Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.7s

Alternatives: 14

Speedup: 1.0×

• 33.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - z, t - x, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 67.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := z \cdot \left(x - t\right)\\ t_3 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y \leq -4.05 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{-58}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-106}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-56}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-6}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+106}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* z (- x t))) (t_3 (* (- y z) t)))
   (if (<= y -4.05e+34)
     t_1
     (if (<= y -1.42e-58)
       t_3
       (if (<= y -1.05e-106)
         (+ x (* z x))
         (if (<= y 1.16e-104)
           t_2
           (if (<= y 5.9e-56)
             (- x (* z t))
             (if (<= y 1.95e-26)
               t_2
               (if (<= y 4.2e-6)
                 (+ x (* y t))
                 (if (<= y 4.7e+71) t_2 (if (<= y 1.25e+106) t_3 t_1)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double t_3 = (y - z) * t;
	double tmp;
	if (y <= -4.05e+34) {
		tmp = t_1;
	} else if (y <= -1.42e-58) {
		tmp = t_3;
	} else if (y <= -1.05e-106) {
		tmp = x + (z * x);
	} else if (y <= 1.16e-104) {
		tmp = t_2;
	} else if (y <= 5.9e-56) {
		tmp = x - (z * t);
	} else if (y <= 1.95e-26) {
		tmp = t_2;
	} else if (y <= 4.2e-6) {
		tmp = x + (y * t);
	} else if (y <= 4.7e+71) {
		tmp = t_2;
	} else if (y <= 1.25e+106) {
		tmp = t_3;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = z * (x - t)
    t_3 = (y - z) * t
    if (y <= (-4.05d+34)) then
        tmp = t_1
    else if (y <= (-1.42d-58)) then
        tmp = t_3
    else if (y <= (-1.05d-106)) then
        tmp = x + (z * x)
    else if (y <= 1.16d-104) then
        tmp = t_2
    else if (y <= 5.9d-56) then
        tmp = x - (z * t)
    else if (y <= 1.95d-26) then
        tmp = t_2
    else if (y <= 4.2d-6) then
        tmp = x + (y * t)
    else if (y <= 4.7d+71) then
        tmp = t_2
    else if (y <= 1.25d+106) then
        tmp = t_3
    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 - x);
	double t_2 = z * (x - t);
	double t_3 = (y - z) * t;
	double tmp;
	if (y <= -4.05e+34) {
		tmp = t_1;
	} else if (y <= -1.42e-58) {
		tmp = t_3;
	} else if (y <= -1.05e-106) {
		tmp = x + (z * x);
	} else if (y <= 1.16e-104) {
		tmp = t_2;
	} else if (y <= 5.9e-56) {
		tmp = x - (z * t);
	} else if (y <= 1.95e-26) {
		tmp = t_2;
	} else if (y <= 4.2e-6) {
		tmp = x + (y * t);
	} else if (y <= 4.7e+71) {
		tmp = t_2;
	} else if (y <= 1.25e+106) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = z * (x - t)
	t_3 = (y - z) * t
	tmp = 0
	if y <= -4.05e+34:
		tmp = t_1
	elif y <= -1.42e-58:
		tmp = t_3
	elif y <= -1.05e-106:
		tmp = x + (z * x)
	elif y <= 1.16e-104:
		tmp = t_2
	elif y <= 5.9e-56:
		tmp = x - (z * t)
	elif y <= 1.95e-26:
		tmp = t_2
	elif y <= 4.2e-6:
		tmp = x + (y * t)
	elif y <= 4.7e+71:
		tmp = t_2
	elif y <= 1.25e+106:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(z * Float64(x - t))
	t_3 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (y <= -4.05e+34)
		tmp = t_1;
	elseif (y <= -1.42e-58)
		tmp = t_3;
	elseif (y <= -1.05e-106)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= 1.16e-104)
		tmp = t_2;
	elseif (y <= 5.9e-56)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 1.95e-26)
		tmp = t_2;
	elseif (y <= 4.2e-6)
		tmp = Float64(x + Float64(y * t));
	elseif (y <= 4.7e+71)
		tmp = t_2;
	elseif (y <= 1.25e+106)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = z * (x - t);
	t_3 = (y - z) * t;
	tmp = 0.0;
	if (y <= -4.05e+34)
		tmp = t_1;
	elseif (y <= -1.42e-58)
		tmp = t_3;
	elseif (y <= -1.05e-106)
		tmp = x + (z * x);
	elseif (y <= 1.16e-104)
		tmp = t_2;
	elseif (y <= 5.9e-56)
		tmp = x - (z * t);
	elseif (y <= 1.95e-26)
		tmp = t_2;
	elseif (y <= 4.2e-6)
		tmp = x + (y * t);
	elseif (y <= 4.7e+71)
		tmp = t_2;
	elseif (y <= 1.25e+106)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -4.05e+34], t$95$1, If[LessEqual[y, -1.42e-58], t$95$3, If[LessEqual[y, -1.05e-106], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.16e-104], t$95$2, If[LessEqual[y, 5.9e-56], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e-26], t$95$2, If[LessEqual[y, 4.2e-6], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e+71], t$95$2, If[LessEqual[y, 1.25e+106], t$95$3, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -4.05e34 or 1.25e106 < y

   1. Initial program 100.0%

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

      1. flip-- 89.5%

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

      2. associate-*r/ 85.3%

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

      3. cancel-sign-sub-inv 85.3%

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

      4. fma-def 87.1%

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

   3. Applied egg-rr 87.1%

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

      1. associate-/l* 91.2%

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

      2. distribute-lft-neg-out 91.2%

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

   5. Simplified 91.2%

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

   6. Taylor expanded in t around inf 95.4%

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

   7. Taylor expanded in y around inf 85.7%

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

   if -4.05e34 < y < -1.4199999999999999e-58 or 4.6999999999999996e71 < y < 1.25e106

