Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.2s

Alternatives: 14

Speedup: 1.0×

• 34.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y - z) * (t - x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y - z) * (t - x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 49.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := y \cdot \left(-x\right)\\ t_3 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+162}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+24}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1650:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-215}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+14}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (* y (- x))) (t_3 (* x (+ z 1.0))))
   (if (<= y -9.5e+162)
     (* y t)
     (if (<= y -1.9e+77)
       t_2
       (if (<= y -9.5e+24)
         (* y t)
         (if (<= y -1650.0)
           t_2
           (if (<= y -1.4e-15)
             t_1
             (if (<= y -2.05e-215)
               t_3
               (if (<= y -1.05e-236)
                 t_1
                 (if (<= y 8.5e+14) t_3 (* y t)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = y * -x;
	double t_3 = x * (z + 1.0);
	double tmp;
	if (y <= -9.5e+162) {
		tmp = y * t;
	} else if (y <= -1.9e+77) {
		tmp = t_2;
	} else if (y <= -9.5e+24) {
		tmp = y * t;
	} else if (y <= -1650.0) {
		tmp = t_2;
	} else if (y <= -1.4e-15) {
		tmp = t_1;
	} else if (y <= -2.05e-215) {
		tmp = t_3;
	} else if (y <= -1.05e-236) {
		tmp = t_1;
	} else if (y <= 8.5e+14) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = z * -t
    t_2 = y * -x
    t_3 = x * (z + 1.0d0)
    if (y <= (-9.5d+162)) then
        tmp = y * t
    else if (y <= (-1.9d+77)) then
        tmp = t_2
    else if (y <= (-9.5d+24)) then
        tmp = y * t
    else if (y <= (-1650.0d0)) then
        tmp = t_2
    else if (y <= (-1.4d-15)) then
        tmp = t_1
    else if (y <= (-2.05d-215)) then
        tmp = t_3
    else if (y <= (-1.05d-236)) then
        tmp = t_1
    else if (y <= 8.5d+14) then
        tmp = t_3
    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 = y * -x;
	double t_3 = x * (z + 1.0);
	double tmp;
	if (y <= -9.5e+162) {
		tmp = y * t;
	} else if (y <= -1.9e+77) {
		tmp = t_2;
	} else if (y <= -9.5e+24) {
		tmp = y * t;
	} else if (y <= -1650.0) {
		tmp = t_2;
	} else if (y <= -1.4e-15) {
		tmp = t_1;
	} else if (y <= -2.05e-215) {
		tmp = t_3;
	} else if (y <= -1.05e-236) {
		tmp = t_1;
	} else if (y <= 8.5e+14) {
		tmp = t_3;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	t_2 = y * -x
	t_3 = x * (z + 1.0)
	tmp = 0
	if y <= -9.5e+162:
		tmp = y * t
	elif y <= -1.9e+77:
		tmp = t_2
	elif y <= -9.5e+24:
		tmp = y * t
	elif y <= -1650.0:
		tmp = t_2
	elif y <= -1.4e-15:
		tmp = t_1
	elif y <= -2.05e-215:
		tmp = t_3
	elif y <= -1.05e-236:
		tmp = t_1
	elif y <= 8.5e+14:
		tmp = t_3
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	t_2 = Float64(y * Float64(-x))
	t_3 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= -9.5e+162)
		tmp = Float64(y * t);
	elseif (y <= -1.9e+77)
		tmp = t_2;
	elseif (y <= -9.5e+24)
		tmp = Float64(y * t);
	elseif (y <= -1650.0)
		tmp = t_2;
	elseif (y <= -1.4e-15)
		tmp = t_1;
	elseif (y <= -2.05e-215)
		tmp = t_3;
	elseif (y <= -1.05e-236)
		tmp = t_1;
	elseif (y <= 8.5e+14)
		tmp = t_3;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	t_2 = y * -x;
	t_3 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= -9.5e+162)
		tmp = y * t;
	elseif (y <= -1.9e+77)
		tmp = t_2;
	elseif (y <= -9.5e+24)
		tmp = y * t;
	elseif (y <= -1650.0)
		tmp = t_2;
	elseif (y <= -1.4e-15)
		tmp = t_1;
	elseif (y <= -2.05e-215)
		tmp = t_3;
	elseif (y <= -1.05e-236)
		tmp = t_1;
	elseif (y <= 8.5e+14)
		tmp = t_3;
	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[(y * (-x)), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+162], N[(y * t), $MachinePrecision], If[LessEqual[y, -1.9e+77], t$95$2, If[LessEqual[y, -9.5e+24], N[(y * t), $MachinePrecision], If[LessEqual[y, -1650.0], t$95$2, If[LessEqual[y, -1.4e-15], t$95$1, If[LessEqual[y, -2.05e-215], t$95$3, If[LessEqual[y, -1.05e-236], t$95$1, If[LessEqual[y, 8.5e+14], t$95$3, N[(y * t), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.50000000000000021e162 or -1.9000000000000001e77 < y < -9.5000000000000001e24 or 8.5e14 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 68.8%

