Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Percentage Accurate: 97.0% → 97.0%

Time: 8.4s

Alternatives: 12

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

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

C

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

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 - y)) * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

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

C

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

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 - y)) * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ t \cdot \frac{x - y}{z - y} \end{array} \]

FPCore

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

C

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

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 = t * ((x - y) / (z - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing
3. Step-by-step derivation

   1. *-commutative N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

   4. /-lowering-/.f64 N/A

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

   5. /-lowering-/.f64 N/A

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

   6. --lowering--.f64 N/A

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

   7. --lowering--.f64 96.0

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

4. Applied egg-rr 96.0%

   \[\leadsto \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]
5. Step-by-step derivation

   1. div-inv N/A

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

   2. clear-num N/A

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

   3. *-lowering-*.f64 N/A

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

   4. /-lowering-/.f64 N/A

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

   5. --lowering--.f64 N/A

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

   6. --lowering--.f64 96.5

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

6. Applied egg-rr 96.5%

   \[\leadsto \color{blue}{t \cdot \frac{x - y}{z - y}} \]
7. Add Preprocessing

Alternative 2: 95.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.6:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t\_1 \leq 100000:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x (- z y)))))
   (if (<= t_1 -1e+15)
     t_2
     (if (<= t_1 0.6)
       (* t (/ (- x y) z))
       (if (<= t_1 100000.0) (fma t (/ (- z x) y) t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / (z - y));
	double tmp;
	if (t_1 <= -1e+15) {
		tmp = t_2;
	} else if (t_1 <= 0.6) {
		tmp = t * ((x - y) / z);
	} else if (t_1 <= 100000.0) {
		tmp = fma(t, ((z - x) / y), t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -1e+15)
		tmp = t_2;
	elseif (t_1 <= 0.6)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (t_1 <= 100000.0)
		tmp = fma(t, Float64(Float64(z - x) / y), t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+15], t$95$2, If[LessEqual[t$95$1, 0.6], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 100000.0], N[(t * N[(N[(z - x), $MachinePrecision] / y), $MachinePrecision] + t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e15 or 1e5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 94.3

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

   5. Simplified 94.3%

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

   if -1e15 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.599999999999999978

   1. Initial program 95.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 90.9

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

   5. Simplified 90.9%

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

   if 0.599999999999999978 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e5

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. distribute-lft-out-- N/A

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

      7. associate-/l* N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

   5. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \frac{z - x}{y}, t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.6:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 100000:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.0004:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t\_1 \leq 100000:\\ \;\;\;\;\mathsf{fma}\left(0 - \frac{x}{y}, t, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x (- z y)))))
   (if (<= t_1 -1e+15)
     t_2
     (if (<= t_1 0.0004)
       (* t (/ (- x y) z))
       (if (<= t_1 100000.0) (fma (- 0.0 (/ x y)) t t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / (z - y));
	double tmp;
	if (t_1 <= -1e+15) {
		tmp = t_2;
	} else if (t_1 <= 0.0004) {
		tmp = t * ((x - y) / z);
	} else if (t_1 <= 100000.0) {
		tmp = fma((0.0 - (x / y)), t, t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -1e+15)
		tmp = t_2;
	elseif (t_1 <= 0.0004)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (t_1 <= 100000.0)
		tmp = fma(Float64(0.0 - Float64(x / y)), t, t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+15], t$95$2, If[LessEqual[t$95$1, 0.0004], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 100000.0], N[(N[(0.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t + t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e15 or 1e5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 94.3

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

   5. Simplified 94.3%

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

   if -1e15 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.00000000000000019e-4

   1. Initial program 95.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 91.6

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

   5. Simplified 91.6%

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

   if 4.00000000000000019e-4 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e5

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 97.7

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

   5. Simplified 97.7%

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

      1. *-commutative N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. distribute-rgt-in N/A

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

      5. *-lft-identity N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. /-lowering-/.f64 N/A