   1. Initial program 99.9%

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

      1. flip-- 73.5%

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

      2. associate-*r/ 69.6%

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

      3. cancel-sign-sub-inv 69.6%

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

      4. fma-def 69.6%

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

   3. Applied egg-rr 69.6%

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

      1. associate-/l* 73.4%

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

      2. distribute-lft-neg-out 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in t around inf 91.9%

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

   7. Taylor expanded in t around inf 69.0%

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

      1. *-commutative 69.0%

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

   9. Simplified 69.0%

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

   if -1.4199999999999999e-58 < y < -1.05000000000000002e-106

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 83.9%

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

      1. *-commutative 83.9%

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

      2. mul-1-neg 83.9%

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

      3. unsub-neg 83.9%

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

      4. distribute-lft-out-- 83.9%

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

      5. *-rgt-identity 83.9%

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

   4. Simplified 83.9%

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

   5. Taylor expanded in y around 0 83.9%

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

      1. associate-*r* 83.9%

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

      2. neg-mul-1 83.9%

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

   7. Simplified 83.9%

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

   8. Taylor expanded in z around 0 83.9%

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

   if -1.05000000000000002e-106 < y < 1.16000000000000001e-104 or 5.8999999999999998e-56 < y < 1.94999999999999993e-26 or 4.1999999999999996e-6 < y < 4.6999999999999996e71

   1. Initial program 100.0%

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

      1. flip-- 78.5%

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

      2. associate-*r/ 75.4%

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

      3. cancel-sign-sub-inv 75.4%

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

      4. fma-def 77.5%

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

   3. Applied egg-rr 77.5%

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

      1. associate-/l* 80.5%

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

      2. distribute-lft-neg-out 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in t around inf 97.8%

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

   7. Taylor expanded in z around inf 78.2%

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

      1. distribute-lft-out-- 78.2%

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

      2. neg-mul-1 78.2%

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

      3. *-commutative 78.2%

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

      4. sub-neg 78.2%

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

      5. distribute-neg-in 78.2%

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

      6. remove-double-neg 78.2%

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

   9. Simplified 78.2%

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

   if 1.16000000000000001e-104 < y < 5.8999999999999998e-56

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 100.0%

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

   3. Taylor expanded in y around 0 89.9%

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

      1. +-commutative 89.9%

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

      2. mul-1-neg 89.9%

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

      3. unsub-neg 89.9%

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

      4. *-commutative 89.9%

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

   5. Simplified 89.9%

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

   if 1.94999999999999993e-26 < y < 4.1999999999999996e-6

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 81.1%

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

   3. Taylor expanded in z around 0 81.1%

      \[\leadsto \color{blue}{y \cdot t + x} \]
3. Recombined 6 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.05 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{-58}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-106}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-104}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{-56}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-26}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-6}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+71}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+106}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 3: 37.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-30}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-86}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-103}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+167} \lor \neg \left(y \leq 2.9 \cdot 10^{+259}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= y -2.4e-30)
     (* y t)
     (if (<= y -2.7e-74)
       t_1
       (if (<= y -1.4e-86)
         (* z x)
         (if (<= y -3.25e-105)
           x
           (if (<= y 8e-250)
             t_1
             (if (<= y 2.05e-103)
               (* z x)
               (if (<= y 8.4e+105)
                 t_1
                 (if (or (<= y 1.1e+167) (not (<= y 2.9e+259)))
                   (* y (- x))
                   (* y t)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -2.4e-30) {
		tmp = y * t;
	} else if (y <= -2.7e-74) {
		tmp = t_1;
	} else if (y <= -1.4e-86) {
		tmp = z * x;
	} else if (y <= -3.25e-105) {
		tmp = x;
	} else if (y <= 8e-250) {
		tmp = t_1;
	} else if (y <= 2.05e-103) {
		tmp = z * x;
	} else if (y <= 8.4e+105) {
		tmp = t_1;
	} else if ((y <= 1.1e+167) || !(y <= 2.9e+259)) {
		tmp = y * -x;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (y <= (-2.4d-30)) then
        tmp = y * t
    else if (y <= (-2.7d-74)) then
        tmp = t_1
    else if (y <= (-1.4d-86)) then
        tmp = z * x
    else if (y <= (-3.25d-105)) then
        tmp = x
    else if (y <= 8d-250) then
        tmp = t_1
    else if (y <= 2.05d-103) then
        tmp = z * x
    else if (y <= 8.4d+105) then
        tmp = t_1
    else if ((y <= 1.1d+167) .or. (.not. (y <= 2.9d+259))) then
        tmp = y * -x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -2.4e-30) {
		tmp = y * t;
	} else if (y <= -2.7e-74) {
		tmp = t_1;
	} else if (y <= -1.4e-86) {
		tmp = z * x;
	} else if (y <= -3.25e-105) {
		tmp = x;
	} else if (y <= 8e-250) {
		tmp = t_1;
	} else if (y <= 2.05e-103) {
		tmp = z * x;
	} else if (y <= 8.4e+105) {
		tmp = t_1;
	} else if ((y <= 1.1e+167) || !(y <= 2.9e+259)) {
		tmp = y * -x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if y <= -2.4e-30:
		tmp = y * t
	elif y <= -2.7e-74:
		tmp = t_1
	elif y <= -1.4e-86:
		tmp = z * x
	elif y <= -3.25e-105:
		tmp = x
	elif y <= 8e-250:
		tmp = t_1
	elif y <= 2.05e-103:
		tmp = z * x
	elif y <= 8.4e+105:
		tmp = t_1
	elif (y <= 1.1e+167) or not (y <= 2.9e+259):
		tmp = y * -x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -2.4e-30)
		tmp = Float64(y * t);
	elseif (y <= -2.7e-74)
		tmp = t_1;
	elseif (y <= -1.4e-86)
		tmp = Float64(z * x);
	elseif (y <= -3.25e-105)
		tmp = x;
	elseif (y <= 8e-250)
		tmp = t_1;
	elseif (y <= 2.05e-103)
		tmp = Float64(z * x);
	elseif (y <= 8.4e+105)
		tmp = t_1;
	elseif ((y <= 1.1e+167) || !(y <= 2.9e+259))
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (y <= -2.4e-30)
		tmp = y * t;
	elseif (y <= -2.7e-74)
		tmp = t_1;
	elseif (y <= -1.4e-86)
		tmp = z * x;
	elseif (y <= -3.25e-105)
		tmp = x;
	elseif (y <= 8e-250)
		tmp = t_1;
	elseif (y <= 2.05e-103)
		tmp = z * x;
	elseif (y <= 8.4e+105)
		tmp = t_1;
	elseif ((y <= 1.1e+167) || ~((y <= 2.9e+259)))
		tmp = y * -x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -2.4e-30], N[(y * t), $MachinePrecision], If[LessEqual[y, -2.7e-74], t$95$1, If[LessEqual[y, -1.4e-86], N[(z * x), $MachinePrecision], If[LessEqual[y, -3.25e-105], x, If[LessEqual[y, 8e-250], t$95$1, If[LessEqual[y, 2.05e-103], N[(z * x), $MachinePrecision], If[LessEqual[y, 8.4e+105], t$95$1, If[Or[LessEqual[y, 1.1e+167], N[Not[LessEqual[y, 2.9e+259]], $MachinePrecision]], N[(y * (-x)), $MachinePrecision], N[(y * t), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.39999999999999985e-30 or 1.10000000000000002e167 < y < 2.8999999999999999e259

