Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.7s

Alternatives: 12

Speedup: 1.0×

• 35.1% 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. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 2: 51.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := z \cdot \left(-t\right)\\ t_3 := x + y \cdot t\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-138}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 118:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (* z (- t))) (t_3 (+ x (* y t))))
   (if (<= z -1.6e+146)
     t_2
     (if (<= z -7.4e-71)
       t_3
       (if (<= z -6.2e-274)
         t_1
         (if (<= z 7.6e-138)
           t_3
           (if (<= z 5.5e-12)
             t_1
             (if (<= z 118.0) t_3 (if (<= z 5.2e+154) t_2 (* z x))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = z * -t;
	double t_3 = x + (y * t);
	double tmp;
	if (z <= -1.6e+146) {
		tmp = t_2;
	} else if (z <= -7.4e-71) {
		tmp = t_3;
	} else if (z <= -6.2e-274) {
		tmp = t_1;
	} else if (z <= 7.6e-138) {
		tmp = t_3;
	} else if (z <= 5.5e-12) {
		tmp = t_1;
	} else if (z <= 118.0) {
		tmp = t_3;
	} else if (z <= 5.2e+154) {
		tmp = t_2;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    t_2 = z * -t
    t_3 = x + (y * t)
    if (z <= (-1.6d+146)) then
        tmp = t_2
    else if (z <= (-7.4d-71)) then
        tmp = t_3
    else if (z <= (-6.2d-274)) then
        tmp = t_1
    else if (z <= 7.6d-138) then
        tmp = t_3
    else if (z <= 5.5d-12) then
        tmp = t_1
    else if (z <= 118.0d0) then
        tmp = t_3
    else if (z <= 5.2d+154) then
        tmp = t_2
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = z * -t;
	double t_3 = x + (y * t);
	double tmp;
	if (z <= -1.6e+146) {
		tmp = t_2;
	} else if (z <= -7.4e-71) {
		tmp = t_3;
	} else if (z <= -6.2e-274) {
		tmp = t_1;
	} else if (z <= 7.6e-138) {
		tmp = t_3;
	} else if (z <= 5.5e-12) {
		tmp = t_1;
	} else if (z <= 118.0) {
		tmp = t_3;
	} else if (z <= 5.2e+154) {
		tmp = t_2;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = z * -t
	t_3 = x + (y * t)
	tmp = 0
	if z <= -1.6e+146:
		tmp = t_2
	elif z <= -7.4e-71:
		tmp = t_3
	elif z <= -6.2e-274:
		tmp = t_1
	elif z <= 7.6e-138:
		tmp = t_3
	elif z <= 5.5e-12:
		tmp = t_1
	elif z <= 118.0:
		tmp = t_3
	elif z <= 5.2e+154:
		tmp = t_2
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	t_2 = Float64(z * Float64(-t))
	t_3 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (z <= -1.6e+146)
		tmp = t_2;
	elseif (z <= -7.4e-71)
		tmp = t_3;
	elseif (z <= -6.2e-274)
		tmp = t_1;
	elseif (z <= 7.6e-138)
		tmp = t_3;
	elseif (z <= 5.5e-12)
		tmp = t_1;
	elseif (z <= 118.0)
		tmp = t_3;
	elseif (z <= 5.2e+154)
		tmp = t_2;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	t_2 = z * -t;
	t_3 = x + (y * t);
	tmp = 0.0;
	if (z <= -1.6e+146)
		tmp = t_2;
	elseif (z <= -7.4e-71)
		tmp = t_3;
	elseif (z <= -6.2e-274)
		tmp = t_1;
	elseif (z <= 7.6e-138)
		tmp = t_3;
	elseif (z <= 5.5e-12)
		tmp = t_1;
	elseif (z <= 118.0)
		tmp = t_3;
	elseif (z <= 5.2e+154)
		tmp = t_2;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * (-t)), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+146], t$95$2, If[LessEqual[z, -7.4e-71], t$95$3, If[LessEqual[z, -6.2e-274], t$95$1, If[LessEqual[z, 7.6e-138], t$95$3, If[LessEqual[z, 5.5e-12], t$95$1, If[LessEqual[z, 118.0], t$95$3, If[LessEqual[z, 5.2e+154], t$95$2, N[(z * x), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.6e146 or 118 < z < 5.19999999999999978e154

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 81.3%

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

      1. mul-1-neg 81.3%

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

      2. unsub-neg 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in t around inf 56.8%