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

   3. Taylor expanded in y around inf 59.4%

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

   if -9.50000000000000021e162 < y < -1.9000000000000001e77 or -9.5000000000000001e24 < y < -1650

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 75.4%

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

      1. *-commutative 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. distribute-lft-out-- 75.4%

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

      5. *-rgt-identity 75.4%

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

   4. Simplified 75.4%

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

   5. Taylor expanded in z around 0 71.8%

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

   6. Taylor expanded in y around inf 55.9%

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

      1. mul-1-neg 55.9%

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

      2. distribute-rgt-neg-in 55.9%

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

   8. Simplified 55.9%

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

   if -1650 < y < -1.40000000000000007e-15 or -2.04999999999999992e-215 < y < -1.04999999999999989e-236

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 94.2%

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

   3. Taylor expanded in z around inf 77.5%

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

      1. mul-1-neg 77.5%

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

      2. distribute-rgt-neg-out 77.5%

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

   5. Simplified 77.5%

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

   if -1.40000000000000007e-15 < y < -2.04999999999999992e-215 or -1.04999999999999989e-236 < y < 8.5e14

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 93.0%

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

      1. +-commutative 93.0%

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

      2. mul-1-neg 93.0%

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

      3. unsub-neg 93.0%

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

      4. *-commutative 93.0%

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

   4. Simplified 93.0%

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

   5. Taylor expanded in x around -inf 62.9%

      \[\leadsto \color{blue}{\left(1 + z\right) \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+162}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+24}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1650:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-15}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-215}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-236}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 3: 37.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+159}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-89}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-301}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+21}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -2.1e+210)
     t_1
     (if (<= z -8e+159)
       (* z x)
       (if (<= z -2.2e-28)
         t_1
         (if (<= z -1.52e-89)
           (* y t)
           (if (<= z -3.2e-184)
             (* y (- x))
             (if (<= z 2.95e-301) x (if (<= z 1.65e+21) (* y t) t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -2.1e+210) {
		tmp = t_1;
	} else if (z <= -8e+159) {
		tmp = z * x;
	} else if (z <= -2.2e-28) {
		tmp = t_1;
	} else if (z <= -1.52e-89) {
		tmp = y * t;
	} else if (z <= -3.2e-184) {
		tmp = y * -x;
	} else if (z <= 2.95e-301) {
		tmp = x;
	} else if (z <= 1.65e+21) {
		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 = z * -t
    if (z <= (-2.1d+210)) then
        tmp = t_1
    else if (z <= (-8d+159)) then
        tmp = z * x
    else if (z <= (-2.2d-28)) then
        tmp = t_1
    else if (z <= (-1.52d-89)) then
        tmp = y * t
    else if (z <= (-3.2d-184)) then
        tmp = y * -x
    else if (z <= 2.95d-301) then
        tmp = x
    else if (z <= 1.65d+21) 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 = z * -t;
	double tmp;
	if (z <= -2.1e+210) {
		tmp = t_1;
	} else if (z <= -8e+159) {
		tmp = z * x;
	} else if (z <= -2.2e-28) {
		tmp = t_1;
	} else if (z <= -1.52e-89) {
		tmp = y * t;
	} else if (z <= -3.2e-184) {
		tmp = y * -x;
	} else if (z <= 2.95e-301) {
		tmp = x;
	} else if (z <= 1.65e+21) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -2.1e+210:
		tmp = t_1
	elif z <= -8e+159:
		tmp = z * x
	elif z <= -2.2e-28:
		tmp = t_1
	elif z <= -1.52e-89:
		tmp = y * t
	elif z <= -3.2e-184:
		tmp = y * -x
	elif z <= 2.95e-301:
		tmp = x
	elif z <= 1.65e+21:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -2.1e+210)
		tmp = t_1;
	elseif (z <= -8e+159)
		tmp = Float64(z * x);
	elseif (z <= -2.2e-28)
		tmp = t_1;
	elseif (z <= -1.52e-89)
		tmp = Float64(y * t);
	elseif (z <= -3.2e-184)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 2.95e-301)
		tmp = x;
	elseif (z <= 1.65e+21)
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -2.1e+210)
		tmp = t_1;
	elseif (z <= -8e+159)
		tmp = z * x;
	elseif (z <= -2.2e-28)
		tmp = t_1;
	elseif (z <= -1.52e-89)
		tmp = y * t;
	elseif (z <= -3.2e-184)
		tmp = y * -x;
	elseif (z <= 2.95e-301)
		tmp = x;
	elseif (z <= 1.65e+21)
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -2.1e+210], t$95$1, If[LessEqual[z, -8e+159], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.2e-28], t$95$1, If[LessEqual[z, -1.52e-89], N[(y * t), $MachinePrecision], If[LessEqual[z, -3.2e-184], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 2.95e-301], x, If[LessEqual[z, 1.65e+21], N[(y * t), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.0999999999999999e210 or -7.9999999999999994e159 < z < -2.19999999999999996e-28 or 1.65e21 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 64.9%