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 65.8%

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

   3. Taylor expanded in y around 0 60.5%

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

   4. Taylor expanded in y around inf 56.8%

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

   if -2.39999999999999985e-30 < y < -2.70000000000000018e-74 or -3.25000000000000003e-105 < y < 8.0000000000000004e-250 or 2.04999999999999998e-103 < y < 8.4000000000000004e105

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 74.6%

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

   3. Taylor expanded in y around 0 73.6%

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

   4. Taylor expanded in z around inf 46.6%

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

      1. associate-*r* 46.6%

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

      2. neg-mul-1 46.6%

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

   6. Simplified 46.6%

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

   if -2.70000000000000018e-74 < y < -1.40000000000000005e-86 or 8.0000000000000004e-250 < y < 2.04999999999999998e-103

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 72.9%

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

      1. *-commutative 72.9%

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

      2. mul-1-neg 72.9%

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

      3. unsub-neg 72.9%

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

      4. distribute-lft-out-- 72.9%

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

      5. *-rgt-identity 72.9%

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

   4. Simplified 72.9%

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

   5. Taylor expanded in y around 0 72.9%

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

      1. associate-*r* 72.9%

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

      2. neg-mul-1 72.9%

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

   7. Simplified 72.9%

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

   8. Taylor expanded in z around inf 54.1%

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

   if -1.40000000000000005e-86 < y < -3.25000000000000003e-105

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   if 8.4000000000000004e105 < y < 1.10000000000000002e167 or 2.8999999999999999e259 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 81.9%

