Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.7s

Alternatives: 15

Speedup: 1.0×

• 34.8% 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: 60.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-165}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-303}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.22 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* (- y z) t)))
   (if (<= y -5.2e+17)
     t_1
     (if (<= y -9.2e-104)
       t_2
       (if (<= y -2.4e-165)
         x
         (if (<= y -1.35e-303)
           t_2
           (if (<= y 2.1e-246)
             x
             (if (<= y 2.35e-116)
               t_2
               (if (<= y 2.22e-66) x (if (<= y 5.2e+19) t_2 t_1))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = (y - z) * t;
	double tmp;
	if (y <= -5.2e+17) {
		tmp = t_1;
	} else if (y <= -9.2e-104) {
		tmp = t_2;
	} else if (y <= -2.4e-165) {
		tmp = x;
	} else if (y <= -1.35e-303) {
		tmp = t_2;
	} else if (y <= 2.1e-246) {
		tmp = x;
	} else if (y <= 2.35e-116) {
		tmp = t_2;
	} else if (y <= 2.22e-66) {
		tmp = x;
	} else if (y <= 5.2e+19) {
		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 = (y - z) * t
    if (y <= (-5.2d+17)) then
        tmp = t_1
    else if (y <= (-9.2d-104)) then
        tmp = t_2
    else if (y <= (-2.4d-165)) then
        tmp = x
    else if (y <= (-1.35d-303)) then
        tmp = t_2
    else if (y <= 2.1d-246) then
        tmp = x
    else if (y <= 2.35d-116) then
        tmp = t_2
    else if (y <= 2.22d-66) then
        tmp = x
    else if (y <= 5.2d+19) 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 = (y - z) * t;
	double tmp;
	if (y <= -5.2e+17) {
		tmp = t_1;
	} else if (y <= -9.2e-104) {
		tmp = t_2;
	} else if (y <= -2.4e-165) {
		tmp = x;
	} else if (y <= -1.35e-303) {
		tmp = t_2;
	} else if (y <= 2.1e-246) {
		tmp = x;
	} else if (y <= 2.35e-116) {
		tmp = t_2;
	} else if (y <= 2.22e-66) {
		tmp = x;
	} else if (y <= 5.2e+19) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = (y - z) * t
	tmp = 0
	if y <= -5.2e+17:
		tmp = t_1
	elif y <= -9.2e-104:
		tmp = t_2
	elif y <= -2.4e-165:
		tmp = x
	elif y <= -1.35e-303:
		tmp = t_2
	elif y <= 2.1e-246:
		tmp = x
	elif y <= 2.35e-116:
		tmp = t_2
	elif y <= 2.22e-66:
		tmp = x
	elif y <= 5.2e+19:
		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(Float64(y - z) * t)
	tmp = 0.0
	if (y <= -5.2e+17)
		tmp = t_1;
	elseif (y <= -9.2e-104)
		tmp = t_2;
	elseif (y <= -2.4e-165)
		tmp = x;
	elseif (y <= -1.35e-303)
		tmp = t_2;
	elseif (y <= 2.1e-246)
		tmp = x;
	elseif (y <= 2.35e-116)
		tmp = t_2;
	elseif (y <= 2.22e-66)
		tmp = x;
	elseif (y <= 5.2e+19)
		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 = (y - z) * t;
	tmp = 0.0;
	if (y <= -5.2e+17)
		tmp = t_1;
	elseif (y <= -9.2e-104)
		tmp = t_2;
	elseif (y <= -2.4e-165)
		tmp = x;
	elseif (y <= -1.35e-303)
		tmp = t_2;
	elseif (y <= 2.1e-246)
		tmp = x;
	elseif (y <= 2.35e-116)
		tmp = t_2;
	elseif (y <= 2.22e-66)
		tmp = x;
	elseif (y <= 5.2e+19)
		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[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -5.2e+17], t$95$1, If[LessEqual[y, -9.2e-104], t$95$2, If[LessEqual[y, -2.4e-165], x, If[LessEqual[y, -1.35e-303], t$95$2, If[LessEqual[y, 2.1e-246], x, If[LessEqual[y, 2.35e-116], t$95$2, If[LessEqual[y, 2.22e-66], x, If[LessEqual[y, 5.2e+19], t$95$2, t$95$1]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2e17 or 5.2e19 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 83.1%