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

   3. Taylor expanded in z around inf 53.7%

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

      1. mul-1-neg 53.7%

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

      2. distribute-rgt-neg-out 53.7%

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

   5. Simplified 53.7%

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

   if -2.0999999999999999e210 < z < -7.9999999999999994e159

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 59.4%

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

      1. *-commutative 59.4%

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

      2. mul-1-neg 59.4%

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

      3. unsub-neg 59.4%

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

      4. distribute-lft-out-- 59.4%

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

      5. *-rgt-identity 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in z around inf 58.7%

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

   if -2.19999999999999996e-28 < z < -1.52e-89 or 2.9499999999999999e-301 < z < 1.65e21

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 82.1%

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

   3. Taylor expanded in y around inf 47.4%

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

   if -1.52e-89 < z < -3.2e-184

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 83.6%

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

      1. *-commutative 83.6%

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

      2. mul-1-neg 83.6%

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

      3. unsub-neg 83.6%

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

      4. distribute-lft-out-- 83.6%

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

      5. *-rgt-identity 83.6%

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

   4. Simplified 83.6%

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

   5. Taylor expanded in z around 0 83.6%

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

   6. Taylor expanded in y around inf 67.4%

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

      1. mul-1-neg 67.4%

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

      2. distribute-rgt-neg-in 67.4%

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

   8. Simplified 67.4%

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

   if -3.2e-184 < z < 2.9499999999999999e-301

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 84.4%

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

   3. Taylor expanded in x around inf 58.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+210}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{+159}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-89}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-301}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+21}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]

Alternative 4: 53.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot t\\ t_2 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+210}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{+171}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-184}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y t))) (t_2 (* z (- t))))
   (if (<= z -6.5e+210)
     t_2
     (if (<= z -6.4e+171)
       (* z x)
       (if (<= z -1.95e+43)
         t_2
         (if (<= z -4.5e-87)
           t_1
           (if (<= z -4.3e-184)
             (- x (* y x))
             (if (<= z 1.35e+19) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double t_2 = z * -t;
	double tmp;
	if (z <= -6.5e+210) {
		tmp = t_2;
	} else if (z <= -6.4e+171) {
		tmp = z * x;
	} else if (z <= -1.95e+43) {
		tmp = t_2;
	} else if (z <= -4.5e-87) {
		tmp = t_1;
	} else if (z <= -4.3e-184) {
		tmp = x - (y * x);
	} else if (z <= 1.35e+19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * t)
    t_2 = z * -t
    if (z <= (-6.5d+210)) then
        tmp = t_2
    else if (z <= (-6.4d+171)) then
        tmp = z * x
    else if (z <= (-1.95d+43)) then
        tmp = t_2
    else if (z <= (-4.5d-87)) then
        tmp = t_1
    else if (z <= (-4.3d-184)) then
        tmp = x - (y * x)
    else if (z <= 1.35d+19) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double t_2 = z * -t;
	double tmp;
	if (z <= -6.5e+210) {
		tmp = t_2;
	} else if (z <= -6.4e+171) {
		tmp = z * x;
	} else if (z <= -1.95e+43) {
		tmp = t_2;
	} else if (z <= -4.5e-87) {
		tmp = t_1;
	} else if (z <= -4.3e-184) {
		tmp = x - (y * x);
	} else if (z <= 1.35e+19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * t)
	t_2 = z * -t
	tmp = 0
	if z <= -6.5e+210:
		tmp = t_2
	elif z <= -6.4e+171:
		tmp = z * x
	elif z <= -1.95e+43:
		tmp = t_2
	elif z <= -4.5e-87:
		tmp = t_1
	elif z <= -4.3e-184:
		tmp = x - (y * x)
	elif z <= 1.35e+19:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * t))
	t_2 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -6.5e+210)
		tmp = t_2;
	elseif (z <= -6.4e+171)
		tmp = Float64(z * x);
	elseif (z <= -1.95e+43)
		tmp = t_2;
	elseif (z <= -4.5e-87)
		tmp = t_1;
	elseif (z <= -4.3e-184)
		tmp = Float64(x - Float64(y * x));
	elseif (z <= 1.35e+19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * t);
	t_2 = z * -t;
	tmp = 0.0;
	if (z <= -6.5e+210)
		tmp = t_2;
	elseif (z <= -6.4e+171)
		tmp = z * x;
	elseif (z <= -1.95e+43)
		tmp = t_2;
	elseif (z <= -4.5e-87)
		tmp = t_1;
	elseif (z <= -4.3e-184)
		tmp = x - (y * x);
	elseif (z <= 1.35e+19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -6.5e+210], t$95$2, If[LessEqual[z, -6.4e+171], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.95e+43], t$95$2, If[LessEqual[z, -4.5e-87], t$95$1, If[LessEqual[z, -4.3e-184], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+19], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.4999999999999996e210 or -6.40000000000000022e171 < z < -1.95e43 or 1.35e19 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 61.4%

