Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.4% → 97.6%

Time: 3.4s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	(x * (y - z)) / (t - z)
END code

Initial Program: 84.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	(x * (y - z)) / (t - z)
END code

Alternative 1: 97.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \frac{\left|x\right| \cdot \left(y - z\right)}{t - z}\\ \mathsf{copysign}\left(1, x\right) \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+273}:\\ \;\;\;\;\frac{y - z}{\frac{t - z}{\left|x\right|}}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+231}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{\left|x\right|}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (* (fabs x) (- y z)) (- t z))))
  (*
   (copysign 1.0 x)
   (if (<= t_1 -4e+273)
     (/ (- y z) (/ (- t z) (fabs x)))
     (if (<= t_1 5e+231) t_1 (* (- y z) (/ (fabs x) (- t z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (fabs(x) * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= -4e+273) {
		tmp = (y - z) / ((t - z) / fabs(x));
	} else if (t_1 <= 5e+231) {
		tmp = t_1;
	} else {
		tmp = (y - z) * (fabs(x) / (t - z));
	}
	return copysign(1.0, x) * tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (Math.abs(x) * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= -4e+273) {
		tmp = (y - z) / ((t - z) / Math.abs(x));
	} else if (t_1 <= 5e+231) {
		tmp = t_1;
	} else {
		tmp = (y - z) * (Math.abs(x) / (t - z));
	}
	return Math.copySign(1.0, x) * tmp;
}

Python

def code(x, y, z, t):
	t_1 = (math.fabs(x) * (y - z)) / (t - z)
	tmp = 0
	if t_1 <= -4e+273:
		tmp = (y - z) / ((t - z) / math.fabs(x))
	elif t_1 <= 5e+231:
		tmp = t_1
	else:
		tmp = (y - z) * (math.fabs(x) / (t - z))
	return math.copysign(1.0, x) * tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(abs(x) * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if (t_1 <= -4e+273)
		tmp = Float64(Float64(y - z) / Float64(Float64(t - z) / abs(x)));
	elseif (t_1 <= 5e+231)
		tmp = t_1;
	else
		tmp = Float64(Float64(y - z) * Float64(abs(x) / Float64(t - z)));
	end
	return Float64(copysign(1.0, x) * tmp)
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (abs(x) * (y - z)) / (t - z);
	tmp = 0.0;
	if (t_1 <= -4e+273)
		tmp = (y - z) / ((t - z) / abs(x));
	elseif (t_1 <= 5e+231)
		tmp = t_1;
	else
		tmp = (y - z) * (abs(x) / (t - z));
	end
	tmp_2 = (sign(x) * abs(1.0)) * tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[Abs[x], $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$1, -4e+273], N[(N[(y - z), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] / N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+231], t$95$1, N[(N[(y - z), $MachinePrecision] * N[(N[Abs[x], $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -3.9999999999999998e273

   1. Initial program 84.4%

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

   3. Applied rewrites 45.6%

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

   5. Applied rewrites 83.6%

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

   if -3.9999999999999998e273 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 5.0000000000000003e231

   1. Initial program 84.4%

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

   if 5.0000000000000003e231 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 84.4%

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

   3. Applied rewrites 84.3%

      \[\leadsto \left(y - z\right) \cdot \frac{x}{t - z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 97.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{\left|x\right|}{t - z}\\ t_2 := \frac{\left|x\right| \cdot \left(y - z\right)}{t - z}\\ \mathsf{copysign}\left(1, x\right) \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+231}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* (- y z) (/ (fabs x) (- t z))))
       (t_2 (/ (* (fabs x) (- y z)) (- t z))))
  (*
   (copysign 1.0 x)
   (if (<= t_2 -4e+273) t_1 (if (<= t_2 5e+231) t_2 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (fabs(x) / (t - z));
	double t_2 = (fabs(x) * (y - z)) / (t - z);
	double tmp;
	if (t_2 <= -4e+273) {
		tmp = t_1;
	} else if (t_2 <= 5e+231) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return copysign(1.0, x) * tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (Math.abs(x) / (t - z));
	double t_2 = (Math.abs(x) * (y - z)) / (t - z);
	double tmp;
	if (t_2 <= -4e+273) {
		tmp = t_1;
	} else if (t_2 <= 5e+231) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return Math.copySign(1.0, x) * tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (math.fabs(x) / (t - z))
	t_2 = (math.fabs(x) * (y - z)) / (t - z)
	tmp = 0
	if t_2 <= -4e+273:
		tmp = t_1
	elif t_2 <= 5e+231:
		tmp = t_2
	else:
		tmp = t_1
	return math.copysign(1.0, x) * tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(abs(x) / Float64(t - z)))
	t_2 = Float64(Float64(abs(x) * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if (t_2 <= -4e+273)
		tmp = t_1;
	elseif (t_2 <= 5e+231)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return Float64(copysign(1.0, x) * tmp)
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (abs(x) / (t - z));
	t_2 = (abs(x) * (y - z)) / (t - z);
	tmp = 0.0;
	if (t_2 <= -4e+273)
		tmp = t_1;
	elseif (t_2 <= 5e+231)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = (sign(x) * abs(1.0)) * tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(N[Abs[x], $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Abs[x], $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$2, -4e+273], t$95$1, If[LessEqual[t$95$2, 5e+231], t$95$2, t$95$1]]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -3.9999999999999998e273 or 5.0000000000000003e231 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 84.4%

