Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.4s

Alternatives: 13

Speedup: 1.0×

• 34.0% 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: 47.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -22000000000000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-221}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-288}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (* x (+ z 1.0))))
   (if (<= y -22000000000000.0)
     (* y (- x))
     (if (<= y -9e-221)
       t_2
       (if (<= y -4.5e-248)
         t_1
         (if (<= y 8.5e-288)
           t_2
           (if (<= y 4e-146) t_1 (if (<= y 6e-5) t_2 (* y t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -22000000000000.0) {
		tmp = y * -x;
	} else if (y <= -9e-221) {
		tmp = t_2;
	} else if (y <= -4.5e-248) {
		tmp = t_1;
	} else if (y <= 8.5e-288) {
		tmp = t_2;
	} else if (y <= 4e-146) {
		tmp = t_1;
	} else if (y <= 6e-5) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = z * -t
    t_2 = x * (z + 1.0d0)
    if (y <= (-22000000000000.0d0)) then
        tmp = y * -x
    else if (y <= (-9d-221)) then
        tmp = t_2
    else if (y <= (-4.5d-248)) then
        tmp = t_1
    else if (y <= 8.5d-288) then
        tmp = t_2
    else if (y <= 4d-146) then
        tmp = t_1
    else if (y <= 6d-5) then
        tmp = t_2
    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 t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -22000000000000.0) {
		tmp = y * -x;
	} else if (y <= -9e-221) {
		tmp = t_2;
	} else if (y <= -4.5e-248) {
		tmp = t_1;
	} else if (y <= 8.5e-288) {
		tmp = t_2;
	} else if (y <= 4e-146) {
		tmp = t_1;
	} else if (y <= 6e-5) {
		tmp = t_2;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	t_2 = x * (z + 1.0)
	tmp = 0
	if y <= -22000000000000.0:
		tmp = y * -x
	elif y <= -9e-221:
		tmp = t_2
	elif y <= -4.5e-248:
		tmp = t_1
	elif y <= 8.5e-288:
		tmp = t_2
	elif y <= 4e-146:
		tmp = t_1
	elif y <= 6e-5:
		tmp = t_2
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	t_2 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= -22000000000000.0)
		tmp = Float64(y * Float64(-x));
	elseif (y <= -9e-221)
		tmp = t_2;
	elseif (y <= -4.5e-248)
		tmp = t_1;
	elseif (y <= 8.5e-288)
		tmp = t_2;
	elseif (y <= 4e-146)
		tmp = t_1;
	elseif (y <= 6e-5)
		tmp = t_2;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	t_2 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= -22000000000000.0)
		tmp = y * -x;
	elseif (y <= -9e-221)
		tmp = t_2;
	elseif (y <= -4.5e-248)
		tmp = t_1;
	elseif (y <= 8.5e-288)
		tmp = t_2;
	elseif (y <= 4e-146)
		tmp = t_1;
	elseif (y <= 6e-5)
		tmp = t_2;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -22000000000000.0], N[(y * (-x)), $MachinePrecision], If[LessEqual[y, -9e-221], t$95$2, If[LessEqual[y, -4.5e-248], t$95$1, If[LessEqual[y, 8.5e-288], t$95$2, If[LessEqual[y, 4e-146], t$95$1, If[LessEqual[y, 6e-5], t$95$2, N[(y * t), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.2e13

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. neg-sub0 61.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0 - \left(y - z\right)\right)}\right) \]

      3. associate-+r- 61.5%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + 0\right) - \left(y - z\right)\right)} \]

      4. metadata-eval 61.5%

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

   4. Simplified 61.5%

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

   5. Taylor expanded in y around inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. *-commutative 50.1%

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

      3. distribute-rgt-neg-out 50.1%

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

   7. Simplified 50.1%

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

   if -2.2e13 < y < -9.00000000000000052e-221 or -4.4999999999999996e-248 < y < 8.4999999999999997e-288 or 4.0000000000000001e-146 < y < 6.00000000000000015e-5

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 65.1%

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

      1. mul-1-neg 65.1%

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

      2. neg-sub0 65.1%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0 - \left(y - z\right)\right)}\right) \]

      3. associate-+r- 65.1%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + 0\right) - \left(y - z\right)\right)} \]