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

   3. Taylor expanded in z around inf 54.5%

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

      1. mul-1-neg 54.5%

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

      2. distribute-rgt-neg-out 54.5%

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

   5. Simplified 54.5%

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

   if -6.4999999999999996e210 < z < -6.40000000000000022e171

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 59.4%

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

      1. *-commutative 59.4%

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

      2. mul-1-neg 59.4%

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

      3. unsub-neg 59.4%

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

      4. distribute-lft-out-- 59.4%

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

      5. *-rgt-identity 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in z around inf 58.7%

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

   if -1.95e43 < z < -4.49999999999999958e-87 or -4.30000000000000007e-184 < z < 1.35e19

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 83.7%

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

   3. Taylor expanded in z around 0 76.3%

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

   if -4.49999999999999958e-87 < z < -4.30000000000000007e-184

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

   3. Taylor expanded in t around 0 83.6%

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

      1. mul-1-neg 83.6%

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

      2. sub-neg 83.6%

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

   5. Simplified 83.6%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+210}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{+171}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{+43}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-87}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-184}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+19}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]

Alternative 5: 53.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot t\\ t_2 := x + y \cdot t\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+216}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+153}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-188}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* z t))) (t_2 (+ x (* y t))))
   (if (<= z -2.3e+216)
     (* z (- t))
     (if (<= z -1.1e+153)
       (* z x)
       (if (<= z -3.5e-28)
         t_1
         (if (<= z -5.8e-91)
           t_2
           (if (<= z -6e-188) (- x (* y x)) (if (<= z 1.4e+19) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -2.3e+216) {
		tmp = z * -t;
	} else if (z <= -1.1e+153) {
		tmp = z * x;
	} else if (z <= -3.5e-28) {
		tmp = t_1;
	} else if (z <= -5.8e-91) {
		tmp = t_2;
	} else if (z <= -6e-188) {
		tmp = x - (y * x);
	} else if (z <= 1.4e+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 = x - (z * t)
    t_2 = x + (y * t)
    if (z <= (-2.3d+216)) then
        tmp = z * -t
    else if (z <= (-1.1d+153)) then
        tmp = z * x
    else if (z <= (-3.5d-28)) then
        tmp = t_1
    else if (z <= (-5.8d-91)) then
        tmp = t_2
    else if (z <= (-6d-188)) then
        tmp = x - (y * x)
    else if (z <= 1.4d+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 = x - (z * t);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -2.3e+216) {
		tmp = z * -t;
	} else if (z <= -1.1e+153) {
		tmp = z * x;
	} else if (z <= -3.5e-28) {
		tmp = t_1;
	} else if (z <= -5.8e-91) {
		tmp = t_2;
	} else if (z <= -6e-188) {
		tmp = x - (y * x);
	} else if (z <= 1.4e+19) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (z * t)
	t_2 = x + (y * t)
	tmp = 0
	if z <= -2.3e+216:
		tmp = z * -t
	elif z <= -1.1e+153:
		tmp = z * x
	elif z <= -3.5e-28:
		tmp = t_1
	elif z <= -5.8e-91:
		tmp = t_2
	elif z <= -6e-188:
		tmp = x - (y * x)
	elif z <= 1.4e+19:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(z * t))
	t_2 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (z <= -2.3e+216)
		tmp = Float64(z * Float64(-t));
	elseif (z <= -1.1e+153)
		tmp = Float64(z * x);
	elseif (z <= -3.5e-28)
		tmp = t_1;
	elseif (z <= -5.8e-91)
		tmp = t_2;
	elseif (z <= -6e-188)
		tmp = Float64(x - Float64(y * x));
	elseif (z <= 1.4e+19)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (z * t);
	t_2 = x + (y * t);
	tmp = 0.0;
	if (z <= -2.3e+216)
		tmp = z * -t;
	elseif (z <= -1.1e+153)
		tmp = z * x;
	elseif (z <= -3.5e-28)
		tmp = t_1;
	elseif (z <= -5.8e-91)
		tmp = t_2;
	elseif (z <= -6e-188)
		tmp = x - (y * x);
	elseif (z <= 1.4e+19)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+216], N[(z * (-t)), $MachinePrecision], If[LessEqual[z, -1.1e+153], N[(z * x), $MachinePrecision], If[LessEqual[z, -3.5e-28], t$95$1, If[LessEqual[z, -5.8e-91], t$95$2, If[LessEqual[z, -6e-188], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+19], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.29999999999999996e216

