Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.8s

Alternatives: 16

Speedup: 1.0×

• 35.2% 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: 59.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z + 1\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;x \leq -3 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 165000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+159} \lor \neg \left(x \leq 2.7 \cdot 10^{+210}\right) \land x \leq 4.1 \cdot 10^{+251}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ z 1.0))) (t_2 (* (- y z) t)))
   (if (<= x -3e-6)
     t_1
     (if (<= x 8.6e-67)
       t_2
       (if (<= x 4.2e-18)
         t_1
         (if (<= x 165000.0)
           t_2
           (if (or (<= x 4.2e+159) (and (not (<= x 2.7e+210)) (<= x 4.1e+251)))
             (* y (- x))
             t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = (y - z) * t;
	double tmp;
	if (x <= -3e-6) {
		tmp = t_1;
	} else if (x <= 8.6e-67) {
		tmp = t_2;
	} else if (x <= 4.2e-18) {
		tmp = t_1;
	} else if (x <= 165000.0) {
		tmp = t_2;
	} else if ((x <= 4.2e+159) || (!(x <= 2.7e+210) && (x <= 4.1e+251))) {
		tmp = y * -x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (z + 1.0d0)
    t_2 = (y - z) * t
    if (x <= (-3d-6)) then
        tmp = t_1
    else if (x <= 8.6d-67) then
        tmp = t_2
    else if (x <= 4.2d-18) then
        tmp = t_1
    else if (x <= 165000.0d0) then
        tmp = t_2
    else if ((x <= 4.2d+159) .or. (.not. (x <= 2.7d+210)) .and. (x <= 4.1d+251)) then
        tmp = y * -x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = (y - z) * t;
	double tmp;
	if (x <= -3e-6) {
		tmp = t_1;
	} else if (x <= 8.6e-67) {
		tmp = t_2;
	} else if (x <= 4.2e-18) {
		tmp = t_1;
	} else if (x <= 165000.0) {
		tmp = t_2;
	} else if ((x <= 4.2e+159) || (!(x <= 2.7e+210) && (x <= 4.1e+251))) {
		tmp = y * -x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z + 1.0)
	t_2 = (y - z) * t
	tmp = 0
	if x <= -3e-6:
		tmp = t_1
	elif x <= 8.6e-67:
		tmp = t_2
	elif x <= 4.2e-18:
		tmp = t_1
	elif x <= 165000.0:
		tmp = t_2
	elif (x <= 4.2e+159) or (not (x <= 2.7e+210) and (x <= 4.1e+251)):
		tmp = y * -x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z + 1.0))
	t_2 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (x <= -3e-6)
		tmp = t_1;
	elseif (x <= 8.6e-67)
		tmp = t_2;
	elseif (x <= 4.2e-18)
		tmp = t_1;
	elseif (x <= 165000.0)
		tmp = t_2;
	elseif ((x <= 4.2e+159) || (!(x <= 2.7e+210) && (x <= 4.1e+251)))
		tmp = Float64(y * Float64(-x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z + 1.0);
	t_2 = (y - z) * t;
	tmp = 0.0;
	if (x <= -3e-6)
		tmp = t_1;
	elseif (x <= 8.6e-67)
		tmp = t_2;
	elseif (x <= 4.2e-18)
		tmp = t_1;
	elseif (x <= 165000.0)
		tmp = t_2;
	elseif ((x <= 4.2e+159) || (~((x <= 2.7e+210)) && (x <= 4.1e+251)))
		tmp = y * -x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[x, -3e-6], t$95$1, If[LessEqual[x, 8.6e-67], t$95$2, If[LessEqual[x, 4.2e-18], t$95$1, If[LessEqual[x, 165000.0], t$95$2, If[Or[LessEqual[x, 4.2e+159], And[N[Not[LessEqual[x, 2.7e+210]], $MachinePrecision], LessEqual[x, 4.1e+251]]], N[(y * (-x)), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.0000000000000001e-6 or 8.60000000000000053e-67 < x < 4.19999999999999999e-18 or 4.19999999999999978e159 < x < 2.6999999999999999e210 or 4.1000000000000001e251 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 69.2%