      4. metadata-eval 65.1%

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

   4. Simplified 65.1%

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

   5. Taylor expanded in y around 0 63.6%

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

      1. +-commutative 63.6%

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

   7. Simplified 63.6%

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

   if -9.00000000000000052e-221 < y < -4.4999999999999996e-248 or 8.4999999999999997e-288 < y < 4.0000000000000001e-146

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-neg-out 100.0%

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

   4. Simplified 100.0%

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

      1. distribute-rgt-neg-out 100.0%

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

      2. unsub-neg 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 66.8%

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

      1. mul-1-neg 66.8%

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

      2. *-commutative 66.8%

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

      3. distribute-rgt-neg-out 66.8%

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

   9. Simplified 66.8%

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

   if 6.00000000000000015e-5 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.6%

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

      1. *-commutative 79.6%

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

   4. Simplified 79.6%

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

   5. Taylor expanded in t around inf 52.1%

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

      1. *-commutative 52.1%

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

   7. Simplified 52.1%

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

   8. Taylor expanded in x around 0 52.4%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -22000000000000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-248}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-288}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-146}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 3: 47.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -255:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-221}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-286}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (* x (+ z 1.0))))
   (if (<= y -255.0)
     (* x (- 1.0 y))
     (if (<= y -3.1e-221)
       t_2
       (if (<= y -4.4e-248)
         t_1
         (if (<= y 2.05e-286)
           t_2
           (if (<= y 3.2e-148) t_1 (if (<= y 2.6e-5) t_2 (* y t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -255.0) {
		tmp = x * (1.0 - y);
	} else if (y <= -3.1e-221) {
		tmp = t_2;
	} else if (y <= -4.4e-248) {
		tmp = t_1;
	} else if (y <= 2.05e-286) {
		tmp = t_2;
	} else if (y <= 3.2e-148) {
		tmp = t_1;
	} else if (y <= 2.6e-5) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = z * -t
    t_2 = x * (z + 1.0d0)
    if (y <= (-255.0d0)) then
        tmp = x * (1.0d0 - y)
    else if (y <= (-3.1d-221)) then
        tmp = t_2
    else if (y <= (-4.4d-248)) then
        tmp = t_1
    else if (y <= 2.05d-286) then
        tmp = t_2
    else if (y <= 3.2d-148) then
        tmp = t_1
    else if (y <= 2.6d-5) then
        tmp = t_2
    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 t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -255.0) {
		tmp = x * (1.0 - y);
	} else if (y <= -3.1e-221) {
		tmp = t_2;
	} else if (y <= -4.4e-248) {
		tmp = t_1;
	} else if (y <= 2.05e-286) {
		tmp = t_2;
	} else if (y <= 3.2e-148) {
		tmp = t_1;
	} else if (y <= 2.6e-5) {
		tmp = t_2;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	t_2 = x * (z + 1.0)
	tmp = 0
	if y <= -255.0:
		tmp = x * (1.0 - y)
	elif y <= -3.1e-221:
		tmp = t_2
	elif y <= -4.4e-248:
		tmp = t_1
	elif y <= 2.05e-286:
		tmp = t_2
	elif y <= 3.2e-148:
		tmp = t_1
	elif y <= 2.6e-5:
		tmp = t_2
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	t_2 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= -255.0)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (y <= -3.1e-221)
		tmp = t_2;
	elseif (y <= -4.4e-248)
		tmp = t_1;
	elseif (y <= 2.05e-286)
		tmp = t_2;
	elseif (y <= 3.2e-148)
		tmp = t_1;
	elseif (y <= 2.6e-5)
		tmp = t_2;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	t_2 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= -255.0)
		tmp = x * (1.0 - y);
	elseif (y <= -3.1e-221)
		tmp = t_2;
	elseif (y <= -4.4e-248)
		tmp = t_1;
	elseif (y <= 2.05e-286)
		tmp = t_2;
	elseif (y <= 3.2e-148)
		tmp = t_1;
	elseif (y <= 2.6e-5)
		tmp = t_2;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -255.0], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.1e-221], t$95$2, If[LessEqual[y, -4.4e-248], t$95$1, If[LessEqual[y, 2.05e-286], t$95$2, If[LessEqual[y, 3.2e-148], t$95$1, If[LessEqual[y, 2.6e-5], t$95$2, N[(y * t), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -255

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. neg-sub0 60.0%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0 - \left(y - z\right)\right)}\right) \]

      3. associate-+r- 60.0%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + 0\right) - \left(y - z\right)\right)} \]