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

   if -5.2e17 < y < -9.1999999999999998e-104 or -2.4000000000000002e-165 < y < -1.34999999999999993e-303 or 2.09999999999999995e-246 < y < 2.34999999999999997e-116 or 2.21999999999999996e-66 < y < 5.2e19

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 57.6%

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

   if -9.1999999999999998e-104 < y < -2.4000000000000002e-165 or -1.34999999999999993e-303 < y < 2.09999999999999995e-246 or 2.34999999999999997e-116 < y < 2.21999999999999996e-66

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.2%

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

      1. +-commutative 97.2%

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

      2. mul-1-neg 97.2%

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

      3. unsub-neg 97.2%

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

      4. *-commutative 97.2%

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

   4. Simplified 97.2%

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

   5. Taylor expanded in z around 0 61.3%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-104}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-165}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-303}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-116}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 2.22 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+19}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 3: 70.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x - z \cdot t\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \left(z - -1\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-97}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-163}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-280}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 10^{+18}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (- x (* z t))))
   (if (<= y -6.4e-15)
     t_1
     (if (<= y -1.3e-73)
       (* x (- z -1.0))
       (if (<= y -1.7e-97)
         (* (- y z) t)
         (if (<= y -2.5e-163)
           t_2
           (if (<= y -1.9e-280) (* z (- x t)) (if (<= y 1e+18) 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 - (z * t);
	double tmp;
	if (y <= -6.4e-15) {
		tmp = t_1;
	} else if (y <= -1.3e-73) {
		tmp = x * (z - -1.0);
	} else if (y <= -1.7e-97) {
		tmp = (y - z) * t;
	} else if (y <= -2.5e-163) {
		tmp = t_2;
	} else if (y <= -1.9e-280) {
		tmp = z * (x - t);
	} else if (y <= 1e+18) {
		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 - (z * t)
    if (y <= (-6.4d-15)) then
        tmp = t_1
    else if (y <= (-1.3d-73)) then
        tmp = x * (z - (-1.0d0))
    else if (y <= (-1.7d-97)) then
        tmp = (y - z) * t
    else if (y <= (-2.5d-163)) then
        tmp = t_2
    else if (y <= (-1.9d-280)) then
        tmp = z * (x - t)
    else if (y <= 1d+18) 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 - (z * t);
	double tmp;
	if (y <= -6.4e-15) {
		tmp = t_1;
	} else if (y <= -1.3e-73) {
		tmp = x * (z - -1.0);
	} else if (y <= -1.7e-97) {
		tmp = (y - z) * t;
	} else if (y <= -2.5e-163) {
		tmp = t_2;
	} else if (y <= -1.9e-280) {
		tmp = z * (x - t);
	} else if (y <= 1e+18) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x - (z * t)
	tmp = 0
	if y <= -6.4e-15:
		tmp = t_1
	elif y <= -1.3e-73:
		tmp = x * (z - -1.0)
	elif y <= -1.7e-97:
		tmp = (y - z) * t
	elif y <= -2.5e-163:
		tmp = t_2
	elif y <= -1.9e-280:
		tmp = z * (x - t)
	elif y <= 1e+18:
		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(z * t))
	tmp = 0.0
	if (y <= -6.4e-15)
		tmp = t_1;
	elseif (y <= -1.3e-73)
		tmp = Float64(x * Float64(z - -1.0));
	elseif (y <= -1.7e-97)
		tmp = Float64(Float64(y - z) * t);
	elseif (y <= -2.5e-163)
		tmp = t_2;
	elseif (y <= -1.9e-280)
		tmp = Float64(z * Float64(x - t));
	elseif (y <= 1e+18)
		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 - (z * t);
	tmp = 0.0;
	if (y <= -6.4e-15)
		tmp = t_1;
	elseif (y <= -1.3e-73)
		tmp = x * (z - -1.0);
	elseif (y <= -1.7e-97)
		tmp = (y - z) * t;
	elseif (y <= -2.5e-163)
		tmp = t_2;
	elseif (y <= -1.9e-280)
		tmp = z * (x - t);
	elseif (y <= 1e+18)
		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[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.4e-15], t$95$1, If[LessEqual[y, -1.3e-73], N[(x * N[(z - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e-97], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, -2.5e-163], t$95$2, If[LessEqual[y, -1.9e-280], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+18], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.3999999999999999e-15 or 1e18 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 81.2%