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

      1. *-commutative 81.9%

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

      2. mul-1-neg 81.9%

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

      3. unsub-neg 81.9%

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

      4. distribute-lft-out-- 81.9%

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

      5. *-rgt-identity 81.9%

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

   4. Simplified 81.9%

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

   5. Taylor expanded in y around inf 77.5%

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

   6. Taylor expanded in y around inf 77.5%

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

      1. associate-*r* 77.5%

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

      2. neg-mul-1 77.5%

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

   8. Simplified 77.5%

      \[\leadsto \color{blue}{\left(-y\right) \cdot x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-30}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-74}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-86}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-250}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-103}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+105}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+167} \lor \neg \left(y \leq 2.9 \cdot 10^{+259}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 4: 80.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ t_2 := x + y \cdot \left(t - x\right)\\ t_3 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+98}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-187}:\\ \;\;\;\;x + t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+31} \lor \neg \left(z \leq 9.6 \cdot 10^{+124}\right) \land z \leq 6.2 \cdot 10^{+162}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)) (t_2 (+ x (* y (- t x)))) (t_3 (* z (- x t))))
   (if (<= z -3e+98)
     t_3
     (if (<= z -8.6e-187)
       (+ x t_1)
       (if (<= z 6.5e-84)
         t_2
         (if (<= z 1.45e-58)
           t_1
           (if (or (<= z 4.5e+31) (and (not (<= z 9.6e+124)) (<= z 6.2e+162)))
             t_2
             t_3)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double t_2 = x + (y * (t - x));
	double t_3 = z * (x - t);
	double tmp;
	if (z <= -3e+98) {
		tmp = t_3;
	} else if (z <= -8.6e-187) {
		tmp = x + t_1;
	} else if (z <= 6.5e-84) {
		tmp = t_2;
	} else if (z <= 1.45e-58) {
		tmp = t_1;
	} else if ((z <= 4.5e+31) || (!(z <= 9.6e+124) && (z <= 6.2e+162))) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (y - z) * t
    t_2 = x + (y * (t - x))
    t_3 = z * (x - t)
    if (z <= (-3d+98)) then
        tmp = t_3
    else if (z <= (-8.6d-187)) then
        tmp = x + t_1
    else if (z <= 6.5d-84) then
        tmp = t_2
    else if (z <= 1.45d-58) then
        tmp = t_1
    else if ((z <= 4.5d+31) .or. (.not. (z <= 9.6d+124)) .and. (z <= 6.2d+162)) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double t_2 = x + (y * (t - x));
	double t_3 = z * (x - t);
	double tmp;
	if (z <= -3e+98) {
		tmp = t_3;
	} else if (z <= -8.6e-187) {
		tmp = x + t_1;
	} else if (z <= 6.5e-84) {
		tmp = t_2;
	} else if (z <= 1.45e-58) {
		tmp = t_1;
	} else if ((z <= 4.5e+31) || (!(z <= 9.6e+124) && (z <= 6.2e+162))) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	t_2 = x + (y * (t - x))
	t_3 = z * (x - t)
	tmp = 0
	if z <= -3e+98:
		tmp = t_3
	elif z <= -8.6e-187:
		tmp = x + t_1
	elif z <= 6.5e-84:
		tmp = t_2
	elif z <= 1.45e-58:
		tmp = t_1
	elif (z <= 4.5e+31) or (not (z <= 9.6e+124) and (z <= 6.2e+162)):
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	t_2 = Float64(x + Float64(y * Float64(t - x)))
	t_3 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -3e+98)
		tmp = t_3;
	elseif (z <= -8.6e-187)
		tmp = Float64(x + t_1);
	elseif (z <= 6.5e-84)
		tmp = t_2;
	elseif (z <= 1.45e-58)
		tmp = t_1;
	elseif ((z <= 4.5e+31) || (!(z <= 9.6e+124) && (z <= 6.2e+162)))
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	t_2 = x + (y * (t - x));
	t_3 = z * (x - t);
	tmp = 0.0;
	if (z <= -3e+98)
		tmp = t_3;
	elseif (z <= -8.6e-187)
		tmp = x + t_1;
	elseif (z <= 6.5e-84)
		tmp = t_2;
	elseif (z <= 1.45e-58)
		tmp = t_1;
	elseif ((z <= 4.5e+31) || (~((z <= 9.6e+124)) && (z <= 6.2e+162)))
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+98], t$95$3, If[LessEqual[z, -8.6e-187], N[(x + t$95$1), $MachinePrecision], If[LessEqual[z, 6.5e-84], t$95$2, If[LessEqual[z, 1.45e-58], t$95$1, If[Or[LessEqual[z, 4.5e+31], And[N[Not[LessEqual[z, 9.6e+124]], $MachinePrecision], LessEqual[z, 6.2e+162]]], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.0000000000000001e98 or 4.4999999999999996e31 < z < 9.60000000000000026e124 or 6.1999999999999999e162 < z

   1. Initial program 100.0%

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

      1. flip-- 87.9%

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

      2. associate-*r/ 84.2%

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

      3. cancel-sign-sub-inv 84.2%

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

      4. fma-def 87.1%

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

   3. Applied egg-rr 87.1%

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

      1. associate-/l* 90.7%

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

      2. distribute-lft-neg-out 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in t around inf 95.1%

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

   7. Taylor expanded in z around inf 86.5%

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

      1. distribute-lft-out-- 86.5%

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

      2. neg-mul-1 86.5%

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

      3. *-commutative 86.5%

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

      4. sub-neg 86.5%

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

      5. distribute-neg-in 86.5%

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

      6. remove-double-neg 86.5%

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

   9. Simplified 86.5%

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

   if -3.0000000000000001e98 < z < -8.60000000000000001e-187

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 78.9%

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

   if -8.60000000000000001e-187 < z < 6.50000000000000022e-84 or 1.44999999999999995e-58 < z < 4.4999999999999996e31 or 9.60000000000000026e124 < z < 6.1999999999999999e162