      4. metadata-eval 60.0%

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

   4. Simplified 60.0%

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

   5. Taylor expanded in z around 0 48.1%

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

   if -255 < y < -3.0999999999999999e-221 or -4.39999999999999999e-248 < y < 2.05e-286 or 3.19999999999999993e-148 < y < 2.59999999999999984e-5

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 66.4%

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

      1. mul-1-neg 66.4%

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

      2. neg-sub0 66.4%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0 - \left(y - z\right)\right)}\right) \]

      3. associate-+r- 66.4%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + 0\right) - \left(y - z\right)\right)} \]

      4. metadata-eval 66.4%

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

   4. Simplified 66.4%

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

   5. Taylor expanded in y around 0 66.4%

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

      1. +-commutative 66.4%

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

   7. Simplified 66.4%

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

   if -3.0999999999999999e-221 < y < -4.39999999999999999e-248 or 2.05e-286 < y < 3.19999999999999993e-148

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-neg-out 100.0%

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

   4. Simplified 100.0%

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

      1. distribute-rgt-neg-out 100.0%

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

      2. unsub-neg 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 66.8%

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

      1. mul-1-neg 66.8%

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

      2. *-commutative 66.8%

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

      3. distribute-rgt-neg-out 66.8%

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

   9. Simplified 66.8%

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

   if 2.59999999999999984e-5 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.6%

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

      1. *-commutative 79.6%

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

   4. Simplified 79.6%

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

   5. Taylor expanded in t around inf 52.1%

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

      1. *-commutative 52.1%

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

   7. Simplified 52.1%

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

   8. Taylor expanded in x around 0 52.4%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -255:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-248}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-286}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-148}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 4: 64.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-106}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-205}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-301}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 10.5:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* x (- 1.0 y))))
   (if (<= z -9.5e+36)
     t_1
     (if (<= z -3.3e-18)
       t_2
       (if (<= z -1.02e-106)
         (* y t)
         (if (<= z -8e-205)
           t_2
           (if (<= z 3.3e-301) (* y t) (if (<= z 10.5) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x * (1.0 - y);
	double tmp;
	if (z <= -9.5e+36) {
		tmp = t_1;
	} else if (z <= -3.3e-18) {
		tmp = t_2;
	} else if (z <= -1.02e-106) {
		tmp = y * t;
	} else if (z <= -8e-205) {
		tmp = t_2;
	} else if (z <= 3.3e-301) {
		tmp = y * t;
	} else if (z <= 10.5) {
		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 = z * (x - t)
    t_2 = x * (1.0d0 - y)
    if (z <= (-9.5d+36)) then
        tmp = t_1
    else if (z <= (-3.3d-18)) then
        tmp = t_2
    else if (z <= (-1.02d-106)) then
        tmp = y * t
    else if (z <= (-8d-205)) then
        tmp = t_2
    else if (z <= 3.3d-301) then
        tmp = y * t
    else if (z <= 10.5d0) 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 = z * (x - t);
	double t_2 = x * (1.0 - y);
	double tmp;
	if (z <= -9.5e+36) {
		tmp = t_1;
	} else if (z <= -3.3e-18) {
		tmp = t_2;
	} else if (z <= -1.02e-106) {
		tmp = y * t;
	} else if (z <= -8e-205) {
		tmp = t_2;
	} else if (z <= 3.3e-301) {
		tmp = y * t;
	} else if (z <= 10.5) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = x * (1.0 - y)
	tmp = 0
	if z <= -9.5e+36:
		tmp = t_1
	elif z <= -3.3e-18:
		tmp = t_2
	elif z <= -1.02e-106:
		tmp = y * t
	elif z <= -8e-205:
		tmp = t_2
	elif z <= 3.3e-301:
		tmp = y * t
	elif z <= 10.5:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -9.5e+36)
		tmp = t_1;
	elseif (z <= -3.3e-18)
		tmp = t_2;
	elseif (z <= -1.02e-106)
		tmp = Float64(y * t);
	elseif (z <= -8e-205)
		tmp = t_2;
	elseif (z <= 3.3e-301)
		tmp = Float64(y * t);
	elseif (z <= 10.5)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -9.5e+36)
		tmp = t_1;
	elseif (z <= -3.3e-18)
		tmp = t_2;
	elseif (z <= -1.02e-106)
		tmp = y * t;
	elseif (z <= -8e-205)
		tmp = t_2;
	elseif (z <= 3.3e-301)
		tmp = y * t;
	elseif (z <= 10.5)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+36], t$95$1, If[LessEqual[z, -3.3e-18], t$95$2, If[LessEqual[z, -1.02e-106], N[(y * t), $MachinePrecision], If[LessEqual[z, -8e-205], t$95$2, If[LessEqual[z, 3.3e-301], N[(y * t), $MachinePrecision], If[LessEqual[z, 10.5], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.49999999999999974e36 or 10.5 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. *-commutative 83.2%