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

   if -6.3999999999999999e-15 < y < -1.3e-73

   1. Initial program 99.9%

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

   2. Taylor expanded in x around -inf 79.8%

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

      1. mul-1-neg 79.8%

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

      2. distribute-rgt-neg-in 79.8%

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

      3. +-commutative 79.8%

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

   4. Simplified 79.8%

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

   5. Taylor expanded in y around 0 79.8%

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

      1. distribute-lft-in 79.8%

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

      2. metadata-eval 79.8%

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

      3. mul-1-neg 79.8%

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

      4. unsub-neg 79.8%

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

   7. Simplified 79.8%

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

   if -1.3e-73 < y < -1.6999999999999999e-97

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

   if -1.6999999999999999e-97 < y < -2.49999999999999989e-163 or -1.9000000000000001e-280 < y < 1e18

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 90.9%

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

      1. +-commutative 90.9%

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

      2. mul-1-neg 90.9%

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

      3. unsub-neg 90.9%

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

      4. *-commutative 90.9%

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

   4. Simplified 90.9%

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

   5. Taylor expanded in t around inf 75.3%

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

      1. *-commutative 75.3%

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

   7. Simplified 75.3%

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

   if -2.49999999999999989e-163 < y < -1.9000000000000001e-280

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 86.9%

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

      1. +-commutative 86.9%

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

      2. mul-1-neg 86.9%

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

      3. sub-neg 86.9%

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

      4. *-commutative 86.9%

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

   7. Simplified 86.9%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-73}:\\ \;\;\;\;x \cdot \left(z - -1\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-97}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-163}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-280}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 10^{+18}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 4: 37.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -y \cdot x\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{+57}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.58 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+166}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y x))))
   (if (<= y -5.4e+144)
     t_1
     (if (<= y -2.15e+57)
       (* y t)
       (if (<= y -1.0)
         t_1
         (if (<= y 1.58e-55) x (if (<= y 2.7e+166) (* y t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -(y * x);
	double tmp;
	if (y <= -5.4e+144) {
		tmp = t_1;
	} else if (y <= -2.15e+57) {
		tmp = y * t;
	} else if (y <= -1.0) {
		tmp = t_1;
	} else if (y <= 1.58e-55) {
		tmp = x;
	} else if (y <= 2.7e+166) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -(y * x)
    if (y <= (-5.4d+144)) then
        tmp = t_1
    else if (y <= (-2.15d+57)) then
        tmp = y * t
    else if (y <= (-1.0d0)) then
        tmp = t_1
    else if (y <= 1.58d-55) then
        tmp = x
    else if (y <= 2.7d+166) then
        tmp = y * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -(y * x);
	double tmp;
	if (y <= -5.4e+144) {
		tmp = t_1;
	} else if (y <= -2.15e+57) {
		tmp = y * t;
	} else if (y <= -1.0) {
		tmp = t_1;
	} else if (y <= 1.58e-55) {
		tmp = x;
	} else if (y <= 2.7e+166) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -(y * x)
	tmp = 0
	if y <= -5.4e+144:
		tmp = t_1
	elif y <= -2.15e+57:
		tmp = y * t
	elif y <= -1.0:
		tmp = t_1
	elif y <= 1.58e-55:
		tmp = x
	elif y <= 2.7e+166:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-Float64(y * x))
	tmp = 0.0
	if (y <= -5.4e+144)
		tmp = t_1;
	elseif (y <= -2.15e+57)
		tmp = Float64(y * t);
	elseif (y <= -1.0)
		tmp = t_1;
	elseif (y <= 1.58e-55)
		tmp = x;
	elseif (y <= 2.7e+166)
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -(y * x);
	tmp = 0.0;
	if (y <= -5.4e+144)
		tmp = t_1;
	elseif (y <= -2.15e+57)
		tmp = y * t;
	elseif (y <= -1.0)
		tmp = t_1;
	elseif (y <= 1.58e-55)
		tmp = x;
	elseif (y <= 2.7e+166)
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = (-N[(y * x), $MachinePrecision])}, If[LessEqual[y, -5.4e+144], t$95$1, If[LessEqual[y, -2.15e+57], N[(y * t), $MachinePrecision], If[LessEqual[y, -1.0], t$95$1, If[LessEqual[y, 1.58e-55], x, If[LessEqual[y, 2.7e+166], N[(y * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.4000000000000003e144 or -2.15000000000000016e57 < y < -1 or 2.70000000000000012e166 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 66.8%