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 78.6%

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

   3. Taylor expanded in z around inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. distribute-rgt-neg-out 72.2%

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

   5. Simplified 72.2%

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

   if -2.29999999999999996e216 < z < -1.1e153

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 59.4%

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

      1. *-commutative 59.4%

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

      2. mul-1-neg 59.4%

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

      3. unsub-neg 59.4%

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

      4. distribute-lft-out-- 59.4%

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

      5. *-rgt-identity 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in z around inf 58.7%

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

   if -1.1e153 < z < -3.5e-28 or 1.4e19 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.7%

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

      1. +-commutative 76.7%

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

      2. mul-1-neg 76.7%

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

      3. unsub-neg 76.7%

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

      4. *-commutative 76.7%

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

   4. Simplified 76.7%

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

   5. Taylor expanded in t around inf 52.6%

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

      1. *-commutative 52.6%

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

   7. Simplified 52.6%

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

   if -3.5e-28 < z < -5.8000000000000001e-91 or -6.00000000000000033e-188 < z < 1.4e19

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 82.7%

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

   3. Taylor expanded in z around 0 79.5%

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

   if -5.8000000000000001e-91 < z < -6.00000000000000033e-188

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

   3. Taylor expanded in t around 0 83.6%

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

      1. mul-1-neg 83.6%

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

      2. sub-neg 83.6%

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

   5. Simplified 83.6%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+216}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+153}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-28}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-91}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-188}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+19}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]

Alternative 6: 38.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+164}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-235}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-302}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+20}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -4.5e+213)
     t_1
     (if (<= z -2.15e+164)
       (* z x)
       (if (<= z -3.5e-28)
         t_1
         (if (<= z -1.2e-235)
           (* y t)
           (if (<= z 8.6e-302) x (if (<= z 1.4e+20) (* y t) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -4.5e+213) {
		tmp = t_1;
	} else if (z <= -2.15e+164) {
		tmp = z * x;
	} else if (z <= -3.5e-28) {
		tmp = t_1;
	} else if (z <= -1.2e-235) {
		tmp = y * t;
	} else if (z <= 8.6e-302) {
		tmp = x;
	} else if (z <= 1.4e+20) {
		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 = z * -t
    if (z <= (-4.5d+213)) then
        tmp = t_1
    else if (z <= (-2.15d+164)) then
        tmp = z * x
    else if (z <= (-3.5d-28)) then
        tmp = t_1
    else if (z <= (-1.2d-235)) then
        tmp = y * t
    else if (z <= 8.6d-302) then
        tmp = x
    else if (z <= 1.4d+20) 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 = z * -t;
	double tmp;
	if (z <= -4.5e+213) {
		tmp = t_1;
	} else if (z <= -2.15e+164) {
		tmp = z * x;
	} else if (z <= -3.5e-28) {
		tmp = t_1;
	} else if (z <= -1.2e-235) {
		tmp = y * t;
	} else if (z <= 8.6e-302) {
		tmp = x;
	} else if (z <= 1.4e+20) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -4.5e+213:
		tmp = t_1
	elif z <= -2.15e+164:
		tmp = z * x
	elif z <= -3.5e-28:
		tmp = t_1
	elif z <= -1.2e-235:
		tmp = y * t
	elif z <= 8.6e-302:
		tmp = x
	elif z <= 1.4e+20:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -4.5e+213)
		tmp = t_1;
	elseif (z <= -2.15e+164)
		tmp = Float64(z * x);
	elseif (z <= -3.5e-28)
		tmp = t_1;
	elseif (z <= -1.2e-235)
		tmp = Float64(y * t);
	elseif (z <= 8.6e-302)
		tmp = x;
	elseif (z <= 1.4e+20)
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -4.5e+213)
		tmp = t_1;
	elseif (z <= -2.15e+164)
		tmp = z * x;
	elseif (z <= -3.5e-28)
		tmp = t_1;
	elseif (z <= -1.2e-235)
		tmp = y * t;
	elseif (z <= 8.6e-302)
		tmp = x;
	elseif (z <= 1.4e+20)
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -4.5e+213], t$95$1, If[LessEqual[z, -2.15e+164], N[(z * x), $MachinePrecision], If[LessEqual[z, -3.5e-28], t$95$1, If[LessEqual[z, -1.2e-235], N[(y * t), $MachinePrecision], If[LessEqual[z, 8.6e-302], x, If[LessEqual[z, 1.4e+20], N[(y * t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.5000000000000002e213 or -2.15e164 < z < -3.5e-28 or 1.4e20 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 64.9%