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

      3. distribute-rgt-neg-out 83.2%

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

   4. Simplified 83.2%

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

      1. distribute-rgt-neg-out 83.2%

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

      2. unsub-neg 83.2%

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

   6. Applied egg-rr 83.2%

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

   7. Taylor expanded in z around inf 83.1%

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

   if -9.49999999999999974e36 < z < -3.3000000000000002e-18 or -1.02e-106 < z < -8e-205 or 3.3e-301 < z < 10.5

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 59.5%

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

      1. mul-1-neg 59.5%

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

      2. neg-sub0 59.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0 - \left(y - z\right)\right)}\right) \]

      3. associate-+r- 59.5%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + 0\right) - \left(y - z\right)\right)} \]

      4. metadata-eval 59.5%

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

   4. Simplified 59.5%

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

   5. Taylor expanded in z around 0 59.0%

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

   if -3.3000000000000002e-18 < z < -1.02e-106 or -8e-205 < z < 3.3e-301

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 86.5%

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

      1. *-commutative 86.5%

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

   4. Simplified 86.5%

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

   5. Taylor expanded in t around inf 69.5%

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

      1. *-commutative 69.5%

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

   7. Simplified 69.5%

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

   8. Taylor expanded in x around 0 59.0%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-106}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-205}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-301}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 10.5:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 5: 81.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+36} \lor \neg \left(t \leq -75000000000\right) \land \left(t \leq -4.2 \cdot 10^{-80} \lor \neg \left(t \leq 1.2 \cdot 10^{-32}\right)\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.2e+36)
         (and (not (<= t -75000000000.0))
              (or (<= t -4.2e-80) (not (<= t 1.2e-32)))))
   (+ x (* (- y z) t))
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.2e+36) || (!(t <= -75000000000.0) && ((t <= -4.2e-80) || !(t <= 1.2e-32)))) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-4.2d+36)) .or. (.not. (t <= (-75000000000.0d0))) .and. (t <= (-4.2d-80)) .or. (.not. (t <= 1.2d-32))) then
        tmp = x + ((y - z) * t)
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.2e+36) || (!(t <= -75000000000.0) && ((t <= -4.2e-80) || !(t <= 1.2e-32)))) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.2e+36) or (not (t <= -75000000000.0) and ((t <= -4.2e-80) or not (t <= 1.2e-32))):
		tmp = x + ((y - z) * t)
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.2e+36) || (!(t <= -75000000000.0) && ((t <= -4.2e-80) || !(t <= 1.2e-32))))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.2e+36) || (~((t <= -75000000000.0)) && ((t <= -4.2e-80) || ~((t <= 1.2e-32)))))
		tmp = x + ((y - z) * t);
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.2e+36], And[N[Not[LessEqual[t, -75000000000.0]], $MachinePrecision], Or[LessEqual[t, -4.2e-80], N[Not[LessEqual[t, 1.2e-32]], $MachinePrecision]]]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.20000000000000009e36 or -7.5e10 < t < -4.20000000000000003e-80 or 1.2000000000000001e-32 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 86.4%

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

   if -4.20000000000000009e36 < t < -7.5e10 or -4.20000000000000003e-80 < t < 1.2000000000000001e-32

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 87.2%

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

      1. mul-1-neg 87.2%

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

      2. neg-sub0 87.2%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0 - \left(y - z\right)\right)}\right) \]

      3. associate-+r- 87.2%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + 0\right) - \left(y - z\right)\right)} \]

      4. metadata-eval 87.2%

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

   4. Simplified 87.2%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+36} \lor \neg \left(t \leq -75000000000\right) \land \left(t \leq -4.2 \cdot 10^{-80} \lor \neg \left(t \leq 1.2 \cdot 10^{-32}\right)\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]