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

      9. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - x}}{y}, t, t\right) \]

      10. --lowering--.f64 97.7

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{0 - x}}{y}, t, t\right) \]

   7. Applied egg-rr 97.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{0 - x}{y}, t, t\right)} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 97.7

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

   9. Applied egg-rr 97.7%

      \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{-x}}{y}, t, t\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.0004:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 100000:\\ \;\;\;\;\mathsf{fma}\left(0 - \frac{x}{y}, t, t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.0004:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;t\_1 \leq 100000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x (- z y)))))
   (if (<= t_1 -1e+15)
     t_2
     (if (<= t_1 0.0004)
       (* t (/ (- x y) z))
       (if (<= t_1 100000.0) (* t (- 1.0 (/ x y))) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / (z - y));
	double tmp;
	if (t_1 <= -1e+15) {
		tmp = t_2;
	} else if (t_1 <= 0.0004) {
		tmp = t * ((x - y) / z);
	} else if (t_1 <= 100000.0) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = t * (x / (z - y))
    if (t_1 <= (-1d+15)) then
        tmp = t_2
    else if (t_1 <= 0.0004d0) then
        tmp = t * ((x - y) / z)
    else if (t_1 <= 100000.0d0) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / (z - y));
	double tmp;
	if (t_1 <= -1e+15) {
		tmp = t_2;
	} else if (t_1 <= 0.0004) {
		tmp = t * ((x - y) / z);
	} else if (t_1 <= 100000.0) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = t * (x / (z - y))
	tmp = 0
	if t_1 <= -1e+15:
		tmp = t_2
	elif t_1 <= 0.0004:
		tmp = t * ((x - y) / z)
	elif t_1 <= 100000.0:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -1e+15)
		tmp = t_2;
	elseif (t_1 <= 0.0004)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (t_1 <= 100000.0)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = t * (x / (z - y));
	tmp = 0.0;
	if (t_1 <= -1e+15)
		tmp = t_2;
	elseif (t_1 <= 0.0004)
		tmp = t * ((x - y) / z);
	elseif (t_1 <= 100000.0)
		tmp = t * (1.0 - (x / y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+15], t$95$2, If[LessEqual[t$95$1, 0.0004], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 100000.0], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e15 or 1e5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 94.3

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

   5. Simplified 94.3%

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

   if -1e15 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.00000000000000019e-4

   1. Initial program 95.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 91.6

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

   5. Simplified 91.6%

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

   if 4.00000000000000019e-4 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e5

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 97.7

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

   5. Simplified 97.7%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.0004:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 100000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;t\_1 \leq -1000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.0004:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;t\_1 \leq 100000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x (- z y)))))
   (if (<= t_1 -1000000000.0)
     t_2
     (if (<= t_1 0.0004)
       (* (- x y) (/ t z))
       (if (<= t_1 100000.0) (* t (- 1.0 (/ x y))) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / (z - y));
	double tmp;
	if (t_1 <= -1000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.0004) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 100000.0) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = t * (x / (z - y))
    if (t_1 <= (-1000000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 0.0004d0) then
        tmp = (x - y) * (t / z)
    else if (t_1 <= 100000.0d0) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / (z - y));
	double tmp;
	if (t_1 <= -1000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.0004) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 100000.0) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = t * (x / (z - y))
	tmp = 0
	if t_1 <= -1000000000.0:
		tmp = t_2
	elif t_1 <= 0.0004:
		tmp = (x - y) * (t / z)
	elif t_1 <= 100000.0:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -1000000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.0004)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (t_1 <= 100000.0)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = t * (x / (z - y));
	tmp = 0.0;
	if (t_1 <= -1000000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.0004)
		tmp = (x - y) * (t / z);
	elseif (t_1 <= 100000.0)
		tmp = t * (1.0 - (x / y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1000000000.0], t$95$2, If[LessEqual[t$95$1, 0.0004], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 100000.0], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e9 or 1e5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 94.4