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

   3. Taylor expanded in z around inf 53.7%

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

      1. mul-1-neg 53.7%

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

      2. distribute-rgt-neg-out 53.7%

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

   5. Simplified 53.7%

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

   if -4.5000000000000002e213 < z < -2.15e164

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 59.4%

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

      1. *-commutative 59.4%

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

      2. mul-1-neg 59.4%

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

      3. unsub-neg 59.4%

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

      4. distribute-lft-out-- 59.4%

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

      5. *-rgt-identity 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in z around inf 58.7%

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

   if -3.5e-28 < z < -1.20000000000000005e-235 or 8.60000000000000041e-302 < z < 1.4e20

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 77.2%

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

   3. Taylor expanded in y around inf 44.6%

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

   if -1.20000000000000005e-235 < z < 8.60000000000000041e-302

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 82.9%

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

   3. Taylor expanded in x around inf 65.4%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+213}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{+164}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-28}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-235}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-302}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+20}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]

Alternative 7: 69.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-110}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-200} \lor \neg \left(t \leq 2.6 \cdot 10^{-35}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) t))))
   (if (<= t -1.35e-64)
     t_1
     (if (<= t -1.25e-110)
       (+ x (* z x))
       (if (or (<= t -1.4e-200) (not (<= t 2.6e-35))) t_1 (- x (* y x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - z) * t);
	double tmp;
	if (t <= -1.35e-64) {
		tmp = t_1;
	} else if (t <= -1.25e-110) {
		tmp = x + (z * x);
	} else if ((t <= -1.4e-200) || !(t <= 2.6e-35)) {
		tmp = t_1;
	} else {
		tmp = x - (y * 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) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * t)
    if (t <= (-1.35d-64)) then
        tmp = t_1
    else if (t <= (-1.25d-110)) then
        tmp = x + (z * x)
    else if ((t <= (-1.4d-200)) .or. (.not. (t <= 2.6d-35))) then
        tmp = t_1
    else
        tmp = x - (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - z) * t);
	double tmp;
	if (t <= -1.35e-64) {
		tmp = t_1;
	} else if (t <= -1.25e-110) {
		tmp = x + (z * x);
	} else if ((t <= -1.4e-200) || !(t <= 2.6e-35)) {
		tmp = t_1;
	} else {
		tmp = x - (y * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y - z) * t)
	tmp = 0
	if t <= -1.35e-64:
		tmp = t_1
	elif t <= -1.25e-110:
		tmp = x + (z * x)
	elif (t <= -1.4e-200) or not (t <= 2.6e-35):
		tmp = t_1
	else:
		tmp = x - (y * x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y - z) * t))
	tmp = 0.0
	if (t <= -1.35e-64)
		tmp = t_1;
	elseif (t <= -1.25e-110)
		tmp = Float64(x + Float64(z * x));
	elseif ((t <= -1.4e-200) || !(t <= 2.6e-35))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y - z) * t);
	tmp = 0.0;
	if (t <= -1.35e-64)
		tmp = t_1;
	elseif (t <= -1.25e-110)
		tmp = x + (z * x);
	elseif ((t <= -1.4e-200) || ~((t <= 2.6e-35)))
		tmp = t_1;
	else
		tmp = x - (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e-64], t$95$1, If[LessEqual[t, -1.25e-110], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1.4e-200], N[Not[LessEqual[t, 2.6e-35]], $MachinePrecision]], t$95$1, N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.34999999999999993e-64 or -1.25e-110 < t < -1.40000000000000003e-200 or 2.60000000000000005e-35 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 85.6%