Alternative 6: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-16} \lor \neg \left(y \leq 3.8 \cdot 10^{-7}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (- t x)))))
   (if (<= y -2e+136)
     t_1
     (if (<= y -1.9e+109)
       (* x (+ (- z y) 1.0))
       (if (or (<= y -1.85e-16) (not (<= y 3.8e-7)))
         t_1
         (+ x (* z (- x t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (t - x));
	double tmp;
	if (y <= -2e+136) {
		tmp = t_1;
	} else if (y <= -1.9e+109) {
		tmp = x * ((z - y) + 1.0);
	} else if ((y <= -1.85e-16) || !(y <= 3.8e-7)) {
		tmp = t_1;
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (t - x))
    if (y <= (-2d+136)) then
        tmp = t_1
    else if (y <= (-1.9d+109)) then
        tmp = x * ((z - y) + 1.0d0)
    else if ((y <= (-1.85d-16)) .or. (.not. (y <= 3.8d-7))) then
        tmp = t_1
    else
        tmp = x + (z * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (t - x));
	double tmp;
	if (y <= -2e+136) {
		tmp = t_1;
	} else if (y <= -1.9e+109) {
		tmp = x * ((z - y) + 1.0);
	} else if ((y <= -1.85e-16) || !(y <= 3.8e-7)) {
		tmp = t_1;
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (t - x))
	tmp = 0
	if y <= -2e+136:
		tmp = t_1
	elif y <= -1.9e+109:
		tmp = x * ((z - y) + 1.0)
	elif (y <= -1.85e-16) or not (y <= 3.8e-7):
		tmp = t_1
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(t - x)))
	tmp = 0.0
	if (y <= -2e+136)
		tmp = t_1;
	elseif (y <= -1.9e+109)
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	elseif ((y <= -1.85e-16) || !(y <= 3.8e-7))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (t - x));
	tmp = 0.0;
	if (y <= -2e+136)
		tmp = t_1;
	elseif (y <= -1.9e+109)
		tmp = x * ((z - y) + 1.0);
	elseif ((y <= -1.85e-16) || ~((y <= 3.8e-7)))
		tmp = t_1;
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+136], t$95$1, If[LessEqual[y, -1.9e+109], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.85e-16], N[Not[LessEqual[y, 3.8e-7]], $MachinePrecision]], t$95$1, N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.00000000000000012e136 or -1.90000000000000019e109 < y < -1.85e-16 or 3.80000000000000015e-7 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.0%

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

      1. *-commutative 79.0%

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

   4. Simplified 79.0%

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

   if -2.00000000000000012e136 < y < -1.90000000000000019e109

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. neg-sub0 100.0%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0 - \left(y - z\right)\right)}\right) \]

      3. associate-+r- 100.0%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + 0\right) - \left(y - z\right)\right)} \]

      4. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   if -1.85e-16 < y < 3.80000000000000015e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 93.9%