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

   5. Simplified 94.4%

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

   if -1e9 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.00000000000000019e-4

   1. Initial program 95.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 91.5

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

   5. Simplified 91.5%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. associate-*r* N/A

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

      5. div-inv N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 86.1

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

   7. Applied egg-rr 86.1%

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

   if 4.00000000000000019e-4 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e5

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 97.7

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

   5. Simplified 97.7%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -1000000000:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.0004:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 100000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := x \cdot \frac{t}{z - y}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.0004:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;t\_1 \leq 100000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* x (/ t (- z y)))))
   (if (<= t_1 -1e+15)
     t_2
     (if (<= t_1 0.0004)
       (* (- x y) (/ t z))
       (if (<= t_1 100000.0) (* t (- 1.0 (/ x y))) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = x * (t / (z - y));
	double tmp;
	if (t_1 <= -1e+15) {
		tmp = t_2;
	} else if (t_1 <= 0.0004) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 100000.0) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = x * (t / (z - y))
    if (t_1 <= (-1d+15)) then
        tmp = t_2
    else if (t_1 <= 0.0004d0) then
        tmp = (x - y) * (t / z)
    else if (t_1 <= 100000.0d0) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = x * (t / (z - y));
	double tmp;
	if (t_1 <= -1e+15) {
		tmp = t_2;
	} else if (t_1 <= 0.0004) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 100000.0) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = x * (t / (z - y))
	tmp = 0
	if t_1 <= -1e+15:
		tmp = t_2
	elif t_1 <= 0.0004:
		tmp = (x - y) * (t / z)
	elif t_1 <= 100000.0:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(x * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -1e+15)
		tmp = t_2;
	elseif (t_1 <= 0.0004)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (t_1 <= 100000.0)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = x * (t / (z - y));
	tmp = 0.0;
	if (t_1 <= -1e+15)
		tmp = t_2;
	elseif (t_1 <= 0.0004)
		tmp = (x - y) * (t / z);
	elseif (t_1 <= 100000.0)
		tmp = t * (1.0 - (x / y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+15], t$95$2, If[LessEqual[t$95$1, 0.0004], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 100000.0], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1e15 or 1e5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 91.6

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

   5. Simplified 91.6%

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

   if -1e15 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.00000000000000019e-4

   1. Initial program 95.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 91.6

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

   5. Simplified 91.6%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. associate-*r* N/A

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

      5. div-inv N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 86.3

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

   7. Applied egg-rr 86.3%

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

   if 4.00000000000000019e-4 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e5

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 97.7

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

   5. Simplified 97.7%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 0.0004:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 100000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := x \cdot \frac{t}{z - y}\\ \mathbf{if}\;t\_1 \leq 10^{-309}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t\_1 \leq 100000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* x (/ t (- z y)))))
   (if (<= t_1 1e-309)
     t_2
     (if (<= t_1 2e-7)
       (* t (/ x z))
       (if (<= t_1 100000.0) (* t (- 1.0 (/ x y))) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = x * (t / (z - y));
	double tmp;
	if (t_1 <= 1e-309) {
		tmp = t_2;
	} else if (t_1 <= 2e-7) {
		tmp = t * (x / z);
	} else if (t_1 <= 100000.0) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = x * (t / (z - y))
    if (t_1 <= 1d-309) then
        tmp = t_2
    else if (t_1 <= 2d-7) then
        tmp = t * (x / z)
    else if (t_1 <= 100000.0d0) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = x * (t / (z - y));
	double tmp;
	if (t_1 <= 1e-309) {
		tmp = t_2;
	} else if (t_1 <= 2e-7) {
		tmp = t * (x / z);
	} else if (t_1 <= 100000.0) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = x * (t / (z - y))
	tmp = 0
	if t_1 <= 1e-309:
		tmp = t_2
	elif t_1 <= 2e-7:
		tmp = t * (x / z)
	elif t_1 <= 100000.0:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(x * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= 1e-309)
		tmp = t_2;
	elseif (t_1 <= 2e-7)
		tmp = Float64(t * Float64(x / z));
	elseif (t_1 <= 100000.0)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = x * (t / (z - y));
	tmp = 0.0;
	if (t_1 <= 1e-309)
		tmp = t_2;
	elseif (t_1 <= 2e-7)
		tmp = t * (x / z);
	elseif (t_1 <= 100000.0)
		tmp = t * (1.0 - (x / y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e-309], t$95$2, If[LessEqual[t$95$1, 2e-7], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 100000.0], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 1.000000000000002e-309 or 1e5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 93.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 79.5