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

      1. mul-1-neg 69.2%

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

      2. unsub-neg 69.2%

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

   4. Simplified 69.2%

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

   5. Taylor expanded in x around inf 62.3%

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

      1. cancel-sign-sub-inv 62.3%

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

      2. metadata-eval 62.3%

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

      3. *-lft-identity 62.3%

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

   7. Simplified 62.3%

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

   if -3.0000000000000001e-6 < x < 8.60000000000000053e-67 or 4.19999999999999999e-18 < x < 165000

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around inf 77.3%

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

   if 165000 < x < 4.19999999999999978e159 or 2.6999999999999999e210 < x < 4.1000000000000001e251

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 91.9%

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

      1. fma-def 94.6%

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

      2. mul-1-neg 94.6%

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

   4. Simplified 94.6%

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

   5. Taylor expanded in y around inf 68.7%

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

      1. neg-mul-1 68.7%

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

      2. sub-neg 68.7%

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

   7. Simplified 68.7%

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

   8. Taylor expanded in t around 0 58.3%

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

      1. associate-*r* 58.3%

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

      2. mul-1-neg 58.3%

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

   10. Simplified 58.3%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-67}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq 165000:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+159} \lor \neg \left(x \leq 2.7 \cdot 10^{+210}\right) \land x \leq 4.1 \cdot 10^{+251}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 3: 67.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-167}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-149}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 88000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* x (+ z 1.0))))
   (if (<= y -3.8e-19)
     t_1
     (if (<= y -1e-134)
       t_2
       (if (<= y -2.6e-167)
         (* (- y z) t)
         (if (<= y 2.3e-176)
           t_2
           (if (<= y 1.75e-149)
             (* z (- t))
             (if (<= y 88000000.0) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -3.8e-19) {
		tmp = t_1;
	} else if (y <= -1e-134) {
		tmp = t_2;
	} else if (y <= -2.6e-167) {
		tmp = (y - z) * t;
	} else if (y <= 2.3e-176) {
		tmp = t_2;
	} else if (y <= 1.75e-149) {
		tmp = z * -t;
	} else if (y <= 88000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = x * (z + 1.0d0)
    if (y <= (-3.8d-19)) then
        tmp = t_1
    else if (y <= (-1d-134)) then
        tmp = t_2
    else if (y <= (-2.6d-167)) then
        tmp = (y - z) * t
    else if (y <= 2.3d-176) then
        tmp = t_2
    else if (y <= 1.75d-149) then
        tmp = z * -t
    else if (y <= 88000000.0d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -3.8e-19) {
		tmp = t_1;
	} else if (y <= -1e-134) {
		tmp = t_2;
	} else if (y <= -2.6e-167) {
		tmp = (y - z) * t;
	} else if (y <= 2.3e-176) {
		tmp = t_2;
	} else if (y <= 1.75e-149) {
		tmp = z * -t;
	} else if (y <= 88000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x * (z + 1.0)
	tmp = 0
	if y <= -3.8e-19:
		tmp = t_1
	elif y <= -1e-134:
		tmp = t_2
	elif y <= -2.6e-167:
		tmp = (y - z) * t
	elif y <= 2.3e-176:
		tmp = t_2
	elif y <= 1.75e-149:
		tmp = z * -t
	elif y <= 88000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= -3.8e-19)
		tmp = t_1;
	elseif (y <= -1e-134)
		tmp = t_2;
	elseif (y <= -2.6e-167)
		tmp = Float64(Float64(y - z) * t);
	elseif (y <= 2.3e-176)
		tmp = t_2;
	elseif (y <= 1.75e-149)
		tmp = Float64(z * Float64(-t));
	elseif (y <= 88000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= -3.8e-19)
		tmp = t_1;
	elseif (y <= -1e-134)
		tmp = t_2;
	elseif (y <= -2.6e-167)
		tmp = (y - z) * t;
	elseif (y <= 2.3e-176)
		tmp = t_2;
	elseif (y <= 1.75e-149)
		tmp = z * -t;
	elseif (y <= 88000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e-19], t$95$1, If[LessEqual[y, -1e-134], t$95$2, If[LessEqual[y, -2.6e-167], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 2.3e-176], t$95$2, If[LessEqual[y, 1.75e-149], N[(z * (-t)), $MachinePrecision], If[LessEqual[y, 88000000.0], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.8e-19 or 8.8e7 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 94.5%