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

   if -1.34999999999999993e-64 < t < -1.25e-110

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 73.9%

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

      3. associate-*r/ 57.2%

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

   3. Applied egg-rr 57.2%

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

      1. associate-/l* 73.9%

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

      2. difference-of-squares 73.9%

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

      3. associate-/r* 100.0%

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

      4. *-inverses 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 64.7%

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

   7. Taylor expanded in t around 0 64.8%

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

   if -1.40000000000000003e-200 < t < 2.60000000000000005e-35

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 65.7%

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

   3. Taylor expanded in t around 0 63.3%

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

      1. mul-1-neg 63.3%

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

      2. sub-neg 63.3%

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

   5. Simplified 63.3%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-64}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-110}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-200} \lor \neg \left(t \leq 2.6 \cdot 10^{-35}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot x\\ \end{array} \]

Alternative 8: 54.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{+168}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{+49} \lor \neg \left(z \leq 6.2 \cdot 10^{+21}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -6.8e+213)
     t_1
     (if (<= z -4.7e+168)
       (* z x)
       (if (or (<= z -4.3e+49) (not (<= z 6.2e+21))) t_1 (+ x (* y t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -6.8e+213) {
		tmp = t_1;
	} else if (z <= -4.7e+168) {
		tmp = z * x;
	} else if ((z <= -4.3e+49) || !(z <= 6.2e+21)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-6.8d+213)) then
        tmp = t_1
    else if (z <= (-4.7d+168)) then
        tmp = z * x
    else if ((z <= (-4.3d+49)) .or. (.not. (z <= 6.2d+21))) then
        tmp = t_1
    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 t_1 = z * -t;
	double tmp;
	if (z <= -6.8e+213) {
		tmp = t_1;
	} else if (z <= -4.7e+168) {
		tmp = z * x;
	} else if ((z <= -4.3e+49) || !(z <= 6.2e+21)) {
		tmp = t_1;
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -6.8e+213:
		tmp = t_1
	elif z <= -4.7e+168:
		tmp = z * x
	elif (z <= -4.3e+49) or not (z <= 6.2e+21):
		tmp = t_1
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -6.8e+213)
		tmp = t_1;
	elseif (z <= -4.7e+168)
		tmp = Float64(z * x);
	elseif ((z <= -4.3e+49) || !(z <= 6.2e+21))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -6.8e+213)
		tmp = t_1;
	elseif (z <= -4.7e+168)
		tmp = z * x;
	elseif ((z <= -4.3e+49) || ~((z <= 6.2e+21)))
		tmp = t_1;
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -6.8e+213], t$95$1, If[LessEqual[z, -4.7e+168], N[(z * x), $MachinePrecision], If[Or[LessEqual[z, -4.3e+49], N[Not[LessEqual[z, 6.2e+21]], $MachinePrecision]], t$95$1, N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.79999999999999983e213 or -4.69999999999999961e168 < z < -4.2999999999999999e49 or 6.2e21 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 61.4%

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

   3. Taylor expanded in z around inf 54.5%

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

      1. mul-1-neg 54.5%

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

      2. distribute-rgt-neg-out 54.5%

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

   5. Simplified 54.5%

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

   if -6.79999999999999983e213 < z < -4.69999999999999961e168

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 59.4%

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

      1. *-commutative 59.4%

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

      2. mul-1-neg 59.4%

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

      3. unsub-neg 59.4%

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

      4. distribute-lft-out-- 59.4%

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

      5. *-rgt-identity 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in z around inf 58.7%

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

   if -4.2999999999999999e49 < z < 6.2e21

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 79.5%

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

   3. Taylor expanded in z around 0 72.8%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+213}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{+168}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{+49} \lor \neg \left(z \leq 6.2 \cdot 10^{+21}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]