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

      1. mul-1-neg 66.8%

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

      2. distribute-rgt-neg-in 66.8%

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

      3. +-commutative 66.8%

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

   4. Simplified 66.8%

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

   5. Taylor expanded in y around inf 60.5%

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

   if -5.4000000000000003e144 < y < -2.15000000000000016e57 or 1.58000000000000007e-55 < y < 2.70000000000000012e166

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 62.8%

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

   3. Taylor expanded in t around inf 46.5%

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

   if -1 < y < 1.58000000000000007e-55

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 92.8%

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

      1. +-commutative 92.8%

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

      2. mul-1-neg 92.8%

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

      3. unsub-neg 92.8%

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

      4. *-commutative 92.8%

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

   4. Simplified 92.8%

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

   5. Taylor expanded in z around 0 35.3%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+144}:\\ \;\;\;\;-y \cdot x\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{+57}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;-y \cdot x\\ \mathbf{elif}\;y \leq 1.58 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+166}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;-y \cdot x\\ \end{array} \]

Alternative 5: 67.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-117}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{+16}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -6.5e+36)
     t_1
     (if (<= y 3.2e-117)
       (* z (- x t))
       (if (<= y 5.4e-65) x (if (<= y 6.9e+16) (* (- y z) t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -6.5e+36) {
		tmp = t_1;
	} else if (y <= 3.2e-117) {
		tmp = z * (x - t);
	} else if (y <= 5.4e-65) {
		tmp = x;
	} else if (y <= 6.9e+16) {
		tmp = (y - z) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t - x)
    if (y <= (-6.5d+36)) then
        tmp = t_1
    else if (y <= 3.2d-117) then
        tmp = z * (x - t)
    else if (y <= 5.4d-65) then
        tmp = x
    else if (y <= 6.9d+16) then
        tmp = (y - z) * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -6.5e+36) {
		tmp = t_1;
	} else if (y <= 3.2e-117) {
		tmp = z * (x - t);
	} else if (y <= 5.4e-65) {
		tmp = x;
	} else if (y <= 6.9e+16) {
		tmp = (y - z) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -6.5e+36:
		tmp = t_1
	elif y <= 3.2e-117:
		tmp = z * (x - t)
	elif y <= 5.4e-65:
		tmp = x
	elif y <= 6.9e+16:
		tmp = (y - z) * t
	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 <= -6.5e+36)
		tmp = t_1;
	elseif (y <= 3.2e-117)
		tmp = Float64(z * Float64(x - t));
	elseif (y <= 5.4e-65)
		tmp = x;
	elseif (y <= 6.9e+16)
		tmp = Float64(Float64(y - z) * t);
	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 <= -6.5e+36)
		tmp = t_1;
	elseif (y <= 3.2e-117)
		tmp = z * (x - t);
	elseif (y <= 5.4e-65)
		tmp = x;
	elseif (y <= 6.9e+16)
		tmp = (y - z) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+36], t$95$1, If[LessEqual[y, 3.2e-117], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e-65], x, If[LessEqual[y, 6.9e+16], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.4999999999999998e36 or 6.9e16 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 84.2%