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

      1. fma-def 96.1%

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

      2. mul-1-neg 96.1%

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

   4. Simplified 96.1%

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

   5. Taylor expanded in y around inf 83.2%

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

      1. neg-mul-1 83.2%

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

      2. sub-neg 83.2%

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

   7. Simplified 83.2%

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

   if -3.8e-19 < y < -1.00000000000000004e-134 or -2.5999999999999999e-167 < y < 2.3000000000000001e-176 or 1.75e-149 < y < 8.8e7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 92.4%

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

      1. mul-1-neg 92.4%

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

      2. unsub-neg 92.4%

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

   4. Simplified 92.4%

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

   5. Taylor expanded in x around inf 68.1%

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

      1. cancel-sign-sub-inv 68.1%

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

      2. metadata-eval 68.1%

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

      3. *-lft-identity 68.1%

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

   7. Simplified 68.1%

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

   if -1.00000000000000004e-134 < y < -2.5999999999999999e-167

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around inf 83.4%

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

   if 2.3000000000000001e-176 < y < 1.75e-149

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around inf 80.3%

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

   6. Taylor expanded in y around 0 80.3%

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

      1. associate-*r* 80.3%

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

      2. mul-1-neg 80.3%

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

   8. Simplified 80.3%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-134}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-167}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-149}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 88000000:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 4: 37.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-184}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-162}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+63}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+157}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+176}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -1.6e+29)
     t_1
     (if (<= z -1.5e-184)
       (* y t)
       (if (<= z 1.6e-162)
         x
         (if (<= z 8.5e+63)
           (* y t)
           (if (<= z 1.6e+157) (* z x) (if (<= z 7.5e+176) (* y t) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -1.6e+29) {
		tmp = t_1;
	} else if (z <= -1.5e-184) {
		tmp = y * t;
	} else if (z <= 1.6e-162) {
		tmp = x;
	} else if (z <= 8.5e+63) {
		tmp = y * t;
	} else if (z <= 1.6e+157) {
		tmp = z * x;
	} else if (z <= 7.5e+176) {
		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 <= (-1.6d+29)) then
        tmp = t_1
    else if (z <= (-1.5d-184)) then
        tmp = y * t
    else if (z <= 1.6d-162) then
        tmp = x
    else if (z <= 8.5d+63) then
        tmp = y * t
    else if (z <= 1.6d+157) then
        tmp = z * x
    else if (z <= 7.5d+176) 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 <= -1.6e+29) {
		tmp = t_1;
	} else if (z <= -1.5e-184) {
		tmp = y * t;
	} else if (z <= 1.6e-162) {
		tmp = x;
	} else if (z <= 8.5e+63) {
		tmp = y * t;
	} else if (z <= 1.6e+157) {
		tmp = z * x;
	} else if (z <= 7.5e+176) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -1.6e+29:
		tmp = t_1
	elif z <= -1.5e-184:
		tmp = y * t
	elif z <= 1.6e-162:
		tmp = x
	elif z <= 8.5e+63:
		tmp = y * t
	elif z <= 1.6e+157:
		tmp = z * x
	elif z <= 7.5e+176:
		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 <= -1.6e+29)
		tmp = t_1;
	elseif (z <= -1.5e-184)
		tmp = Float64(y * t);
	elseif (z <= 1.6e-162)
		tmp = x;
	elseif (z <= 8.5e+63)
		tmp = Float64(y * t);
	elseif (z <= 1.6e+157)
		tmp = Float64(z * x);
	elseif (z <= 7.5e+176)
		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 <= -1.6e+29)
		tmp = t_1;
	elseif (z <= -1.5e-184)
		tmp = y * t;
	elseif (z <= 1.6e-162)
		tmp = x;
	elseif (z <= 8.5e+63)
		tmp = y * t;
	elseif (z <= 1.6e+157)
		tmp = z * x;
	elseif (z <= 7.5e+176)
		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, -1.6e+29], t$95$1, If[LessEqual[z, -1.5e-184], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.6e-162], x, If[LessEqual[z, 8.5e+63], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.6e+157], N[(z * x), $MachinePrecision], If[LessEqual[z, 7.5e+176], N[(y * t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.59999999999999993e29 or 7.499999999999999e176 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 94.4%