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

      1. mul-1-neg 93.9%

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

      2. *-commutative 93.9%

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

      3. distribute-rgt-neg-out 93.9%

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

   4. Simplified 93.9%

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

      1. distribute-rgt-neg-out 93.9%

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

      2. unsub-neg 93.9%

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

   6. Applied egg-rr 93.9%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+136}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-16} \lor \neg \left(y \leq 3.8 \cdot 10^{-7}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 7: 37.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -21000000000000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-185}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-286}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= y -21000000000000.0)
     (* y (- x))
     (if (<= y -1.85e-185)
       (* z x)
       (if (<= y -1.45e-252)
         t_1
         (if (<= y 2.7e-286) (* z x) (if (<= y 4.2e-7) t_1 (* y t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -21000000000000.0) {
		tmp = y * -x;
	} else if (y <= -1.85e-185) {
		tmp = z * x;
	} else if (y <= -1.45e-252) {
		tmp = t_1;
	} else if (y <= 2.7e-286) {
		tmp = z * x;
	} else if (y <= 4.2e-7) {
		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 <= (-21000000000000.0d0)) then
        tmp = y * -x
    else if (y <= (-1.85d-185)) then
        tmp = z * x
    else if (y <= (-1.45d-252)) then
        tmp = t_1
    else if (y <= 2.7d-286) then
        tmp = z * x
    else if (y <= 4.2d-7) 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 <= -21000000000000.0) {
		tmp = y * -x;
	} else if (y <= -1.85e-185) {
		tmp = z * x;
	} else if (y <= -1.45e-252) {
		tmp = t_1;
	} else if (y <= 2.7e-286) {
		tmp = z * x;
	} else if (y <= 4.2e-7) {
		tmp = t_1;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if y <= -21000000000000.0:
		tmp = y * -x
	elif y <= -1.85e-185:
		tmp = z * x
	elif y <= -1.45e-252:
		tmp = t_1
	elif y <= 2.7e-286:
		tmp = z * x
	elif y <= 4.2e-7:
		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 <= -21000000000000.0)
		tmp = Float64(y * Float64(-x));
	elseif (y <= -1.85e-185)
		tmp = Float64(z * x);
	elseif (y <= -1.45e-252)
		tmp = t_1;
	elseif (y <= 2.7e-286)
		tmp = Float64(z * x);
	elseif (y <= 4.2e-7)
		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 <= -21000000000000.0)
		tmp = y * -x;
	elseif (y <= -1.85e-185)
		tmp = z * x;
	elseif (y <= -1.45e-252)
		tmp = t_1;
	elseif (y <= 2.7e-286)
		tmp = z * x;
	elseif (y <= 4.2e-7)
		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, -21000000000000.0], N[(y * (-x)), $MachinePrecision], If[LessEqual[y, -1.85e-185], N[(z * x), $MachinePrecision], If[LessEqual[y, -1.45e-252], t$95$1, If[LessEqual[y, 2.7e-286], N[(z * x), $MachinePrecision], If[LessEqual[y, 4.2e-7], t$95$1, N[(y * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.1e13

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. neg-sub0 61.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0 - \left(y - z\right)\right)}\right) \]

      3. associate-+r- 61.5%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + 0\right) - \left(y - z\right)\right)} \]

      4. metadata-eval 61.5%

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

   4. Simplified 61.5%

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

   5. Taylor expanded in y around inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. *-commutative 50.1%

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

      3. distribute-rgt-neg-out 50.1%

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

   7. Simplified 50.1%

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

   if -2.1e13 < y < -1.85e-185 or -1.45e-252 < y < 2.7000000000000002e-286

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 67.8%

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

      1. mul-1-neg 67.8%

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

      2. neg-sub0 67.8%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0 - \left(y - z\right)\right)}\right) \]

      3. associate-+r- 67.8%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + 0\right) - \left(y - z\right)\right)} \]

      4. metadata-eval 67.8%

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

   4. Simplified 67.8%

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

   5. Taylor expanded in z around inf 40.4%

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

   if -1.85e-185 < y < -1.45e-252 or 2.7000000000000002e-286 < y < 4.2e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 94.9%