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

   7. Taylor expanded in x around 0 56.2%

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

      1. mul-1-neg 56.2%

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

      2. distribute-rgt-neg-out 56.2%

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

   9. Simplified 56.2%

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

   if -1.6e146 < z < -7.3999999999999993e-71 or -6.19999999999999956e-274 < z < 7.6000000000000005e-138 or 5.5000000000000004e-12 < z < 118

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 96.8%

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

   4. Applied egg-rr 96.8%

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

   5. Taylor expanded in z around 0 82.9%

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

   6. Taylor expanded in x around 0 69.5%

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

   if -7.3999999999999993e-71 < z < -6.19999999999999956e-274 or 7.6000000000000005e-138 < z < 5.5000000000000004e-12

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 74.0%

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

      1. mul-1-neg 74.0%

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

      2. unsub-neg 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in z around 0 73.8%

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

   if 5.19999999999999978e154 < z

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. unsub-neg 61.5%

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

   5. Simplified 61.5%

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

   6. Taylor expanded in y around 0 54.6%

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

      1. +-commutative 54.6%

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

   8. Simplified 54.6%

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

   9. Taylor expanded in z around inf 54.6%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+146}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-71}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-274}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-138}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 118:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+154}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 38.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+30}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 960:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -4e+137)
     t_1
     (if (<= z -6.2e+30)
       (* z x)
       (if (<= z -6.2e-62)
         t_1
         (if (<= z 960.0) x (if (<= z 5.3e+157) t_1 (* z x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -4e+137) {
		tmp = t_1;
	} else if (z <= -6.2e+30) {
		tmp = z * x;
	} else if (z <= -6.2e-62) {
		tmp = t_1;
	} else if (z <= 960.0) {
		tmp = x;
	} else if (z <= 5.3e+157) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-4d+137)) then
        tmp = t_1
    else if (z <= (-6.2d+30)) then
        tmp = z * x
    else if (z <= (-6.2d-62)) then
        tmp = t_1
    else if (z <= 960.0d0) then
        tmp = x
    else if (z <= 5.3d+157) then
        tmp = t_1
    else
        tmp = z * x
    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 <= -4e+137) {
		tmp = t_1;
	} else if (z <= -6.2e+30) {
		tmp = z * x;
	} else if (z <= -6.2e-62) {
		tmp = t_1;
	} else if (z <= 960.0) {
		tmp = x;
	} else if (z <= 5.3e+157) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -4e+137:
		tmp = t_1
	elif z <= -6.2e+30:
		tmp = z * x
	elif z <= -6.2e-62:
		tmp = t_1
	elif z <= 960.0:
		tmp = x
	elif z <= 5.3e+157:
		tmp = t_1
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -4e+137)
		tmp = t_1;
	elseif (z <= -6.2e+30)
		tmp = Float64(z * x);
	elseif (z <= -6.2e-62)
		tmp = t_1;
	elseif (z <= 960.0)
		tmp = x;
	elseif (z <= 5.3e+157)
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -4e+137)
		tmp = t_1;
	elseif (z <= -6.2e+30)
		tmp = z * x;
	elseif (z <= -6.2e-62)
		tmp = t_1;
	elseif (z <= 960.0)
		tmp = x;
	elseif (z <= 5.3e+157)
		tmp = t_1;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -4e+137], t$95$1, If[LessEqual[z, -6.2e+30], N[(z * x), $MachinePrecision], If[LessEqual[z, -6.2e-62], t$95$1, If[LessEqual[z, 960.0], x, If[LessEqual[z, 5.3e+157], t$95$1, N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0000000000000001e137 or -6.1999999999999995e30 < z < -6.1999999999999999e-62 or 960 < z < 5.2999999999999998e157

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 78.8%

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

      1. mul-1-neg 78.8%

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

      2. unsub-neg 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in t around inf 55.9%

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

   7. Taylor expanded in x around 0 53.4%

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

      1. mul-1-neg 53.4%

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

      2. distribute-rgt-neg-out 53.4%

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

   9. Simplified 53.4%

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

   if -4.0000000000000001e137 < z < -6.1999999999999995e30 or 5.2999999999999998e157 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 61.9%

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

      1. mul-1-neg 61.9%

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

      2. unsub-neg 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in y around 0 52.3%