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

   if -6.4999999999999998e36 < y < 3.19999999999999995e-117

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 62.6%

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

      1. +-commutative 62.6%

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

      2. mul-1-neg 62.6%

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

      3. sub-neg 62.6%

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

      4. *-commutative 62.6%

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

   7. Simplified 62.6%

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

   if 3.19999999999999995e-117 < y < 5.3999999999999997e-65

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 87.6%

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

      1. +-commutative 87.6%

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

      2. mul-1-neg 87.6%

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

      3. unsub-neg 87.6%

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

      4. *-commutative 87.6%

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

   4. Simplified 87.6%

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

   5. Taylor expanded in z around 0 75.4%

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

   if 5.3999999999999997e-65 < y < 6.9e16

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 74.4%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-117}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{+16}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 6: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := z \cdot \left(x - t\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-20}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* z (- x t))))
   (if (<= y -7.2e+34)
     t_1
     (if (<= y 1.3e-116)
       t_2
       (if (<= y 2.2e-20) (+ x (* y t)) (if (<= y 3e+29) t_2 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 tmp;
	if (y <= -7.2e+34) {
		tmp = t_1;
	} else if (y <= 1.3e-116) {
		tmp = t_2;
	} else if (y <= 2.2e-20) {
		tmp = x + (y * t);
	} else if (y <= 3e+29) {
		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 = z * (x - t)
    if (y <= (-7.2d+34)) then
        tmp = t_1
    else if (y <= 1.3d-116) then
        tmp = t_2
    else if (y <= 2.2d-20) then
        tmp = x + (y * t)
    else if (y <= 3d+29) 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 = z * (x - t);
	double tmp;
	if (y <= -7.2e+34) {
		tmp = t_1;
	} else if (y <= 1.3e-116) {
		tmp = t_2;
	} else if (y <= 2.2e-20) {
		tmp = x + (y * t);
	} else if (y <= 3e+29) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = z * (x - t)
	tmp = 0
	if y <= -7.2e+34:
		tmp = t_1
	elif y <= 1.3e-116:
		tmp = t_2
	elif y <= 2.2e-20:
		tmp = x + (y * t)
	elif y <= 3e+29:
		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(z * Float64(x - t))
	tmp = 0.0
	if (y <= -7.2e+34)
		tmp = t_1;
	elseif (y <= 1.3e-116)
		tmp = t_2;
	elseif (y <= 2.2e-20)
		tmp = Float64(x + Float64(y * t));
	elseif (y <= 3e+29)
		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 = z * (x - t);
	tmp = 0.0;
	if (y <= -7.2e+34)
		tmp = t_1;
	elseif (y <= 1.3e-116)
		tmp = t_2;
	elseif (y <= 2.2e-20)
		tmp = x + (y * t);
	elseif (y <= 3e+29)
		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[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e+34], t$95$1, If[LessEqual[y, 1.3e-116], t$95$2, If[LessEqual[y, 2.2e-20], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+29], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.2000000000000001e34 or 2.9999999999999999e29 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 85.4%

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

   if -7.2000000000000001e34 < y < 1.3e-116 or 2.19999999999999991e-20 < y < 2.9999999999999999e29

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 99.1%

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

      1. fma-def 99.1%

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

      2. mul-1-neg 99.1%

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

   4. Simplified 99.1%

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

   5. Taylor expanded in z around inf 63.5%

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

      1. +-commutative 63.5%

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

      2. mul-1-neg 63.5%

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

      3. sub-neg 63.5%

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

      4. *-commutative 63.5%

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

   7. Simplified 63.5%

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

   if 1.3e-116 < y < 2.19999999999999991e-20

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 75.5%

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

   3. Taylor expanded in t around inf 75.5%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+34}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-116}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-20}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 7: 54.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-258}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -4.5e-69)
     t_1
     (if (<= t 1.8e-258) (* z x) (if (<= t 6.9e-119) (* y (- x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -4.5e-69) {
		tmp = t_1;
	} else if (t <= 1.8e-258) {
		tmp = z * x;
	} else if (t <= 6.9e-119) {
		tmp = y * -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 <= (-4.5d-69)) then
        tmp = t_1
    else if (t <= 1.8d-258) then
        tmp = z * x
    else if (t <= 6.9d-119) then
        tmp = y * -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 <= -4.5e-69) {
		tmp = t_1;
	} else if (t <= 1.8e-258) {
		tmp = z * x;
	} else if (t <= 6.9e-119) {
		tmp = y * -x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -4.5e-69:
		tmp = t_1
	elif t <= 1.8e-258:
		tmp = z * x
	elif t <= 6.9e-119:
		tmp = y * -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 <= -4.5e-69)
		tmp = t_1;
	elseif (t <= 1.8e-258)
		tmp = Float64(z * x);
	elseif (t <= 6.9e-119)
		tmp = Float64(y * Float64(-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 <= -4.5e-69)
		tmp = t_1;
	elseif (t <= 1.8e-258)
		tmp = z * x;
	elseif (t <= 6.9e-119)
		tmp = y * -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, -4.5e-69], t$95$1, If[LessEqual[t, 1.8e-258], N[(z * x), $MachinePrecision], If[LessEqual[t, 6.9e-119], N[(y * (-x)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.50000000000000009e-69 or 6.89999999999999953e-119 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 75.2%