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

      1. fma-def 96.6%

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

      2. mul-1-neg 96.6%

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

   4. Simplified 96.6%

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

   5. Taylor expanded in t around inf 57.0%

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

   6. Taylor expanded in y around 0 52.6%

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

      1. associate-*r* 52.6%

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

      2. mul-1-neg 52.6%

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

   8. Simplified 52.6%

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

   if -1.59999999999999993e29 < z < -1.49999999999999996e-184 or 1.59999999999999988e-162 < z < 8.5000000000000004e63 or 1.6e157 < z < 7.499999999999999e176

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 96.8%

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

      1. fma-def 97.9%

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

      2. mul-1-neg 97.9%

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

   4. Simplified 97.9%

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

   5. Taylor expanded in t around inf 57.7%

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

   6. Taylor expanded in y around inf 45.7%

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

      1. *-commutative 45.7%

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

   8. Simplified 45.7%

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

   if -1.49999999999999996e-184 < z < 1.59999999999999988e-162

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 72.0%

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

   3. Taylor expanded in x around inf 47.3%

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

   if 8.5000000000000004e63 < z < 1.6e157

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.9%

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

      1. fma-def 100.0%

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

      2. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. sub-neg 67.6%

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

   7. Simplified 67.6%

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

   8. Taylor expanded in x around inf 47.7%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-184}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-162}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+63}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+157}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+176}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]

Alternative 5: 70.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-291}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 14000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -7.5e+28)
     t_1
     (if (<= z -4.7e-184)
       (* y (- t x))
       (if (<= z 2.15e-291)
         (- x (* y x))
         (if (<= z 14000.0) (+ x (* y t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -7.5e+28) {
		tmp = t_1;
	} else if (z <= -4.7e-184) {
		tmp = y * (t - x);
	} else if (z <= 2.15e-291) {
		tmp = x - (y * x);
	} else if (z <= 14000.0) {
		tmp = x + (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 * (x - t)
    if (z <= (-7.5d+28)) then
        tmp = t_1
    else if (z <= (-4.7d-184)) then
        tmp = y * (t - x)
    else if (z <= 2.15d-291) then
        tmp = x - (y * x)
    else if (z <= 14000.0d0) then
        tmp = x + (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 * (x - t);
	double tmp;
	if (z <= -7.5e+28) {
		tmp = t_1;
	} else if (z <= -4.7e-184) {
		tmp = y * (t - x);
	} else if (z <= 2.15e-291) {
		tmp = x - (y * x);
	} else if (z <= 14000.0) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -7.5e+28:
		tmp = t_1
	elif z <= -4.7e-184:
		tmp = y * (t - x)
	elif z <= 2.15e-291:
		tmp = x - (y * x)
	elif z <= 14000.0:
		tmp = x + (y * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -7.5e+28)
		tmp = t_1;
	elseif (z <= -4.7e-184)
		tmp = Float64(y * Float64(t - x));
	elseif (z <= 2.15e-291)
		tmp = Float64(x - Float64(y * x));
	elseif (z <= 14000.0)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -7.5e+28)
		tmp = t_1;
	elseif (z <= -4.7e-184)
		tmp = y * (t - x);
	elseif (z <= 2.15e-291)
		tmp = x - (y * x);
	elseif (z <= 14000.0)
		tmp = x + (y * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+28], t$95$1, If[LessEqual[z, -4.7e-184], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e-291], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 14000.0], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.4999999999999998e28 or 14000 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 95.9%