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 90.9%

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

   if 6.50000000000000022e-84 < z < 1.44999999999999995e-58

   1. Initial program 100.0%

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

      1. flip-- 53.1%

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

      2. associate-*r/ 53.1%

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

      3. cancel-sign-sub-inv 53.1%

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

      4. fma-def 53.1%

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

   3. Applied egg-rr 53.1%

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

      1. associate-/l* 53.1%

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

      2. distribute-lft-neg-out 53.1%

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

   5. Simplified 53.1%

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

   6. Taylor expanded in t around inf 100.0%

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

   7. Taylor expanded in t around inf 100.0%

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

      1. *-commutative 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+98}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-187}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-84}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-58}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+31} \lor \neg \left(z \leq 9.6 \cdot 10^{+124}\right) \land z \leq 6.2 \cdot 10^{+162}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 5: 35.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{-30}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-87}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-105}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= y -1.65e-30)
     (* y t)
     (if (<= y -3.3e-73)
       t_1
       (if (<= y -4.8e-87)
         (* z x)
         (if (<= y -1.25e-104)
           x
           (if (<= y 6e-250)
             t_1
             (if (<= y 6.2e-105)
               (* z x)
               (if (<= y 5.2e+166) t_1 (* y t))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -1.65e-30) {
		tmp = y * t;
	} else if (y <= -3.3e-73) {
		tmp = t_1;
	} else if (y <= -4.8e-87) {
		tmp = z * x;
	} else if (y <= -1.25e-104) {
		tmp = x;
	} else if (y <= 6e-250) {
		tmp = t_1;
	} else if (y <= 6.2e-105) {
		tmp = z * x;
	} else if (y <= 5.2e+166) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (y <= (-1.65d-30)) then
        tmp = y * t
    else if (y <= (-3.3d-73)) then
        tmp = t_1
    else if (y <= (-4.8d-87)) then
        tmp = z * x
    else if (y <= (-1.25d-104)) then
        tmp = x
    else if (y <= 6d-250) then
        tmp = t_1
    else if (y <= 6.2d-105) then
        tmp = z * x
    else if (y <= 5.2d+166) then
        tmp = t_1
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -1.65e-30) {
		tmp = y * t;
	} else if (y <= -3.3e-73) {
		tmp = t_1;
	} else if (y <= -4.8e-87) {
		tmp = z * x;
	} else if (y <= -1.25e-104) {
		tmp = x;
	} else if (y <= 6e-250) {
		tmp = t_1;
	} else if (y <= 6.2e-105) {
		tmp = z * x;
	} else if (y <= 5.2e+166) {
		tmp = t_1;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if y <= -1.65e-30:
		tmp = y * t
	elif y <= -3.3e-73:
		tmp = t_1
	elif y <= -4.8e-87:
		tmp = z * x
	elif y <= -1.25e-104:
		tmp = x
	elif y <= 6e-250:
		tmp = t_1
	elif y <= 6.2e-105:
		tmp = z * x
	elif y <= 5.2e+166:
		tmp = t_1
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -1.65e-30)
		tmp = Float64(y * t);
	elseif (y <= -3.3e-73)
		tmp = t_1;
	elseif (y <= -4.8e-87)
		tmp = Float64(z * x);
	elseif (y <= -1.25e-104)
		tmp = x;
	elseif (y <= 6e-250)
		tmp = t_1;
	elseif (y <= 6.2e-105)
		tmp = Float64(z * x);
	elseif (y <= 5.2e+166)
		tmp = t_1;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (y <= -1.65e-30)
		tmp = y * t;
	elseif (y <= -3.3e-73)
		tmp = t_1;
	elseif (y <= -4.8e-87)
		tmp = z * x;
	elseif (y <= -1.25e-104)
		tmp = x;
	elseif (y <= 6e-250)
		tmp = t_1;
	elseif (y <= 6.2e-105)
		tmp = z * x;
	elseif (y <= 5.2e+166)
		tmp = t_1;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -1.65e-30], N[(y * t), $MachinePrecision], If[LessEqual[y, -3.3e-73], t$95$1, If[LessEqual[y, -4.8e-87], N[(z * x), $MachinePrecision], If[LessEqual[y, -1.25e-104], x, If[LessEqual[y, 6e-250], t$95$1, If[LessEqual[y, 6.2e-105], N[(z * x), $MachinePrecision], If[LessEqual[y, 5.2e+166], t$95$1, N[(y * t), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6500000000000001e-30 or 5.1999999999999999e166 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 62.6%

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

   3. Taylor expanded in y around 0 57.8%

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

   4. Taylor expanded in y around inf 54.5%

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

   if -1.6500000000000001e-30 < y < -3.30000000000000004e-73 or -1.24999999999999995e-104 < y < 6.00000000000000032e-250 or 6.20000000000000029e-105 < y < 5.1999999999999999e166

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 68.3%

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

   3. Taylor expanded in y around 0 67.4%

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

   4. Taylor expanded in z around inf 43.4%

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

      1. associate-*r* 43.4%

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

      2. neg-mul-1 43.4%

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

   6. Simplified 43.4%

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

   if -3.30000000000000004e-73 < y < -4.7999999999999999e-87 or 6.00000000000000032e-250 < y < 6.20000000000000029e-105

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 72.9%

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

      1. *-commutative 72.9%

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

      2. mul-1-neg 72.9%

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

      3. unsub-neg 72.9%

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

      4. distribute-lft-out-- 72.9%

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

      5. *-rgt-identity 72.9%

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

   4. Simplified 72.9%

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

   5. Taylor expanded in y around 0 72.9%

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

      1. associate-*r* 72.9%

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

      2. neg-mul-1 72.9%

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

   7. Simplified 72.9%

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

   8. Taylor expanded in z around inf 54.1%

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

   if -4.7999999999999999e-87 < y < -1.24999999999999995e-104

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-30}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-73}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-87}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-250}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-105}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+166}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 6: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-241}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-107}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (+ x (* (- y z) t))))
   (if (<= y -1.12e+36)
     t_1
     (if (<= y -1.1e-241)
       t_2
       (if (<= y 4e-107) (* z (- x t)) (if (<= y 8.4e+105) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x + ((y - z) * t);
	double tmp;
	if (y <= -1.12e+36) {
		tmp = t_1;
	} else if (y <= -1.1e-241) {
		tmp = t_2;
	} else if (y <= 4e-107) {
		tmp = z * (x - t);
	} else if (y <= 8.4e+105) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = x + ((y - z) * t)
    if (y <= (-1.12d+36)) then
        tmp = t_1
    else if (y <= (-1.1d-241)) then
        tmp = t_2
    else if (y <= 4d-107) then
        tmp = z * (x - t)
    else if (y <= 8.4d+105) then
        tmp = t_2
    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 - x);
	double t_2 = x + ((y - z) * t);
	double tmp;
	if (y <= -1.12e+36) {
		tmp = t_1;
	} else if (y <= -1.1e-241) {
		tmp = t_2;
	} else if (y <= 4e-107) {
		tmp = z * (x - t);
	} else if (y <= 8.4e+105) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x + ((y - z) * t)
	tmp = 0
	if y <= -1.12e+36:
		tmp = t_1
	elif y <= -1.1e-241:
		tmp = t_2
	elif y <= 4e-107:
		tmp = z * (x - t)
	elif y <= 8.4e+105:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(x + Float64(Float64(y - z) * t))
	tmp = 0.0
	if (y <= -1.12e+36)
		tmp = t_1;
	elseif (y <= -1.1e-241)
		tmp = t_2;
	elseif (y <= 4e-107)
		tmp = Float64(z * Float64(x - t));
	elseif (y <= 8.4e+105)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = x + ((y - z) * t);
	tmp = 0.0;
	if (y <= -1.12e+36)
		tmp = t_1;
	elseif (y <= -1.1e-241)
		tmp = t_2;
	elseif (y <= 4e-107)
		tmp = z * (x - t);
	elseif (y <= 8.4e+105)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.12e+36], t$95$1, If[LessEqual[y, -1.1e-241], t$95$2, If[LessEqual[y, 4e-107], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.4e+105], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.11999999999999999e36 or 8.4000000000000004e105 < y