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

   5. Simplified 79.5%

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

   if 1.000000000000002e-309 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.9999999999999999e-7

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 71.5

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

   5. Simplified 71.5%

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

   if 1.9999999999999999e-7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e5

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. --lowering--.f64 N/A

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

      11. /-lowering-/.f64 95.7

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

   5. Simplified 95.7%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 10^{-309}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 100000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := x \cdot \frac{t}{z - y}\\ \mathbf{if}\;t\_1 \leq 10^{-309}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* x (/ t (- z y)))))
   (if (<= t_1 1e-309)
     t_2
     (if (<= t_1 2e-7) (* t (/ x z)) (if (<= t_1 2.0) t t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = x * (t / (z - y));
	double tmp;
	if (t_1 <= 1e-309) {
		tmp = t_2;
	} else if (t_1 <= 2e-7) {
		tmp = t * (x / z);
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = x * (t / (z - y))
    if (t_1 <= 1d-309) then
        tmp = t_2
    else if (t_1 <= 2d-7) then
        tmp = t * (x / z)
    else if (t_1 <= 2.0d0) then
        tmp = t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = x * (t / (z - y));
	double tmp;
	if (t_1 <= 1e-309) {
		tmp = t_2;
	} else if (t_1 <= 2e-7) {
		tmp = t * (x / z);
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = x * (t / (z - y))
	tmp = 0
	if t_1 <= 1e-309:
		tmp = t_2
	elif t_1 <= 2e-7:
		tmp = t * (x / z)
	elif t_1 <= 2.0:
		tmp = t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(x * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= 1e-309)
		tmp = t_2;
	elseif (t_1 <= 2e-7)
		tmp = Float64(t * Float64(x / z));
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = x * (t / (z - y));
	tmp = 0.0;
	if (t_1 <= 1e-309)
		tmp = t_2;
	elseif (t_1 <= 2e-7)
		tmp = t * (x / z);
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e-309], t$95$2, If[LessEqual[t$95$1, 2e-7], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], t, t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 1.000000000000002e-309 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 93.3%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 79.2

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

   5. Simplified 79.2%

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

   if 1.000000000000002e-309 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1.9999999999999999e-7

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 71.5

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

   5. Simplified 71.5%

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

   if 1.9999999999999999e-7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Simplified 92.4%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 10^{-309}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 2:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t\_1 \leq 100000:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 2e-7) (* t (/ x z)) (if (<= t_1 100000.0) t (/ (* t x) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 2e-7) {
		tmp = t * (x / z);
	} else if (t_1 <= 100000.0) {
		tmp = t;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 2d-7) then
        tmp = t * (x / z)
    else if (t_1 <= 100000.0d0) then
        tmp = t
    else
        tmp = (t * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 2e-7) {
		tmp = t * (x / z);
	} else if (t_1 <= 100000.0) {
		tmp = t;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 2e-7:
		tmp = t * (x / z)
	elif t_1 <= 100000.0:
		tmp = t
	else:
		tmp = (t * x) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 2e-7)
		tmp = Float64(t * Float64(x / z));
	elseif (t_1 <= 100000.0)
		tmp = t;
	else
		tmp = Float64(Float64(t * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 2e-7)
		tmp = t * (x / z);
	elseif (t_1 <= 100000.0)
		tmp = t;
	else
		tmp = (t * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e-7], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 100000.0], t, N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 1.9999999999999999e-7

