *-commutative 97.6%

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

      3. associate-*l/ 99.1%

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

      4. fma-def 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 64.0%

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

   if 5.3999999999999998e76 < z

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. *-commutative 81.2%

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

      3. associate-*l/ 90.0%

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

      4. fma-def 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in t around 0 77.9%

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

   5. Taylor expanded in y around inf 44.8%

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

      1. associate-*r/ 49.9%

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

   7. Simplified 49.9%

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

      1. clear-num 49.9%

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

      2. un-div-inv 50.6%

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

   9. Applied egg-rr 50.6%

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

       1. associate-/r/ 53.2%

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

   11. Applied egg-rr 53.2%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-38}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 17: 93.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.4%

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

   1. associate-*l/ 60.9%

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

3. Applied egg-rr 95.6%

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

4. Final simplification 95.6%

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

Alternative 18: 38.5% 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%

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

   1. +-commutative 92.4%

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

   2. *-commutative 92.4%

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

   3. associate-*l/ 96.3%

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

   4. fma-def 96.3%

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

3. Simplified 96.3%

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

4. Taylor expanded in z around 0 37.6%

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

5. Final simplification 37.6%

   \[\leadsto x \]

Developer target: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x < -9.025511195533005 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x < 4.275032163700715 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (< x -9.025511195533005e-135)
   (- x (* (/ z t) (- x y)))
   (if (< x 4.275032163700715e-250)
     (+ x (* (/ (- y x) t) z))
     (+ x (/ (- y x) (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x < (-9.025511195533005d-135)) then
        tmp = x - ((z / t) * (x - y))
    else if (x < 4.275032163700715d-250) then
        tmp = x + (((y - x) / t) * z)
    else
        tmp = x + ((y - x) / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x < -9.025511195533005e-135) {
		tmp = x - ((z / t) * (x - y));
	} else if (x < 4.275032163700715e-250) {
		tmp = x + (((y - x) / t) * z);
	} else {
		tmp = x + ((y - x) / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x < -9.025511195533005e-135:
		tmp = x - ((z / t) * (x - y))
	elif x < 4.275032163700715e-250:
		tmp = x + (((y - x) / t) * z)
	else:
		tmp = x + ((y - x) / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x < -9.025511195533005e-135)
		tmp = Float64(x - Float64(Float64(z / t) * Float64(x - y)));
	elseif (x < 4.275032163700715e-250)
		tmp = Float64(x + Float64(Float64(Float64(y - x) / t) * z));
	else
		tmp = Float64(x + Float64(Float64(y - x) / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x < -9.025511195533005e-135)
		tmp = x - ((z / t) * (x - y));
	elseif (x < 4.275032163700715e-250)
		tmp = x + (((y - x) / t) * z);
	else
		tmp = x + ((y - x) / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Less[x, -9.025511195533005e-135], N[(x - N[(N[(z / t), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[x, 4.275032163700715e-250], N[(x + N[(N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023192 
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< x -9.025511195533005e-135) (- x (* (/ z t) (- x y))) (if (< x 4.275032163700715e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

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