   1. Initial program 100.0%

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

      1. flip-- 89.5%

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

      2. associate-*r/ 85.3%

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

      3. cancel-sign-sub-inv 85.3%

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

      4. fma-def 87.1%

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

   3. Applied egg-rr 87.1%

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

      1. associate-/l* 91.2%

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

      2. distribute-lft-neg-out 91.2%

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

   5. Simplified 91.2%

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

   6. Taylor expanded in t around inf 95.4%

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

   7. Taylor expanded in y around inf 85.7%

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

   if -1.11999999999999999e36 < y < -1.1e-241 or 4e-107 < y < 8.4000000000000004e105

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 74.4%

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

   if -1.1e-241 < y < 4e-107

   1. Initial program 100.0%

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

      1. flip-- 80.1%

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

      2. associate-*r/ 78.4%

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

      3. cancel-sign-sub-inv 78.4%

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

      4. fma-def 81.8%

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

   3. Applied egg-rr 81.8%

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

      1. associate-/l* 83.5%

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

      2. distribute-lft-neg-out 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in t around inf 98.3%

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

   7. Taylor expanded in z around inf 79.7%

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

      1. distribute-lft-out-- 79.7%

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

      2. neg-mul-1 79.7%

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

      3. *-commutative 79.7%

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

      4. sub-neg 79.7%

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

      5. distribute-neg-in 79.7%

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

      6. remove-double-neg 79.7%

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

   9. Simplified 79.7%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-241}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-107}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+105}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 7: 55.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-250}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-101}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -3.2e-31)
     t_1
     (if (<= y 7.5e-250)
       (* z (- t))
       (if (<= y 6e-101) (* z x) (if (<= y 5.2e-15) x t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -3.2e-31) {
		tmp = t_1;
	} else if (y <= 7.5e-250) {
		tmp = z * -t;
	} else if (y <= 6e-101) {
		tmp = z * x;
	} else if (y <= 5.2e-15) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t - x)
    if (y <= (-3.2d-31)) then
        tmp = t_1
    else if (y <= 7.5d-250) then
        tmp = z * -t
    else if (y <= 6d-101) then
        tmp = z * x
    else if (y <= 5.2d-15) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -3.2e-31) {
		tmp = t_1;
	} else if (y <= 7.5e-250) {
		tmp = z * -t;
	} else if (y <= 6e-101) {
		tmp = z * x;
	} else if (y <= 5.2e-15) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -3.2e-31:
		tmp = t_1
	elif y <= 7.5e-250:
		tmp = z * -t
	elif y <= 6e-101:
		tmp = z * x
	elif y <= 5.2e-15:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -3.2e-31)
		tmp = t_1;
	elseif (y <= 7.5e-250)
		tmp = Float64(z * Float64(-t));
	elseif (y <= 6e-101)
		tmp = Float64(z * x);
	elseif (y <= 5.2e-15)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -3.2e-31)
		tmp = t_1;
	elseif (y <= 7.5e-250)
		tmp = z * -t;
	elseif (y <= 6e-101)
		tmp = z * x;
	elseif (y <= 5.2e-15)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e-31], t$95$1, If[LessEqual[y, 7.5e-250], N[(z * (-t)), $MachinePrecision], If[LessEqual[y, 6e-101], N[(z * x), $MachinePrecision], If[LessEqual[y, 5.2e-15], x, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.20000000000000018e-31 or 5.20000000000000009e-15 < y

   1. Initial program 99.9%

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

      1. flip-- 84.8%

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

      2. associate-*r/ 81.0%

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

      3. cancel-sign-sub-inv 81.0%

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

      4. fma-def 82.3%

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

   3. Applied egg-rr 82.3%

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

      1. associate-/l* 86.1%

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

      2. distribute-lft-neg-out 86.1%

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

   5. Simplified 86.1%

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

   6. Taylor expanded in t around inf 95.1%

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

   7. Taylor expanded in y around inf 75.0%

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

   if -3.20000000000000018e-31 < y < 7.50000000000000009e-250

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 78.5%

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

   3. Taylor expanded in y around 0 78.5%

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

   4. Taylor expanded in z around inf 47.8%

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

      1. associate-*r* 47.8%

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

      2. neg-mul-1 47.8%

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

   6. Simplified 47.8%

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

   if 7.50000000000000009e-250 < y < 6.0000000000000006e-101

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 71.3%

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

      1. *-commutative 71.3%

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

      2. mul-1-neg 71.3%

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

      3. unsub-neg 71.3%

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

      4. distribute-lft-out-- 71.3%

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

      5. *-rgt-identity 71.3%

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

   4. Simplified 71.3%

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

   5. Taylor expanded in y around 0 71.3%

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

      1. associate-*r* 71.3%

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

      2. neg-mul-1 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in z around inf 51.4%