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

      1. mul-1-neg 94.9%

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

      2. *-commutative 94.9%

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

      3. distribute-rgt-neg-out 94.9%

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

   4. Simplified 94.9%

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

      1. distribute-rgt-neg-out 94.9%

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

      2. unsub-neg 94.9%

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

   6. Applied egg-rr 94.9%

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

   7. Taylor expanded in x around 0 52.3%

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

      1. mul-1-neg 52.3%

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

      2. *-commutative 52.3%

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

      3. distribute-rgt-neg-out 52.3%

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

   9. Simplified 52.3%

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

   if 4.2e-7 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.6%

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

      1. *-commutative 79.6%

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

   4. Simplified 79.6%

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

   5. Taylor expanded in t around inf 52.1%

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

      1. *-commutative 52.1%

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

   7. Simplified 52.1%

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

   8. Taylor expanded in x around 0 52.4%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -21000000000000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-185}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-252}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-286}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 8: 70.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-75}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+56}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -2.9e+49)
     t_1
     (if (<= z 5.6e-75)
       (+ x (* y t))
       (if (<= z 4.2e+32)
         (* x (+ (- z y) 1.0))
         (if (<= z 1.45e+56) (* z (- t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -2.9e+49) {
		tmp = t_1;
	} else if (z <= 5.6e-75) {
		tmp = x + (y * t);
	} else if (z <= 4.2e+32) {
		tmp = x * ((z - y) + 1.0);
	} else if (z <= 1.45e+56) {
		tmp = z * -t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-2.9d+49)) then
        tmp = t_1
    else if (z <= 5.6d-75) then
        tmp = x + (y * t)
    else if (z <= 4.2d+32) then
        tmp = x * ((z - y) + 1.0d0)
    else if (z <= 1.45d+56) then
        tmp = z * -t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -2.9e+49) {
		tmp = t_1;
	} else if (z <= 5.6e-75) {
		tmp = x + (y * t);
	} else if (z <= 4.2e+32) {
		tmp = x * ((z - y) + 1.0);
	} else if (z <= 1.45e+56) {
		tmp = z * -t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -2.9e+49:
		tmp = t_1
	elif z <= 5.6e-75:
		tmp = x + (y * t)
	elif z <= 4.2e+32:
		tmp = x * ((z - y) + 1.0)
	elif z <= 1.45e+56:
		tmp = z * -t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -2.9e+49)
		tmp = t_1;
	elseif (z <= 5.6e-75)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 4.2e+32)
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	elseif (z <= 1.45e+56)
		tmp = Float64(z * Float64(-t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -2.9e+49)
		tmp = t_1;
	elseif (z <= 5.6e-75)
		tmp = x + (y * t);
	elseif (z <= 4.2e+32)
		tmp = x * ((z - y) + 1.0);
	elseif (z <= 1.45e+56)
		tmp = z * -t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+49], t$95$1, If[LessEqual[z, 5.6e-75], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+32], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+56], N[(z * (-t)), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.9e49 or 1.45000000000000004e56 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 87.0%

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

      1. mul-1-neg 87.0%

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

      2. *-commutative 87.0%

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

      3. distribute-rgt-neg-out 87.0%

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

   4. Simplified 87.0%

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

      1. distribute-rgt-neg-out 87.0%

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

      2. unsub-neg 87.0%

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

   6. Applied egg-rr 87.0%

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

   7. Taylor expanded in z around inf 87.0%

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

   if -2.9e49 < z < 5.59999999999999996e-75

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 89.7%

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

      1. *-commutative 89.7%

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

   4. Simplified 89.7%

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

   5. Taylor expanded in t around inf 66.5%

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

      1. *-commutative 66.5%

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

   7. Simplified 66.5%

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

   if 5.59999999999999996e-75 < z < 4.2000000000000001e32

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 57.8%

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

      1. mul-1-neg 57.8%

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

      2. neg-sub0 57.8%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0 - \left(y - z\right)\right)}\right) \]

      3. associate-+r- 57.8%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + 0\right) - \left(y - z\right)\right)} \]

      4. metadata-eval 57.8%

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

   4. Simplified 57.8%

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

   if 4.2000000000000001e32 < z < 1.45000000000000004e56

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 57.3%

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

      1. mul-1-neg 57.3%

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

      2. *-commutative 57.3%

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

      3. distribute-rgt-neg-out 57.3%

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

   4. Simplified 57.3%

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

      1. distribute-rgt-neg-out 57.3%

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

      2. unsub-neg 57.3%

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

   6. Applied egg-rr 57.3%

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

   7. Taylor expanded in x around 0 71.5%

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

      1. mul-1-neg 71.5%

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

      2. *-commutative 71.5%

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

      3. distribute-rgt-neg-out 71.5%

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

   9. Simplified 71.5%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-75}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+56}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 9: 37.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+86}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-188}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+76}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.45e+86)
   (* z x)
   (if (<= z 2.55e-188)
     (* y t)
     (if (<= z 2.9e-170) x (if (<= z 4.7e+76) (* y t) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e+86) {
		tmp = z * x;
	} else if (z <= 2.55e-188) {
		tmp = y * t;
	} else if (z <= 2.9e-170) {
		tmp = x;
	} else if (z <= 4.7e+76) {
		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 (z <= (-1.45d+86)) then
        tmp = z * x
    else if (z <= 2.55d-188) then
        tmp = y * t
    else if (z <= 2.9d-170) then
        tmp = x
    else if (z <= 4.7d+76) 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 (z <= -1.45e+86) {
		tmp = z * x;
	} else if (z <= 2.55e-188) {
		tmp = y * t;
	} else if (z <= 2.9e-170) {
		tmp = x;
	} else if (z <= 4.7e+76) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.45e+86:
		tmp = z * x
	elif z <= 2.55e-188:
		tmp = y * t
	elif z <= 2.9e-170:
		tmp = x
	elif z <= 4.7e+76:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.45e+86)
		tmp = Float64(z * x);
	elseif (z <= 2.55e-188)
		tmp = Float64(y * t);
	elseif (z <= 2.9e-170)
		tmp = x;
	elseif (z <= 4.7e+76)
		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 (z <= -1.45e+86)
		tmp = z * x;
	elseif (z <= 2.55e-188)
		tmp = y * t;
	elseif (z <= 2.9e-170)
		tmp = x;
	elseif (z <= 4.7e+76)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.45e+86], N[(z * x), $MachinePrecision], If[LessEqual[z, 2.55e-188], N[(y * t), $MachinePrecision], If[LessEqual[z, 2.9e-170], x, If[LessEqual[z, 4.7e+76], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.44999999999999995e86 or 4.7000000000000003e76 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 63.4%