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

   if -4.50000000000000009e-69 < t < 1.79999999999999989e-258

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 48.1%

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

      1. +-commutative 48.1%

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

      2. mul-1-neg 48.1%

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

      3. sub-neg 48.1%

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

      4. *-commutative 48.1%

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

   7. Simplified 48.1%

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

   8. Taylor expanded in x around inf 46.0%

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

   if 1.79999999999999989e-258 < t < 6.89999999999999953e-119

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 89.9%

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

      1. mul-1-neg 89.9%

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

      2. distribute-rgt-neg-in 89.9%

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

      3. +-commutative 89.9%

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

   4. Simplified 89.9%

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

   5. Taylor expanded in y around inf 44.6%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-69}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-258}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]

Alternative 8: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -30000000000 \lor \neg \left(z \leq 1.3 \cdot 10^{+36}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -30000000000.0) (not (<= z 1.3e+36)))
   (* z (- x t))
   (- x (* y (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -30000000000.0) || !(z <= 1.3e+36)) {
		tmp = z * (x - t);
	} else {
		tmp = x - (y * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-30000000000.0d0)) .or. (.not. (z <= 1.3d+36))) then
        tmp = z * (x - t)
    else
        tmp = x - (y * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -30000000000.0) || !(z <= 1.3e+36)) {
		tmp = z * (x - t);
	} else {
		tmp = x - (y * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -30000000000.0) or not (z <= 1.3e+36):
		tmp = z * (x - t)
	else:
		tmp = x - (y * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -30000000000.0) || !(z <= 1.3e+36))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x - Float64(y * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -30000000000.0) || ~((z <= 1.3e+36)))
		tmp = z * (x - t);
	else
		tmp = x - (y * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -30000000000.0], N[Not[LessEqual[z, 1.3e+36]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3e10 or 1.3000000000000001e36 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 94.8%

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

      1. fma-def 97.4%

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

      2. mul-1-neg 97.4%

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

   4. Simplified 97.4%

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

   5. Taylor expanded in z around inf 82.3%

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

      1. +-commutative 82.3%

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

      2. mul-1-neg 82.3%

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

      3. sub-neg 82.3%

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

      4. *-commutative 82.3%

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

   7. Simplified 82.3%

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

   if -3e10 < z < 1.3000000000000001e36

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 87.3%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -30000000000 \lor \neg \left(z \leq 1.3 \cdot 10^{+36}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \]

Alternative 9: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+31}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.4e+35)
   (* y (- t x))
   (if (<= y 1.75e+31) (+ x (* z (- x t))) (- x (* y (- x t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e+35) {
		tmp = y * (t - x);
	} else if (y <= 1.75e+31) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x - (y * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.4d+35)) then
        tmp = y * (t - x)
    else if (y <= 1.75d+31) then
        tmp = x + (z * (x - t))
    else
        tmp = x - (y * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e+35) {
		tmp = y * (t - x);
	} else if (y <= 1.75e+31) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x - (y * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.4e+35:
		tmp = y * (t - x)
	elif y <= 1.75e+31:
		tmp = x + (z * (x - t))
	else:
		tmp = x - (y * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.4e+35)
		tmp = Float64(y * Float64(t - x));
	elseif (y <= 1.75e+31)
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = Float64(x - Float64(y * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.4e+35)
		tmp = y * (t - x);
	elseif (y <= 1.75e+31)
		tmp = x + (z * (x - t));
	else
		tmp = x - (y * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.4e+35], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e+31], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4000000000000001e35