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

      1. fma-def 97.5%

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

      2. mul-1-neg 97.5%

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

   4. Simplified 97.5%

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

   5. Taylor expanded in z around inf 80.4%

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

      1. mul-1-neg 80.4%

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

      2. sub-neg 80.4%

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

   7. Simplified 80.4%

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

   if -7.4999999999999998e28 < z < -4.70000000000000019e-184

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 98.0%

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

      1. fma-def 100.0%

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

      2. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 71.4%

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

      1. neg-mul-1 71.4%

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

      2. sub-neg 71.4%

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

   7. Simplified 71.4%

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

   if -4.70000000000000019e-184 < z < 2.15000000000000018e-291

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 97.0%

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

      1. *-commutative 97.0%

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

   4. Simplified 97.0%

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

   5. Taylor expanded in t around 0 82.2%

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

      1. mul-1-neg 82.2%

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

      2. distribute-lft-neg-out 82.2%

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

      3. *-commutative 82.2%

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

   7. Simplified 82.2%

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

      1. distribute-rgt-neg-out 82.2%

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

      2. unsub-neg 82.2%

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

      3. *-commutative 82.2%

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

   9. Applied egg-rr 82.2%

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

   if 2.15000000000000018e-291 < z < 14000

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 83.3%

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

   3. Taylor expanded in y around inf 77.5%

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

      1. *-commutative 43.9%

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

   5. Simplified 77.5%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+28}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-184}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-291}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 14000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 6: 38.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+28}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-186}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-162}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+68}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.2e+28)
   (* z x)
   (if (<= z -2.45e-186)
     (* y t)
     (if (<= z 3.7e-162) x (if (<= z 1.8e+68) (* y t) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.2e+28) {
		tmp = z * x;
	} else if (z <= -2.45e-186) {
		tmp = y * t;
	} else if (z <= 3.7e-162) {
		tmp = x;
	} else if (z <= 1.8e+68) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.2d+28)) then
        tmp = z * x
    else if (z <= (-2.45d-186)) then
        tmp = y * t
    else if (z <= 3.7d-162) then
        tmp = x
    else if (z <= 1.8d+68) then
        tmp = y * t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.2e+28) {
		tmp = z * x;
	} else if (z <= -2.45e-186) {
		tmp = y * t;
	} else if (z <= 3.7e-162) {
		tmp = x;
	} else if (z <= 1.8e+68) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.2e+28:
		tmp = z * x
	elif z <= -2.45e-186:
		tmp = y * t
	elif z <= 3.7e-162:
		tmp = x
	elif z <= 1.8e+68:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.2e+28)
		tmp = Float64(z * x);
	elseif (z <= -2.45e-186)
		tmp = Float64(y * t);
	elseif (z <= 3.7e-162)
		tmp = x;
	elseif (z <= 1.8e+68)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.2e+28)
		tmp = z * x;
	elseif (z <= -2.45e-186)
		tmp = y * t;
	elseif (z <= 3.7e-162)
		tmp = x;
	elseif (z <= 1.8e+68)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.2e+28], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.45e-186], N[(y * t), $MachinePrecision], If[LessEqual[z, 3.7e-162], x, If[LessEqual[z, 1.8e+68], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2000000000000004e28 or 1.7999999999999999e68 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 95.3%

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

      1. fma-def 97.2%

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

      2. mul-1-neg 97.2%

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

   4. Simplified 97.2%

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

   5. Taylor expanded in z around inf 83.6%

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

      1. mul-1-neg 83.6%

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

      2. sub-neg 83.6%

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

   7. Simplified 83.6%

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

   8. Taylor expanded in x around inf 45.3%

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

   if -5.2000000000000004e28 < z < -2.4499999999999998e-186 or 3.7000000000000002e-162 < z < 1.7999999999999999e68