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

   if 6.0000000000000006e-101 < y < 5.20000000000000009e-15

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 86.3%

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

   3. Taylor expanded in x around inf 51.4%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-250}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-101}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 8: 56.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-212}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -1.4e-171)
     t_1
     (if (<= t 1.1e-212) (* z x) (if (<= t 1.46e+41) (* y (- t x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -1.4e-171) {
		tmp = t_1;
	} else if (t <= 1.1e-212) {
		tmp = z * x;
	} else if (t <= 1.46e+41) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if (t <= (-1.4d-171)) then
        tmp = t_1
    else if (t <= 1.1d-212) then
        tmp = z * x
    else if (t <= 1.46d+41) then
        tmp = y * (t - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -1.4e-171) {
		tmp = t_1;
	} else if (t <= 1.1e-212) {
		tmp = z * x;
	} else if (t <= 1.46e+41) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -1.4e-171:
		tmp = t_1
	elif t <= 1.1e-212:
		tmp = z * x
	elif t <= 1.46e+41:
		tmp = y * (t - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -1.4e-171)
		tmp = t_1;
	elseif (t <= 1.1e-212)
		tmp = Float64(z * x);
	elseif (t <= 1.46e+41)
		tmp = Float64(y * Float64(t - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -1.4e-171)
		tmp = t_1;
	elseif (t <= 1.1e-212)
		tmp = z * x;
	elseif (t <= 1.46e+41)
		tmp = y * (t - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.4e-171], t$95$1, If[LessEqual[t, 1.1e-212], N[(z * x), $MachinePrecision], If[LessEqual[t, 1.46e+41], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.40000000000000011e-171 or 1.4600000000000001e41 < t

   1. Initial program 100.0%

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

      1. flip-- 77.8%

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

      2. associate-*r/ 75.2%

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

      3. cancel-sign-sub-inv 75.2%

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

      4. fma-def 77.9%

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

   3. Applied egg-rr 77.9%

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

      1. associate-/l* 80.3%

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

      2. distribute-lft-neg-out 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in t around inf 94.0%

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

   7. Taylor expanded in t around inf 76.6%

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

      1. *-commutative 76.6%

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

   9. Simplified 76.6%

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

   if -1.40000000000000011e-171 < t < 1.10000000000000002e-212

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 92.6%

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

      1. *-commutative 92.6%

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

      2. mul-1-neg 92.6%

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

      3. unsub-neg 92.6%

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

      4. distribute-lft-out-- 92.6%

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

      5. *-rgt-identity 92.6%

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

   4. Simplified 92.6%

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

   5. Taylor expanded in y around 0 73.0%

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

      1. associate-*r* 73.0%

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

      2. neg-mul-1 73.0%

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

   7. Simplified 73.0%

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

   8. Taylor expanded in z around inf 51.5%

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

   if 1.10000000000000002e-212 < t < 1.4600000000000001e41

   1. Initial program 99.9%

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

      1. flip-- 89.6%

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

      2. associate-*r/ 86.3%

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

      3. cancel-sign-sub-inv 86.3%

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

      4. fma-def 86.3%

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

   3. Applied egg-rr 86.3%

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

      1. associate-/l* 89.6%

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

      2. distribute-lft-neg-out 89.6%

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

   5. Simplified 89.6%

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

   6. Taylor expanded in t around inf 99.9%

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

   7. Taylor expanded in y around inf 56.3%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-171}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-212}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]

Alternative 9: 62.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-202}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+40}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -1.3e-24)
     t_1
     (if (<= t 2.7e-202)
       (+ x (* z x))
       (if (<= t 2.9e+40) (* y (- t x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -1.3e-24) {
		tmp = t_1;
	} else if (t <= 2.7e-202) {
		tmp = x + (z * x);
	} else if (t <= 2.9e+40) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if (t <= (-1.3d-24)) then
        tmp = t_1
    else if (t <= 2.7d-202) then
        tmp = x + (z * x)
    else if (t <= 2.9d+40) then
        tmp = y * (t - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -1.3e-24) {
		tmp = t_1;
	} else if (t <= 2.7e-202) {
		tmp = x + (z * x);
	} else if (t <= 2.9e+40) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -1.3e-24:
		tmp = t_1
	elif t <= 2.7e-202:
		tmp = x + (z * x)
	elif t <= 2.9e+40:
		tmp = y * (t - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -1.3e-24)
		tmp = t_1;
	elseif (t <= 2.7e-202)
		tmp = Float64(x + Float64(z * x));
	elseif (t <= 2.9e+40)
		tmp = Float64(y * Float64(t - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -1.3e-24)
		tmp = t_1;
	elseif (t <= 2.7e-202)
		tmp = x + (z * x);
	elseif (t <= 2.9e+40)
		tmp = y * (t - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.3e-24], t$95$1, If[LessEqual[t, 2.7e-202], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+40], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3e-24 or 2.90000000000000017e40 < t