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 91.2%

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

   if -3.4000000000000001e35 < y < 1.75e31

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 89.1%

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

      1. +-commutative 89.1%

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

      2. mul-1-neg 89.1%

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

      3. unsub-neg 89.1%

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

      4. *-commutative 89.1%

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

   4. Simplified 89.1%

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

   if 1.75e31 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 80.8%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+31}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \]

Alternative 10: 34.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-47}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-258}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.05e-47)
   (* y t)
   (if (<= t 2.1e-258) (* z x) (if (<= t 4.9e-119) (* y (- x)) (* t (- z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.05e-47) {
		tmp = y * t;
	} else if (t <= 2.1e-258) {
		tmp = z * x;
	} else if (t <= 4.9e-119) {
		tmp = y * -x;
	} else {
		tmp = t * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.05d-47)) then
        tmp = y * t
    else if (t <= 2.1d-258) then
        tmp = z * x
    else if (t <= 4.9d-119) then
        tmp = y * -x
    else
        tmp = t * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.05e-47) {
		tmp = y * t;
	} else if (t <= 2.1e-258) {
		tmp = z * x;
	} else if (t <= 4.9e-119) {
		tmp = y * -x;
	} else {
		tmp = t * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.05e-47:
		tmp = y * t
	elif t <= 2.1e-258:
		tmp = z * x
	elif t <= 4.9e-119:
		tmp = y * -x
	else:
		tmp = t * -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.05e-47)
		tmp = Float64(y * t);
	elseif (t <= 2.1e-258)
		tmp = Float64(z * x);
	elseif (t <= 4.9e-119)
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(t * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.05e-47)
		tmp = y * t;
	elseif (t <= 2.1e-258)
		tmp = z * x;
	elseif (t <= 4.9e-119)
		tmp = y * -x;
	else
		tmp = t * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.05e-47], N[(y * t), $MachinePrecision], If[LessEqual[t, 2.1e-258], N[(z * x), $MachinePrecision], If[LessEqual[t, 4.9e-119], N[(y * (-x)), $MachinePrecision], N[(t * (-z)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.05e-47

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 66.8%

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

   3. Taylor expanded in t around inf 54.4%

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

   if -1.05e-47 < t < 2.0999999999999999e-258

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 48.3%

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

      1. +-commutative 48.3%

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

      2. mul-1-neg 48.3%

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

      3. sub-neg 48.3%

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

      4. *-commutative 48.3%

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

   7. Simplified 48.3%

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

   8. Taylor expanded in x around inf 42.9%

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

   if 2.0999999999999999e-258 < t < 4.9e-119

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 89.9%

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

      1. mul-1-neg 89.9%

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

      2. distribute-rgt-neg-in 89.9%

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

      3. +-commutative 89.9%

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

   4. Simplified 89.9%

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

   5. Taylor expanded in y around inf 44.6%

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

   if 4.9e-119 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 52.7%

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

      1. mul-1-neg 52.7%

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

      2. distribute-lft-neg-out 52.7%

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

      3. *-commutative 52.7%

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

   4. Simplified 52.7%

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

   5. Taylor expanded in t around inf 43.3%

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

      1. associate-*r* 43.3%

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

      2. mul-1-neg 43.3%

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

   7. Simplified 43.3%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-47}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-258}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-119}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \end{array} \]

Alternative 11: 34.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-48}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-208}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.15e-48)
   (* y t)
   (if (<= t 1.15e-208) (* z x) (if (<= t 4.8e-83) x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.15e-48) {
		tmp = y * t;
	} else if (t <= 1.15e-208) {
		tmp = z * x;
	} else if (t <= 4.8e-83) {
		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 (t <= (-2.15d-48)) then
        tmp = y * t
    else if (t <= 1.15d-208) then
        tmp = z * x
    else if (t <= 4.8d-83) 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 (t <= -2.15e-48) {
		tmp = y * t;
	} else if (t <= 1.15e-208) {
		tmp = z * x;
	} else if (t <= 4.8e-83) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.15e-48:
		tmp = y * t
	elif t <= 1.15e-208:
		tmp = z * x
	elif t <= 4.8e-83:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.15e-48)
		tmp = Float64(y * t);
	elseif (t <= 1.15e-208)
		tmp = Float64(z * x);
	elseif (t <= 4.8e-83)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.15e-48)
		tmp = y * t;
	elseif (t <= 1.15e-208)
		tmp = z * x;
	elseif (t <= 4.8e-83)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.15e-48], N[(y * t), $MachinePrecision], If[LessEqual[t, 1.15e-208], N[(z * x), $MachinePrecision], If[LessEqual[t, 4.8e-83], x, N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.15e-48 or 4.8000000000000002e-83 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 55.5%