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

      1. +-commutative 52.3%

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

   8. Simplified 52.3%

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

   9. Taylor expanded in z around inf 52.3%

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

   if -6.1999999999999999e-62 < z < 960

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 37.6%

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

      1. mul-1-neg 37.6%

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

      2. unsub-neg 37.6%

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

   5. Simplified 37.6%

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

   6. Taylor expanded in z around 0 33.2%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+137}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+30}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-62}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 960:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+157}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+31}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -14.2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 26000:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -8e+145)
     t_1
     (if (<= z -1.85e+31)
       (* z x)
       (if (<= z -14.2)
         t_1
         (if (<= z 26000.0)
           (* x (- 1.0 y))
           (if (<= z 4.2e+165) t_1 (* z x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -8e+145) {
		tmp = t_1;
	} else if (z <= -1.85e+31) {
		tmp = z * x;
	} else if (z <= -14.2) {
		tmp = t_1;
	} else if (z <= 26000.0) {
		tmp = x * (1.0 - y);
	} else if (z <= 4.2e+165) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-8d+145)) then
        tmp = t_1
    else if (z <= (-1.85d+31)) then
        tmp = z * x
    else if (z <= (-14.2d0)) then
        tmp = t_1
    else if (z <= 26000.0d0) then
        tmp = x * (1.0d0 - y)
    else if (z <= 4.2d+165) then
        tmp = t_1
    else
        tmp = z * x
    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 <= -8e+145) {
		tmp = t_1;
	} else if (z <= -1.85e+31) {
		tmp = z * x;
	} else if (z <= -14.2) {
		tmp = t_1;
	} else if (z <= 26000.0) {
		tmp = x * (1.0 - y);
	} else if (z <= 4.2e+165) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -8e+145:
		tmp = t_1
	elif z <= -1.85e+31:
		tmp = z * x
	elif z <= -14.2:
		tmp = t_1
	elif z <= 26000.0:
		tmp = x * (1.0 - y)
	elif z <= 4.2e+165:
		tmp = t_1
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -8e+145)
		tmp = t_1;
	elseif (z <= -1.85e+31)
		tmp = Float64(z * x);
	elseif (z <= -14.2)
		tmp = t_1;
	elseif (z <= 26000.0)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 4.2e+165)
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -8e+145)
		tmp = t_1;
	elseif (z <= -1.85e+31)
		tmp = z * x;
	elseif (z <= -14.2)
		tmp = t_1;
	elseif (z <= 26000.0)
		tmp = x * (1.0 - y);
	elseif (z <= 4.2e+165)
		tmp = t_1;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -8e+145], t$95$1, If[LessEqual[z, -1.85e+31], N[(z * x), $MachinePrecision], If[LessEqual[z, -14.2], t$95$1, If[LessEqual[z, 26000.0], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+165], t$95$1, N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.9999999999999999e145 or -1.8499999999999999e31 < z < -14.199999999999999 or 26000 < z < 4.2000000000000001e165

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 81.6%

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

      1. mul-1-neg 81.6%

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

      2. unsub-neg 81.6%

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

   5. Simplified 81.6%

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

   6. Taylor expanded in t around inf 56.4%

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

   7. Taylor expanded in x around 0 55.9%

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

      1. mul-1-neg 55.9%

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

      2. distribute-rgt-neg-out 55.9%

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

   9. Simplified 55.9%

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

   if -7.9999999999999999e145 < z < -1.8499999999999999e31 or 4.2000000000000001e165 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 61.9%

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

      1. mul-1-neg 61.9%

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

      2. unsub-neg 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in y around 0 52.3%

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

      1. +-commutative 52.3%

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

   8. Simplified 52.3%

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

   9. Taylor expanded in z around inf 52.3%

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

   if -14.199999999999999 < z < 26000

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. unsub-neg 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in z around 0 62.7%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+145}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+31}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -14.2:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 26000:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+165}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-88}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (- t x)))))
   (if (<= y -3.3e+18)
     t_1
     (if (<= y -1.05e-51)
       (* x (+ (- z y) 1.0))
       (if (<= y 3.2e-88) (- x (* z t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (t - x));
	double tmp;
	if (y <= -3.3e+18) {
		tmp = t_1;
	} else if (y <= -1.05e-51) {
		tmp = x * ((z - y) + 1.0);
	} else if (y <= 3.2e-88) {
		tmp = x - (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (t - x))
    if (y <= (-3.3d+18)) then
        tmp = t_1
    else if (y <= (-1.05d-51)) then
        tmp = x * ((z - y) + 1.0d0)
    else if (y <= 3.2d-88) then
        tmp = x - (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (t - x));
	double tmp;
	if (y <= -3.3e+18) {
		tmp = t_1;
	} else if (y <= -1.05e-51) {
		tmp = x * ((z - y) + 1.0);
	} else if (y <= 3.2e-88) {
		tmp = x - (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (t - x))
	tmp = 0
	if y <= -3.3e+18:
		tmp = t_1
	elif y <= -1.05e-51:
		tmp = x * ((z - y) + 1.0)
	elif y <= 3.2e-88:
		tmp = x - (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(t - x)))
	tmp = 0.0
	if (y <= -3.3e+18)
		tmp = t_1;
	elseif (y <= -1.05e-51)
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	elseif (y <= 3.2e-88)
		tmp = Float64(x - Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (t - x));
	tmp = 0.0;
	if (y <= -3.3e+18)
		tmp = t_1;
	elseif (y <= -1.05e-51)
		tmp = x * ((z - y) + 1.0);
	elseif (y <= 3.2e-88)
		tmp = x - (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.3e+18], t$95$1, If[LessEqual[y, -1.05e-51], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-88], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.3e18 or 3.20000000000000012e-88 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 78.5%