   1. Initial program 94.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 62.4

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

   5. Simplified 62.4%

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

   if 1.9999999999999999e-7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e5

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Simplified 91.5%

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

   if 1e5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 96.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 54.7

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

   5. Simplified 54.7%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 100000:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t \cdot \frac{x}{z}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-7}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 100000:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t (/ x z))))
   (if (<= t_1 2e-7) t_2 (if (<= t_1 100000.0) t t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / z);
	double tmp;
	if (t_1 <= 2e-7) {
		tmp = t_2;
	} else if (t_1 <= 100000.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = t * (x / z)
    if (t_1 <= 2d-7) then
        tmp = t_2
    else if (t_1 <= 100000.0d0) then
        tmp = t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t * (x / z);
	double tmp;
	if (t_1 <= 2e-7) {
		tmp = t_2;
	} else if (t_1 <= 100000.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = t * (x / z)
	tmp = 0
	if t_1 <= 2e-7:
		tmp = t_2
	elif t_1 <= 100000.0:
		tmp = t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (t_1 <= 2e-7)
		tmp = t_2;
	elseif (t_1 <= 100000.0)
		tmp = t;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = t * (x / z);
	tmp = 0.0;
	if (t_1 <= 2e-7)
		tmp = t_2;
	elseif (t_1 <= 100000.0)
		tmp = t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e-7], t$95$2, If[LessEqual[t$95$1, 100000.0], t, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 1.9999999999999999e-7 or 1e5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 61.2

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

   5. Simplified 61.2%

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

   if 1.9999999999999999e-7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e5

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Simplified 91.5%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 2 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 100000:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-7}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 100000:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* x (/ t z))))
   (if (<= t_1 2e-7) t_2 (if (<= t_1 100000.0) t t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = x * (t / z);
	double tmp;
	if (t_1 <= 2e-7) {
		tmp = t_2;
	} else if (t_1 <= 100000.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = x * (t / z)
    if (t_1 <= 2d-7) then
        tmp = t_2
    else if (t_1 <= 100000.0d0) then
        tmp = t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = x * (t / z);
	double tmp;
	if (t_1 <= 2e-7) {
		tmp = t_2;
	} else if (t_1 <= 100000.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = x * (t / z)
	tmp = 0
	if t_1 <= 2e-7:
		tmp = t_2
	elif t_1 <= 100000.0:
		tmp = t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t_1 <= 2e-7)
		tmp = t_2;
	elseif (t_1 <= 100000.0)
		tmp = t;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = x * (t / z);
	tmp = 0.0;
	if (t_1 <= 2e-7)
		tmp = t_2;
	elseif (t_1 <= 100000.0)
		tmp = t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e-7], t$95$2, If[LessEqual[t$95$1, 100000.0], t, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 1.9999999999999999e-7 or 1e5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 74.7

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

   5. Simplified 74.7%

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

   6. Taylor expanded in z around inf

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

   8. Simplified 58.2%

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

   if 1.9999999999999999e-7 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e5

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Simplified 91.5%

      \[\leadsto \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 35.6% accurate, 23.0× speedup

Math

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

FPCore

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

C

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

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 = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing

3. Taylor expanded in y around inf

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

5. Simplified 33.3%

   \[\leadsto \color{blue}{t} \]
6. Add Preprocessing

Developer Target 1: 97.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{t}{\frac{z - y}{x - y}} \end{array} \]

FPCore

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

C

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

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 = t / ((z - y) / (x - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024195 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (! :herbie-platform default (/ t (/ (- z y) (- x y))))

  (* (/ (- x y) (- z y)) t))