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

   3. Taylor expanded in t around inf 43.9%

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

   if -2.15e-48 < t < 1.14999999999999998e-208

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 46.6%

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

      1. +-commutative 46.6%

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

      2. mul-1-neg 46.6%

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

      3. sub-neg 46.6%

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

      4. *-commutative 46.6%

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

   7. Simplified 46.6%

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

   8. Taylor expanded in x around inf 41.3%

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

   if 1.14999999999999998e-208 < t < 4.8000000000000002e-83

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 64.6%

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

      1. +-commutative 64.6%

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

      2. mul-1-neg 64.6%

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

      3. unsub-neg 64.6%

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

      4. *-commutative 64.6%

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

   4. Simplified 64.6%

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

   5. Taylor expanded in z around 0 41.2%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-48}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-208}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 12: 71.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+34} \lor \neg \left(y \leq 10^{+18}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.6e+34) (not (<= y 1e+18))) (* y (- t x)) (- x (* z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.6e+34) || !(y <= 1e+18)) {
		tmp = y * (t - x);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.6d+34)) .or. (.not. (y <= 1d+18))) then
        tmp = y * (t - x)
    else
        tmp = x - (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.6e+34) || !(y <= 1e+18)) {
		tmp = y * (t - x);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.6e+34) or not (y <= 1e+18):
		tmp = y * (t - x)
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.6e+34) || !(y <= 1e+18))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.6e+34) || ~((y <= 1e+18)))
		tmp = y * (t - x);
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.6e+34], N[Not[LessEqual[y, 1e+18]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6e34 or 1e18 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 84.2%

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

   if -3.6e34 < y < 1e18

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 89.5%

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

      1. +-commutative 89.5%

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

      2. mul-1-neg 89.5%

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

      3. unsub-neg 89.5%

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

      4. *-commutative 89.5%

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

   4. Simplified 89.5%

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

   5. Taylor expanded in t around inf 68.2%

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

      1. *-commutative 68.2%

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

   7. Simplified 68.2%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+34} \lor \neg \left(y \leq 10^{+18}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]

Alternative 13: 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 14: 36.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-17}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2e-17) (* y t) (if (<= y 6e-61) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2e-17) {
		tmp = y * t;
	} else if (y <= 6e-61) {
		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 <= (-2d-17)) then
        tmp = y * t
    else if (y <= 6d-61) 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 <= -2e-17) {
		tmp = y * t;
	} else if (y <= 6e-61) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2e-17:
		tmp = y * t
	elif y <= 6e-61:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2e-17)
		tmp = Float64(y * t);
	elseif (y <= 6e-61)
		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 <= -2e-17)
		tmp = y * t;
	elseif (y <= 6e-61)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2e-17], N[(y * t), $MachinePrecision], If[LessEqual[y, 6e-61], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.00000000000000014e-17 or 6.00000000000000024e-61 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 75.2%

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

   3. Taylor expanded in t around inf 42.2%

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

   if -2.00000000000000014e-17 < y < 6.00000000000000024e-61

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 94.2%

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

      1. +-commutative 94.2%

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

      2. mul-1-neg 94.2%

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

      3. unsub-neg 94.2%

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

      4. *-commutative 94.2%

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

   4. Simplified 94.2%

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

   5. Taylor expanded in z around 0 36.3%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-17}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 15: 17.9% 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 0 60.0%

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

   1. +-commutative 60.0%

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

   2. mul-1-neg 60.0%

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

   3. unsub-neg 60.0%

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

   4. *-commutative 60.0%

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

4. Simplified 60.0%

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

5. Taylor expanded in z around 0 17.0%

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

6. Final simplification 17.0%

   \[\leadsto x \]

Developer target: 96.0% 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 2023208 
(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))))