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

   3. Applied rewrites 84.3%

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

   if -3.9999999999999998e273 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 5.0000000000000003e231

   1. Initial program 84.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	x * ((z - y) / (z - t))
END code

Derivation

1. Initial program 84.4%

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

3. Applied rewrites 97.0%

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

Alternative 4: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -5.524060034400675 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -3.2844961741444462 \cdot 10^{-236}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;z \leq 2.074714056229024 \cdot 10^{+46}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= z -5.524060034400675e+35)
  (* x (/ (- z y) z))
  (if (<= z -3.2844961741444462e-236)
    (/ (* x y) (- t z))
    (if (<= z 2.074714056229024e+46)
      (/ (* x (- y z)) t)
      (* x (/ z (- z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.524060034400675e+35) {
		tmp = x * ((z - y) / z);
	} else if (z <= -3.2844961741444462e-236) {
		tmp = (x * y) / (t - z);
	} else if (z <= 2.074714056229024e+46) {
		tmp = (x * (y - z)) / t;
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 <= (-5.524060034400675d+35)) then
        tmp = x * ((z - y) / z)
    else if (z <= (-3.2844961741444462d-236)) then
        tmp = (x * y) / (t - z)
    else if (z <= 2.074714056229024d+46) then
        tmp = (x * (y - z)) / t
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.524060034400675e+35) {
		tmp = x * ((z - y) / z);
	} else if (z <= -3.2844961741444462e-236) {
		tmp = (x * y) / (t - z);
	} else if (z <= 2.074714056229024e+46) {
		tmp = (x * (y - z)) / t;
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.524060034400675e+35:
		tmp = x * ((z - y) / z)
	elif z <= -3.2844961741444462e-236:
		tmp = (x * y) / (t - z)
	elif z <= 2.074714056229024e+46:
		tmp = (x * (y - z)) / t
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.524060034400675e+35)
		tmp = Float64(x * Float64(Float64(z - y) / z));
	elseif (z <= -3.2844961741444462e-236)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	elseif (z <= 2.074714056229024e+46)
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.524060034400675e+35)
		tmp = x * ((z - y) / z);
	elseif (z <= -3.2844961741444462e-236)
		tmp = (x * y) / (t - z);
	elseif (z <= 2.074714056229024e+46)
		tmp = (x * (y - z)) / t;
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.524060034400675e+35], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.2844961741444462e-236], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.074714056229024e+46], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (z <= (20747140562290239249715802397516968849152409600)) THEN ((x * (y - z)) / t) ELSE (x * (z / (z - t))) ENDIF IN
	LET tmp_1 = IF (z <= (-32844961741444462407173143795749739974701126406467838095056216990617528458067347094640456071441275836155037741846885054743112287472860711622981152164436567913439115133936772053663851953692406589091911118541846472020236181485724313490639542360503101971746148350806046265550989094901477206415095837289016999630806012893271664879255699092656468410149596487281201441181590312132915275111232949861268724547305148452532047566418142377839744759493454073577949224300530595419665224841802191638095593694155564304654910453370178141578801912575089681955746530705032674990473395837398129515349864959716796875e-831)) THEN ((x * y) / (t - z)) ELSE tmp_2 ENDIF IN
	LET tmp = IF (z <= (-552406003440067519028647541124104192)) THEN (x * ((z - y) / z)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if z < -5.5240600344006752e35