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

      1. *-commutative 78.5%

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

   5. Simplified 78.5%

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

   if -3.3e18 < y < -1.05000000000000001e-51

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 77.6%

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

      1. mul-1-neg 77.6%

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

      2. unsub-neg 77.6%

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

   5. Simplified 77.6%

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

   if -1.05000000000000001e-51 < y < 3.20000000000000012e-88

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 91.9%

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

      1. mul-1-neg 91.9%

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

      2. unsub-neg 91.9%

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

   5. Simplified 91.9%

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

   6. Taylor expanded in t around inf 76.2%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-88}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-20}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq 3600000:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))))
   (if (<= y -9e+87)
     t_1
     (if (<= y -3.7e-20)
       (+ x (* y t))
       (if (<= y 3600000.0) (- x (* z t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double tmp;
	if (y <= -9e+87) {
		tmp = t_1;
	} else if (y <= -3.7e-20) {
		tmp = x + (y * t);
	} else if (y <= 3600000.0) {
		tmp = x - (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    if (y <= (-9d+87)) then
        tmp = t_1
    else if (y <= (-3.7d-20)) then
        tmp = x + (y * t)
    else if (y <= 3600000.0d0) then
        tmp = x - (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double tmp;
	if (y <= -9e+87) {
		tmp = t_1;
	} else if (y <= -3.7e-20) {
		tmp = x + (y * t);
	} else if (y <= 3600000.0) {
		tmp = x - (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	tmp = 0
	if y <= -9e+87:
		tmp = t_1
	elif y <= -3.7e-20:
		tmp = x + (y * t)
	elif y <= 3600000.0:
		tmp = x - (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (y <= -9e+87)
		tmp = t_1;
	elseif (y <= -3.7e-20)
		tmp = Float64(x + Float64(y * t));
	elseif (y <= 3600000.0)
		tmp = Float64(x - Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	tmp = 0.0;
	if (y <= -9e+87)
		tmp = t_1;
	elseif (y <= -3.7e-20)
		tmp = x + (y * t);
	elseif (y <= 3600000.0)
		tmp = x - (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+87], t$95$1, If[LessEqual[y, -3.7e-20], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3600000.0], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.0000000000000005e87 or 3.6e6 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 57.7%

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

      1. mul-1-neg 57.7%

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

      2. unsub-neg 57.7%

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

   5. Simplified 57.7%

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

   6. Taylor expanded in z around 0 52.0%

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

   if -9.0000000000000005e87 < y < -3.7000000000000001e-20

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-lft-in 93.2%

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

   4. Applied egg-rr 93.2%

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

   5. Taylor expanded in z around 0 63.8%

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

   6. Taylor expanded in x around 0 58.7%

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

   if -3.7000000000000001e-20 < y < 3.6e6

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 88.9%

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

      1. mul-1-neg 88.9%

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

      2. unsub-neg 88.9%

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

   5. Simplified 88.9%

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

   6. Taylor expanded in t around inf 69.6%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-20}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq 3600000:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2000 \lor \neg \left(z \leq 10800\right):\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2000.0) (not (<= z 10800.0)))
   (- x (* z (- t x)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2000.0) || !(z <= 10800.0)) {
		tmp = x - (z * (t - x));
	} else {
		tmp = x + (y * (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 ((z <= (-2000.0d0)) .or. (.not. (z <= 10800.0d0))) then
        tmp = x - (z * (t - x))
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2000.0) || !(z <= 10800.0)) {
		tmp = x - (z * (t - x));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2000.0) or not (z <= 10800.0):
		tmp = x - (z * (t - x))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2000.0) || !(z <= 10800.0))
		tmp = Float64(x - Float64(z * Float64(t - x)));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2000.0) || ~((z <= 10800.0)))
		tmp = x - (z * (t - x));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2000.0], N[Not[LessEqual[z, 10800.0]], $MachinePrecision]], N[(x - N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2e3 or 10800 < z