   1. Initial program 100.0%

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

      1. flip-- 75.6%

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

      2. associate-*r/ 72.5%

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

      3. cancel-sign-sub-inv 72.5%

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

      4. fma-def 75.8%

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

   3. Applied egg-rr 75.8%

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

      1. associate-/l* 78.9%

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

      2. distribute-lft-neg-out 78.9%

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

   5. Simplified 78.9%

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

   6. Taylor expanded in t around inf 92.5%

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

   7. Taylor expanded in t around inf 84.7%

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

      1. *-commutative 84.7%

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

   9. Simplified 84.7%

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

   if -1.3e-24 < t < 2.6999999999999999e-202

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 80.9%

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

      1. *-commutative 80.9%

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

      2. mul-1-neg 80.9%

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

      3. unsub-neg 80.9%

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

      4. distribute-lft-out-- 80.9%

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

      5. *-rgt-identity 80.9%

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

   4. Simplified 80.9%

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

   5. Taylor expanded in y around 0 63.4%

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

      1. associate-*r* 63.4%

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

      2. neg-mul-1 63.4%

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

   7. Simplified 63.4%

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

   8. Taylor expanded in z around 0 63.4%

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

   if 2.6999999999999999e-202 < t < 2.90000000000000017e40

   1. Initial program 99.9%

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

      1. flip-- 89.6%

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

      2. associate-*r/ 86.3%

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

      3. cancel-sign-sub-inv 86.3%

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

      4. fma-def 86.3%

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

   3. Applied egg-rr 86.3%

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

      1. associate-/l* 89.6%

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

      2. distribute-lft-neg-out 89.6%

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

   5. Simplified 89.6%

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

   6. Taylor expanded in t around inf 99.9%

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

   7. Taylor expanded in y around inf 56.3%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-24}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-202}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+40}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]

Alternative 10: 80.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-5} \lor \neg \left(x \leq 4.1 \cdot 10^{-27}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.85e-5) (not (<= x 4.1e-27)))
   (+ x (* x (- z y)))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.85e-5) || !(x <= 4.1e-27)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.85d-5)) .or. (.not. (x <= 4.1d-27))) then
        tmp = x + (x * (z - y))
    else
        tmp = x + ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.85e-5) || !(x <= 4.1e-27)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.85e-5) or not (x <= 4.1e-27):
		tmp = x + (x * (z - y))
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.85e-5) || !(x <= 4.1e-27))
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.85e-5) || ~((x <= 4.1e-27)))
		tmp = x + (x * (z - y));
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.85e-5], N[Not[LessEqual[x, 4.1e-27]], $MachinePrecision]], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.84999999999999991e-5 or 4.0999999999999999e-27 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 86.1%

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

      1. *-commutative 86.1%

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

      2. mul-1-neg 86.1%

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

      3. unsub-neg 86.1%

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

      4. distribute-lft-out-- 86.1%

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

      5. *-rgt-identity 86.1%

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

   4. Simplified 86.1%

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

   if -1.84999999999999991e-5 < x < 4.0999999999999999e-27

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 85.5%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-5} \lor \neg \left(x \leq 4.1 \cdot 10^{-27}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]

Alternative 11: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

   \[\leadsto x + \left(y - z\right) \cdot \left(t - x\right) \]

Alternative 12: 38.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-58}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.1e-58) (* y t) (if (<= y 4.4e-20) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.1e-58) {
		tmp = y * t;
	} else if (y <= 4.4e-20) {
		tmp = x;
	} else {
		tmp = 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 (y <= (-1.1d-58)) then
        tmp = y * t
    else if (y <= 4.4d-20) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.1e-58) {
		tmp = y * t;
	} else if (y <= 4.4e-20) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.1e-58:
		tmp = y * t
	elif y <= 4.4e-20:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.1e-58)
		tmp = Float64(y * t);
	elseif (y <= 4.4e-20)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.1e-58)
		tmp = y * t;
	elseif (y <= 4.4e-20)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.1e-58], N[(y * t), $MachinePrecision], If[LessEqual[y, 4.4e-20], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.10000000000000003e-58 or 4.39999999999999982e-20 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 59.8%

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

   3. Taylor expanded in y around 0 55.8%

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

   4. Taylor expanded in y around inf 42.9%

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

   if -1.10000000000000003e-58 < y < 4.39999999999999982e-20

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 72.1%

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

   3. Taylor expanded in x around inf 29.2%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-58}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 13: 34.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+99}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-33}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.02e+99) (* z x) (if (<= x 1.35e-33) (* y t) (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.02e+99) {
		tmp = z * x;
	} else if (x <= 1.35e-33) {
		tmp = y * t;
	} else {
		tmp = z * 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 <= (-1.02d+99)) then
        tmp = z * x
    else if (x <= 1.35d-33) then
        tmp = y * t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.02e+99) {
		tmp = z * x;
	} else if (x <= 1.35e-33) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.02e+99:
		tmp = z * x
	elif x <= 1.35e-33:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.02e+99)
		tmp = Float64(z * x);
	elseif (x <= 1.35e-33)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.02e+99)
		tmp = z * x;
	elseif (x <= 1.35e-33)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.02e+99], N[(z * x), $MachinePrecision], If[LessEqual[x, 1.35e-33], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.01999999999999998e99 or 1.35e-33 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 90.9%

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

      1. *-commutative 90.9%

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

      2. mul-1-neg 90.9%

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

      3. unsub-neg 90.9%

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

      4. distribute-lft-out-- 90.9%

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

      5. *-rgt-identity 90.9%

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

   4. Simplified 90.9%

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

   5. Taylor expanded in y around 0 64.6%

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

      1. associate-*r* 64.6%

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

      2. neg-mul-1 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in z around inf 46.2%

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

   if -1.01999999999999998e99 < x < 1.35e-33

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 79.6%

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

   3. Taylor expanded in y around 0 77.1%

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

   4. Taylor expanded in y around inf 41.0%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+99}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-33}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 14: 18.5% 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 100.0%

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

2. Taylor expanded in t around inf 64.8%

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

3. Taylor expanded in x around inf 13.5%

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

4. Final simplification 13.5%

   \[\leadsto x \]

Developer target: 96.7% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023258 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

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