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

      1. mul-1-neg 63.4%

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

      2. neg-sub0 63.4%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0 - \left(y - z\right)\right)}\right) \]

      3. associate-+r- 63.4%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + 0\right) - \left(y - z\right)\right)} \]

      4. metadata-eval 63.4%

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

   4. Simplified 63.4%

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

   5. Taylor expanded in z around inf 58.3%

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

   if -1.44999999999999995e86 < z < 2.55000000000000005e-188 or 2.9e-170 < z < 4.7000000000000003e76

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 81.2%

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

      1. *-commutative 81.2%

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

   4. Simplified 81.2%

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

   5. Taylor expanded in t around inf 56.9%

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

      1. *-commutative 56.9%

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

   7. Simplified 56.9%

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

   8. Taylor expanded in x around 0 37.0%

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

   if 2.55000000000000005e-188 < z < 2.9e-170

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 84.3%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+86}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-188}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+76}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 10: 70.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+49} \lor \neg \left(z \leq 1.22 \cdot 10^{+19}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.9e+49) (not (<= z 1.22e+19))) (* z (- x t)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9e+49) || !(z <= 1.22e+19)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.9d+49)) .or. (.not. (z <= 1.22d+19))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9e+49) || !(z <= 1.22e+19)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.9e+49) or not (z <= 1.22e+19):
		tmp = z * (x - t)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.9e+49) || !(z <= 1.22e+19))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.9e+49) || ~((z <= 1.22e+19)))
		tmp = z * (x - t);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.9e+49], N[Not[LessEqual[z, 1.22e+19]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9e49 or 1.22e19 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 84.8%

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

      1. mul-1-neg 84.8%

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

      2. *-commutative 84.8%

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

      3. distribute-rgt-neg-out 84.8%

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

   4. Simplified 84.8%

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

      1. distribute-rgt-neg-out 84.8%

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

      2. unsub-neg 84.8%

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

   6. Applied egg-rr 84.8%

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

   7. Taylor expanded in z around inf 84.8%

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

   if -2.9e49 < z < 1.22e19

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 86.2%

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

      1. *-commutative 86.2%

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

   4. Simplified 86.2%

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

   5. Taylor expanded in t around inf 62.6%

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

      1. *-commutative 62.6%

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

   7. Simplified 62.6%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+49} \lor \neg \left(z \leq 1.22 \cdot 10^{+19}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]

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: 36.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-29}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.1e-29) (* y t) (if (<= y 1.4e-82) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.1e-29) {
		tmp = y * t;
	} else if (y <= 1.4e-82) {
		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 <= (-2.1d-29)) then
        tmp = y * t
    else if (y <= 1.4d-82) 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 <= -2.1e-29) {
		tmp = y * t;
	} else if (y <= 1.4e-82) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.1e-29:
		tmp = y * t
	elif y <= 1.4e-82:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.1e-29)
		tmp = Float64(y * t);
	elseif (y <= 1.4e-82)
		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 <= -2.1e-29)
		tmp = y * t;
	elseif (y <= 1.4e-82)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.1e-29], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.4e-82], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.09999999999999989e-29 or 1.40000000000000012e-82 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 70.3%

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

      1. *-commutative 70.3%

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

   4. Simplified 70.3%

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

   5. Taylor expanded in t around inf 40.4%

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

      1. *-commutative 40.4%

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

   7. Simplified 40.4%

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

   8. Taylor expanded in x around 0 38.6%

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

   if -2.09999999999999989e-29 < y < 1.40000000000000012e-82

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 36.0%

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

      1. *-commutative 36.0%

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

   4. Simplified 36.0%

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

   5. Taylor expanded in y around 0 33.3%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-29}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 13: 17.5% 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 y around inf 56.7%

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

   1. *-commutative 56.7%

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

4. Simplified 56.7%

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

5. Taylor expanded in y around 0 16.0%

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

6. Final simplification 16.0%

   \[\leadsto x \]

Developer target: 96.2% 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 2023297 
(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))))