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 96.7%

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

      1. fma-def 97.8%

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

      2. mul-1-neg 97.8%

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

   4. Simplified 97.8%

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

   5. Taylor expanded in t around inf 56.4%

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

   6. Taylor expanded in y around inf 44.9%

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

      1. *-commutative 44.9%

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

   8. Simplified 44.9%

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

   if -2.4499999999999998e-186 < z < 3.7000000000000002e-162

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 72.0%

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

   3. Taylor expanded in x around inf 47.3%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+28}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-186}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-162}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+68}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 7: 71.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-233}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 84000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -5.8e+29)
     t_1
     (if (<= z -9.5e-233)
       (* y (- t x))
       (if (<= z 84000.0) (+ x (* y t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -5.8e+29) {
		tmp = t_1;
	} else if (z <= -9.5e-233) {
		tmp = y * (t - x);
	} else if (z <= 84000.0) {
		tmp = x + (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 * (x - t)
    if (z <= (-5.8d+29)) then
        tmp = t_1
    else if (z <= (-9.5d-233)) then
        tmp = y * (t - x)
    else if (z <= 84000.0d0) then
        tmp = x + (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 * (x - t);
	double tmp;
	if (z <= -5.8e+29) {
		tmp = t_1;
	} else if (z <= -9.5e-233) {
		tmp = y * (t - x);
	} else if (z <= 84000.0) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -5.8e+29:
		tmp = t_1
	elif z <= -9.5e-233:
		tmp = y * (t - x)
	elif z <= 84000.0:
		tmp = x + (y * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -5.8e+29)
		tmp = t_1;
	elseif (z <= -9.5e-233)
		tmp = Float64(y * Float64(t - x));
	elseif (z <= 84000.0)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -5.8e+29)
		tmp = t_1;
	elseif (z <= -9.5e-233)
		tmp = y * (t - x);
	elseif (z <= 84000.0)
		tmp = x + (y * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+29], t$95$1, If[LessEqual[z, -9.5e-233], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 84000.0], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.7999999999999999e29 or 84000 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 95.9%

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

      1. fma-def 97.5%

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

      2. mul-1-neg 97.5%

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

   4. Simplified 97.5%

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

   5. Taylor expanded in z around inf 80.4%

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

      1. mul-1-neg 80.4%

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

      2. sub-neg 80.4%

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

   7. Simplified 80.4%

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

   if -5.7999999999999999e29 < z < -9.5000000000000003e-233

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 96.8%

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

      1. fma-def 98.4%

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

      2. mul-1-neg 98.4%

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

   4. Simplified 98.4%

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

   5. Taylor expanded in y around inf 69.7%

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

      1. neg-mul-1 69.7%

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

      2. sub-neg 69.7%

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

   7. Simplified 69.7%

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

   if -9.5000000000000003e-233 < z < 84000

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 79.7%

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

   3. Taylor expanded in y around inf 75.5%

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

      1. *-commutative 36.6%

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

   5. Simplified 75.5%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-233}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 84000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 8: 76.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-35} \lor \neg \left(x \leq 2.5 \cdot 10^{-63}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.8e-35) (not (<= x 2.5e-63)))
   (* x (+ (- z y) 1.0))
   (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.8e-35) || !(x <= 2.5e-63)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.8d-35)) .or. (.not. (x <= 2.5d-63))) then
        tmp = x * ((z - y) + 1.0d0)
    else
        tmp = (y - z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.8e-35) || !(x <= 2.5e-63)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.8e-35) or not (x <= 2.5e-63):
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.8e-35) || !(x <= 2.5e-63))
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.8e-35) || ~((x <= 2.5e-63)))
		tmp = x * ((z - y) + 1.0);
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.8e-35], N[Not[LessEqual[x, 2.5e-63]], $MachinePrecision]], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.8000000000000001e-35 or 2.5000000000000001e-63 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 81.3%

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

      1. mul-1-neg 81.3%

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

      2. unsub-neg 81.3%

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

   4. Simplified 81.3%

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

   if -3.8000000000000001e-35 < x < 2.5000000000000001e-63

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around inf 78.8%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-35} \lor \neg \left(x \leq 2.5 \cdot 10^{-63}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]

Alternative 9: 81.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2050000 \lor \neg \left(x \leq 18\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2050000.0) (not (<= x 18.0)))
   (* x (+ (- z y) 1.0))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2050000.0) || !(x <= 18.0)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2050000.0d0)) .or. (.not. (x <= 18.0d0))) then
        tmp = x * ((z - y) + 1.0d0)
    else
        tmp = x + ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2050000.0) || !(x <= 18.0)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2050000.0) or not (x <= 18.0):
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2050000.0) || !(x <= 18.0))
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2050000.0) || ~((x <= 18.0)))
		tmp = x * ((z - y) + 1.0);
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2050000.0], N[Not[LessEqual[x, 18.0]], $MachinePrecision]], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.05e6 or 18 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 87.2%

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

      1. mul-1-neg 87.2%

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

      2. unsub-neg 87.2%

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

   4. Simplified 87.2%

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

   if -2.05e6 < x < 18

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 81.2%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2050000 \lor \neg \left(x \leq 18\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]