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 52.3%

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

   if -5.5240600344006752e35 < z < -3.2844961741444462e-236

   1. Initial program 84.4%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 50.0%

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

   if -3.2844961741444462e-236 < z < 2.0747140562290239e46

   1. Initial program 84.4%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 47.5%

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

   if 2.0747140562290239e46 < z

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 53.9%

      \[\leadsto x \cdot \frac{z}{z - t} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 5: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -5.524060034400675 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -2.186412909082924 \cdot 10^{-296}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{elif}\;z \leq 2.074714056229024 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= z -5.524060034400675e+35)
  (* x (/ (- z y) z))
  (if (<= z -2.186412909082924e-296)
    (/ (* x y) (- t z))
    (if (<= z 2.074714056229024e+46)
      (* x (/ (- y z) t))
      (* x (/ z (- z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.524060034400675e+35) {
		tmp = x * ((z - y) / z);
	} else if (z <= -2.186412909082924e-296) {
		tmp = (x * y) / (t - z);
	} else if (z <= 2.074714056229024e+46) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 <= (-5.524060034400675d+35)) then
        tmp = x * ((z - y) / z)
    else if (z <= (-2.186412909082924d-296)) then
        tmp = (x * y) / (t - z)
    else if (z <= 2.074714056229024d+46) then
        tmp = x * ((y - z) / t)
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.524060034400675e+35) {
		tmp = x * ((z - y) / z);
	} else if (z <= -2.186412909082924e-296) {
		tmp = (x * y) / (t - z);
	} else if (z <= 2.074714056229024e+46) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.524060034400675e+35:
		tmp = x * ((z - y) / z)
	elif z <= -2.186412909082924e-296:
		tmp = (x * y) / (t - z)
	elif z <= 2.074714056229024e+46:
		tmp = x * ((y - z) / t)
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.524060034400675e+35)
		tmp = Float64(x * Float64(Float64(z - y) / z));
	elseif (z <= -2.186412909082924e-296)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	elseif (z <= 2.074714056229024e+46)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.524060034400675e+35)
		tmp = x * ((z - y) / z);
	elseif (z <= -2.186412909082924e-296)
		tmp = (x * y) / (t - z);
	elseif (z <= 2.074714056229024e+46)
		tmp = x * ((y - z) / t);
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.524060034400675e+35], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.186412909082924e-296], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.074714056229024e+46], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (z <= (20747140562290239249715802397516968849152409600)) THEN (x * ((y - z) / t)) ELSE (x * (z / (z - t))) ENDIF IN
	LET tmp_1 = IF (z <= (-21864129090829239673723633396604793658176196911142394031872415849189028253984685441090432057217485644662857252002827347019789515455094722318099710350876356607352941295661003992469716624628661915381556767172163492087810413126255899618779018225311666788287229687725407520018194635424542925220296868741029840929081757276584582219452296386554228333432655812007084545082294756408542642144445690622061106565719000039179271588586234680908550462442979274557100327860505293969008260501779253325304610729647633223139487863861853743199548346180855515928592309943698240298248553066627922352291302381664902462113502857160578695237752657067707914991916479864148602923302425365376171217697078154575245766846774996862434736755176345468498766422271728515625e-1035)) THEN ((x * y) / (t - z)) ELSE tmp_2 ENDIF IN
	LET tmp = IF (z <= (-552406003440067519028647541124104192)) THEN (x * ((z - y) / z)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if z < -5.5240600344006752e35