Alternative 9: 76.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-5} \lor \neg \left(y \leq 5.1 \cdot 10^{+35}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.2e-5) (not (<= y 5.1e+35)))
   (+ x (* y (- t x)))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.2e-5) || !(y <= 5.1e+35)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.2d-5)) .or. (.not. (y <= 5.1d+35))) then
        tmp = x + (y * (t - x))
    else
        tmp = x + ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.2e-5) || !(y <= 5.1e+35)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.2e-5) or not (y <= 5.1e+35):
		tmp = x + (y * (t - x))
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.2e-5) || !(y <= 5.1e+35))
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.2e-5) || ~((y <= 5.1e+35)))
		tmp = x + (y * (t - x));
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.2e-5], N[Not[LessEqual[y, 5.1e+35]], $MachinePrecision]], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.19999999999999986e-5 or 5.10000000000000017e35 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 83.6%

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

   if -3.19999999999999986e-5 < y < 5.10000000000000017e35

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 79.9%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-5} \lor \neg \left(y \leq 5.1 \cdot 10^{+35}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]

Alternative 10: 82.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-63} \lor \neg \left(t \leq 2.8 \cdot 10^{-33}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.6e-63) (not (<= t 2.8e-33)))
   (+ x (* (- y z) t))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.6e-63) || !(t <= 2.8e-33)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.6d-63)) .or. (.not. (t <= 2.8d-33))) then
        tmp = x + ((y - z) * t)
    else
        tmp = x + (x * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.6e-63) || !(t <= 2.8e-33)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.6e-63) or not (t <= 2.8e-33):
		tmp = x + ((y - z) * t)
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.6e-63) || !(t <= 2.8e-33))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.6e-63) || ~((t <= 2.8e-33)))
		tmp = x + ((y - z) * t);
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.6e-63], N[Not[LessEqual[t, 2.8e-33]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.59999999999999994e-63 or 2.8e-33 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 88.6%

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

   if -1.59999999999999994e-63 < t < 2.8e-33

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 83.9%

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

      1. *-commutative 83.9%

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

      2. mul-1-neg 83.9%

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

      3. unsub-neg 83.9%

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

      4. distribute-lft-out-- 83.9%

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

      5. *-rgt-identity 83.9%

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

   4. Simplified 83.9%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-63} \lor \neg \left(t \leq 2.8 \cdot 10^{-33}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 11: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0135 \lor \neg \left(y \leq 1.05 \cdot 10^{+35}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -0.0135) (not (<= y 1.05e+35)))
   (+ x (* y (- t x)))
   (- x (* z (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.0135) || !(y <= 1.05e+35)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x - (z * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-0.0135d0)) .or. (.not. (y <= 1.05d+35))) then
        tmp = x + (y * (t - x))
    else
        tmp = x - (z * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.0135) || !(y <= 1.05e+35)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x - (z * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -0.0135) or not (y <= 1.05e+35):
		tmp = x + (y * (t - x))
	else:
		tmp = x - (z * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -0.0135) || !(y <= 1.05e+35))
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x - Float64(z * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -0.0135) || ~((y <= 1.05e+35)))
		tmp = x + (y * (t - x));
	else
		tmp = x - (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -0.0135], N[Not[LessEqual[y, 1.05e+35]], $MachinePrecision]], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0134999999999999998 or 1.0499999999999999e35 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 83.6%

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

   if -0.0134999999999999998 < y < 1.0499999999999999e35

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.7%

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

      1. +-commutative 91.7%

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

      2. mul-1-neg 91.7%

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

      3. unsub-neg 91.7%

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

      4. *-commutative 91.7%

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

   4. Simplified 91.7%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0135 \lor \neg \left(y \leq 1.05 \cdot 10^{+35}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \end{array} \]

Alternative 12: 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 13: 37.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.054:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-106}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.054) (* y t) (if (<= y 1.5e-106) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.054) {
		tmp = y * t;
	} else if (y <= 1.5e-106) {
		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 <= (-0.054d0)) then
        tmp = y * t
    else if (y <= 1.5d-106) 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 <= -0.054) {
		tmp = y * t;
	} else if (y <= 1.5e-106) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.054:
		tmp = y * t
	elif y <= 1.5e-106:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.054)
		tmp = Float64(y * t);
	elseif (y <= 1.5e-106)
		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 <= -0.054)
		tmp = y * t;
	elseif (y <= 1.5e-106)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.054], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.5e-106], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0539999999999999994 or 1.50000000000000009e-106 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 60.7%

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

   3. Taylor expanded in y around inf 47.6%

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

   if -0.0539999999999999994 < y < 1.50000000000000009e-106

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 81.7%

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

   3. Taylor expanded in x around inf 40.4%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.054:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-106}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 14: 18.0% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in t around inf 70.3%

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

3. Taylor expanded in x around inf 20.5%

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

4. Final simplification 20.5%

   \[\leadsto x \]

Developer target: 96.4% 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 2023214 
(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))))