Alternative 10: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+29} \lor \neg \left(z \leq 6200000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3e+29) (not (<= z 6200000.0)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3e+29) || !(z <= 6200000.0)) {
		tmp = z * (x - t);
	} 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 <= (-3d+29)) .or. (.not. (z <= 6200000.0d0))) then
        tmp = z * (x - t)
    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 <= -3e+29) || !(z <= 6200000.0)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3e+29) or not (z <= 6200000.0):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3e+29) || !(z <= 6200000.0))
		tmp = Float64(z * Float64(x - t));
	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 <= -3e+29) || ~((z <= 6200000.0)))
		tmp = z * (x - t);
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3e+29], N[Not[LessEqual[z, 6200000.0]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9999999999999999e29 or 6.2e6 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 95.9%

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

      1. fma-def 97.5%

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

      2. mul-1-neg 97.5%

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

   4. Simplified 97.5%

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

   5. Taylor expanded in z around inf 80.4%

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

      1. mul-1-neg 80.4%

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

      2. sub-neg 80.4%

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

   7. Simplified 80.4%

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

   if -2.9999999999999999e29 < z < 6.2e6

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 92.3%

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

      1. *-commutative 92.3%

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

   4. Simplified 92.3%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+29} \lor \neg \left(z \leq 6200000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 11: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -7.7 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1550000:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -7.7e+28)
     t_1
     (if (<= z 1550000.0) (+ x (* y (- t x))) (+ x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -7.7e+28) {
		tmp = t_1;
	} else if (z <= 1550000.0) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-7.7d+28)) then
        tmp = t_1
    else if (z <= 1550000.0d0) then
        tmp = x + (y * (t - x))
    else
        tmp = x + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -7.7e+28) {
		tmp = t_1;
	} else if (z <= 1550000.0) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -7.7e+28:
		tmp = t_1
	elif z <= 1550000.0:
		tmp = x + (y * (t - x))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -7.7e+28)
		tmp = t_1;
	elseif (z <= 1550000.0)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -7.7e+28)
		tmp = t_1;
	elseif (z <= 1550000.0)
		tmp = x + (y * (t - x));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.7e+28], t$95$1, If[LessEqual[z, 1550000.0], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.6999999999999997e28

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 91.6%

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

      1. fma-def 95.0%

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

      2. mul-1-neg 95.0%

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

   4. Simplified 95.0%

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

   5. Taylor expanded in z around inf 83.5%

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

      1. mul-1-neg 83.5%

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

      2. sub-neg 83.5%

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

   7. Simplified 83.5%

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

   if -7.6999999999999997e28 < z < 1.55e6

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 92.3%

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

      1. *-commutative 92.3%

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

   4. Simplified 92.3%

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

   if 1.55e6 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 78.3%

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

      1. mul-1-neg 78.3%

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

      2. unsub-neg 78.3%

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

   4. Simplified 78.3%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.7 \cdot 10^{+28}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 1550000:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 12: 52.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9200000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 58000:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+290}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -9200000.0)
   (* z x)
   (if (<= x 58000.0)
     (* (- y z) t)
     (if (<= x 1.22e+290) (* y (- x)) (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9200000.0) {
		tmp = z * x;
	} else if (x <= 58000.0) {
		tmp = (y - z) * t;
	} else if (x <= 1.22e+290) {
		tmp = y * -x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-9200000.0d0)) then
        tmp = z * x
    else if (x <= 58000.0d0) then
        tmp = (y - z) * t
    else if (x <= 1.22d+290) then
        tmp = y * -x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9200000.0) {
		tmp = z * x;
	} else if (x <= 58000.0) {
		tmp = (y - z) * t;
	} else if (x <= 1.22e+290) {
		tmp = y * -x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -9200000.0:
		tmp = z * x
	elif x <= 58000.0:
		tmp = (y - z) * t
	elif x <= 1.22e+290:
		tmp = y * -x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -9200000.0)
		tmp = Float64(z * x);
	elseif (x <= 58000.0)
		tmp = Float64(Float64(y - z) * t);
	elseif (x <= 1.22e+290)
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -9200000.0)
		tmp = z * x;
	elseif (x <= 58000.0)
		tmp = (y - z) * t;
	elseif (x <= 1.22e+290)
		tmp = y * -x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -9200000.0], N[(z * x), $MachinePrecision], If[LessEqual[x, 58000.0], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[x, 1.22e+290], N[(y * (-x)), $MachinePrecision], N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.2e6 or 1.22000000000000006e290 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 91.2%