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 79.8%

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

      1. mul-1-neg 79.8%

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

      2. unsub-neg 79.8%

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

   5. Simplified 79.8%

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

   if -2e3 < z < 10800

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 94.7%

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

      1. *-commutative 94.7%

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

   5. Simplified 94.7%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2000 \lor \neg \left(z \leq 10800\right):\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.04 \cdot 10^{+26}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.04e+26)
   (- x (* z t))
   (if (<= t 5.6e+34) (* x (+ (- z y) 1.0)) (+ x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.04e+26) {
		tmp = x - (z * t);
	} else if (t <= 5.6e+34) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.04d+26)) then
        tmp = x - (z * t)
    else if (t <= 5.6d+34) then
        tmp = x * ((z - y) + 1.0d0)
    else
        tmp = x + (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.04e+26) {
		tmp = x - (z * t);
	} else if (t <= 5.6e+34) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.04e+26:
		tmp = x - (z * t)
	elif t <= 5.6e+34:
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.04e+26)
		tmp = Float64(x - Float64(z * t));
	elseif (t <= 5.6e+34)
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.04e+26)
		tmp = x - (z * t);
	elseif (t <= 5.6e+34)
		tmp = x * ((z - y) + 1.0);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.04e+26], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e+34], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.0399999999999999e26

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 61.3%

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

      1. mul-1-neg 61.3%

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

      2. unsub-neg 61.3%

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

   5. Simplified 61.3%

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

   6. Taylor expanded in t around inf 58.2%

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

   if -1.0399999999999999e26 < t < 5.60000000000000016e34

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 81.6%

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

      1. mul-1-neg 81.6%

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

      2. unsub-neg 81.6%

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

   5. Simplified 81.6%

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

   if 5.60000000000000016e34 < t

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 89.2%

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

   4. Applied egg-rr 89.2%

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

   5. Taylor expanded in z around 0 59.2%

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

   6. Taylor expanded in x around 0 56.6%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.04 \cdot 10^{+26}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+18} \lor \neg \left(t \leq 6 \cdot 10^{+50}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1e+18) (not (<= t 6e+50))) (* z (- t)) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1e+18) || !(t <= 6e+50)) {
		tmp = z * -t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1d+18)) .or. (.not. (t <= 6d+50))) then
        tmp = z * -t
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1e+18) || !(t <= 6e+50)) {
		tmp = z * -t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1e+18) or not (t <= 6e+50):
		tmp = z * -t
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1e+18) || !(t <= 6e+50))
		tmp = Float64(z * Float64(-t));
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1e+18) || ~((t <= 6e+50)))
		tmp = z * -t;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1e+18], N[Not[LessEqual[t, 6e+50]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1e18 or 5.9999999999999996e50 < t

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 54.6%

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

      1. mul-1-neg 54.6%

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

      2. unsub-neg 54.6%

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

   5. Simplified 54.6%

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

   6. Taylor expanded in t around inf 50.7%

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

   7. Taylor expanded in x around 0 44.3%

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

      1. mul-1-neg 44.3%

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

      2. distribute-rgt-neg-out 44.3%

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

   9. Simplified 44.3%

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

   if -1e18 < t < 5.9999999999999996e50

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 79.4%

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

      1. mul-1-neg 79.4%

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

      2. unsub-neg 79.4%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in y around 0 52.4%

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

      1. +-commutative 52.4%

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

   8. Simplified 52.4%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+18} \lor \neg \left(t \leq 6 \cdot 10^{+50}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.0))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.0):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.0))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.0)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 47.2%

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

      1. mul-1-neg 47.2%

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

      2. unsub-neg 47.2%

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

   5. Simplified 47.2%

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

   6. Taylor expanded in y around 0 36.7%

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

      1. +-commutative 36.7%

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

   8. Simplified 36.7%

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

   9. Taylor expanded in z around inf 36.0%

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

   if -1 < z < 1

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 38.6%

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

      1. mul-1-neg 38.6%

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

      2. unsub-neg 38.6%

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

   5. Simplified 38.6%

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

   6. Taylor expanded in z around 0 33.1%

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

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto x + \left(y - z\right) \cdot \left(t - x\right) \]
4. Add Preprocessing

Alternative 12: 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. Add Preprocessing

3. Taylor expanded in y around 0 57.1%

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

   1. mul-1-neg 57.1%

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

   2. unsub-neg 57.1%

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

5. Simplified 57.1%

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

6. Taylor expanded in z around 0 19.4%

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

7. Final simplification 19.4%

   \[\leadsto x \]
8. Add Preprocessing

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 2024024 
(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))))