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

      1. fma-def 94.1%

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

      2. mul-1-neg 94.1%

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

   4. Simplified 94.1%

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

   5. Taylor expanded in z around inf 52.3%

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

      1. mul-1-neg 52.3%

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

      2. sub-neg 52.3%

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

   7. Simplified 52.3%

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

   8. Taylor expanded in x around inf 46.8%

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

   if -9.2e6 < x < 58000

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. mul-1-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around inf 70.8%

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

   if 58000 < x < 1.22000000000000006e290

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 90.7%

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

      1. fma-def 94.4%

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

      2. mul-1-neg 94.4%

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

   4. Simplified 94.4%

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

   5. Taylor expanded in y around inf 56.6%

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

      1. neg-mul-1 56.6%

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

      2. sub-neg 56.6%

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

   7. Simplified 56.6%

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

   8. Taylor expanded in t around 0 47.6%

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

      1. associate-*r* 47.6%

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

      2. mul-1-neg 47.6%

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

   10. Simplified 47.6%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9200000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 58000:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+290}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 13: 69.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+30} \lor \neg \left(z \leq 140000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.15e+30) (not (<= z 140000.0))) (* z (- x t)) (* y (- t x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15e+30) || !(z <= 140000.0)) {
		tmp = z * (x - t);
	} else {
		tmp = 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 <= (-1.15d+30)) .or. (.not. (z <= 140000.0d0))) then
        tmp = z * (x - t)
    else
        tmp = 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 <= -1.15e+30) || !(z <= 140000.0)) {
		tmp = z * (x - t);
	} else {
		tmp = y * (t - x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.15e+30) or not (z <= 140000.0):
		tmp = z * (x - t)
	else:
		tmp = y * (t - x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.15e+30) || !(z <= 140000.0))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(y * Float64(t - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.15e+30) || ~((z <= 140000.0)))
		tmp = z * (x - t);
	else
		tmp = y * (t - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.15e+30], N[Not[LessEqual[z, 140000.0]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e30 or 1.4e5 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 95.9%

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

      1. fma-def 97.5%

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

      2. mul-1-neg 97.5%

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

   4. Simplified 97.5%

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

   5. Taylor expanded in z around inf 80.4%

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

      1. mul-1-neg 80.4%

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

      2. sub-neg 80.4%

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

   7. Simplified 80.4%

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

   if -1.15e30 < z < 1.4e5

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 95.5%

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

      1. fma-def 97.0%

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

      2. mul-1-neg 97.0%

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

   4. Simplified 97.0%

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

   5. Taylor expanded in y around inf 62.4%

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

      1. neg-mul-1 62.4%

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

      2. sub-neg 62.4%

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

   7. Simplified 62.4%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+30} \lor \neg \left(z \leq 140000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 14: 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 15: 36.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-33} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.85e-33) (not (<= z 1.0))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.85e-33) || !(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 <= (-1.85d-33)) .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 <= -1.85e-33) || !(z <= 1.0)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.85e-33) 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 <= -1.85e-33) || !(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 <= -1.85e-33) || ~((z <= 1.0)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.85e-33], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.85000000000000007e-33 or 1 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 96.2%

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

      1. fma-def 97.7%

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

      2. mul-1-neg 97.7%

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

   4. Simplified 97.7%

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

   5. Taylor expanded in z around inf 74.8%

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

      1. mul-1-neg 74.8%

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

      2. sub-neg 74.8%

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

   7. Simplified 74.8%

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

   8. Taylor expanded in x around inf 40.4%

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

   if -1.85000000000000007e-33 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 74.2%

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

   3. Taylor expanded in x around inf 34.2%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-33} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 17.7% 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 65.7%

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

3. Taylor expanded in x around inf 17.7%

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

4. Final simplification 17.7%

   \[\leadsto x \]

Developer target: 96.1% 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 2023322 
(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))))