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 52.3%

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

   if -5.5240600344006752e35 < z < -2.186412909082924e-296

   1. Initial program 84.4%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 50.0%

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

   if -2.186412909082924e-296 < z < 2.0747140562290239e46

   1. Initial program 84.4%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 47.5%

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

   6. Applied rewrites 50.2%

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

   if 2.0747140562290239e46 < z

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 53.9%

      \[\leadsto x \cdot \frac{z}{z - t} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := x \cdot \frac{z - y}{z}\\ \mathbf{if}\;z \leq -5.524060034400675 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.049736435618952 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 6.124997616673152 \cdot 10^{+124}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* x (/ (- z y) z))))
  (if (<= z -5.524060034400675e+35)
    t_1
    (if (<= z 3.049736435618952e-54)
      (* x (/ y (- t z)))
      (if (<= z 6.124997616673152e+124) (* z (/ x (- z t))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - y) / z);
	double tmp;
	if (z <= -5.524060034400675e+35) {
		tmp = t_1;
	} else if (z <= 3.049736435618952e-54) {
		tmp = x * (y / (t - z));
	} else if (z <= 6.124997616673152e+124) {
		tmp = z * (x / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 * ((z - y) / z)
    if (z <= (-5.524060034400675d+35)) then
        tmp = t_1
    else if (z <= 3.049736435618952d-54) then
        tmp = x * (y / (t - z))
    else if (z <= 6.124997616673152d+124) then
        tmp = z * (x / (z - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - y) / z);
	double tmp;
	if (z <= -5.524060034400675e+35) {
		tmp = t_1;
	} else if (z <= 3.049736435618952e-54) {
		tmp = x * (y / (t - z));
	} else if (z <= 6.124997616673152e+124) {
		tmp = z * (x / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - y) / z)
	tmp = 0
	if z <= -5.524060034400675e+35:
		tmp = t_1
	elif z <= 3.049736435618952e-54:
		tmp = x * (y / (t - z))
	elif z <= 6.124997616673152e+124:
		tmp = z * (x / (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (z <= -5.524060034400675e+35)
		tmp = t_1;
	elseif (z <= 3.049736435618952e-54)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 6.124997616673152e+124)
		tmp = Float64(z * Float64(x / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((z - y) / z);
	tmp = 0.0;
	if (z <= -5.524060034400675e+35)
		tmp = t_1;
	elseif (z <= 3.049736435618952e-54)
		tmp = x * (y / (t - z));
	elseif (z <= 6.124997616673152e+124)
		tmp = z * (x / (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.524060034400675e+35], t$95$1, If[LessEqual[z, 3.049736435618952e-54], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.124997616673152e+124], N[(z * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = (x * ((z - y) / z)) IN
		LET tmp_2 = IF (z <= (61249976166731522906934581557197212554645393748741591510323568985448843784042427184983842657044006637387295090704308418641920)) THEN (z * (x / (z - t))) ELSE t_1 ENDIF IN
		LET tmp_1 = IF (z <= (30497364356189517969252979243968149751591776223761867884329846740193425364128785200371790718222351583251997069754795077307905222565036391924042646905945730395615100860595703125e-229)) THEN (x * (y / (t - z))) ELSE tmp_2 ENDIF IN
		LET tmp = IF (z <= (-552406003440067519028647541124104192)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if z < -5.5240600344006752e35 or 6.1249976166731523e124 < z

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 52.3%

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

   if -5.5240600344006752e35 < z < 3.0497364356189518e-54

   1. Initial program 84.4%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 47.5%

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

   6. Applied rewrites 50.2%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 52.6%

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

   if 3.0497364356189518e-54 < z < 6.1249976166731523e124

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 44.6%

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

   8. Applied rewrites 45.3%

      \[\leadsto z \cdot \frac{x}{z - t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -5.524060034400675 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq 2.074714056229024 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= z -5.524060034400675e+35)
  (* x (/ (- z y) z))
  (if (<= z 2.074714056229024e+46)
    (* x (/ y (- t z)))
    (* x (/ z (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.524060034400675e+35) {
		tmp = x * ((z - y) / z);
	} else if (z <= 2.074714056229024e+46) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 <= (-5.524060034400675d+35)) then
        tmp = x * ((z - y) / z)
    else if (z <= 2.074714056229024d+46) then
        tmp = x * (y / (t - z))
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.524060034400675e+35) {
		tmp = x * ((z - y) / z);
	} else if (z <= 2.074714056229024e+46) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.524060034400675e+35:
		tmp = x * ((z - y) / z)
	elif z <= 2.074714056229024e+46:
		tmp = x * (y / (t - z))
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.524060034400675e+35)
		tmp = Float64(x * Float64(Float64(z - y) / z));
	elseif (z <= 2.074714056229024e+46)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.524060034400675e+35)
		tmp = x * ((z - y) / z);
	elseif (z <= 2.074714056229024e+46)
		tmp = x * (y / (t - z));
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.524060034400675e+35], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.074714056229024e+46], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_1 = IF (z <= (20747140562290239249715802397516968849152409600)) THEN (x * (y / (t - z))) ELSE (x * (z / (z - t))) ENDIF IN
	LET tmp = IF (z <= (-552406003440067519028647541124104192)) THEN (x * ((z - y) / z)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if z < -5.5240600344006752e35

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 52.3%

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

   if -5.5240600344006752e35 < z < 2.0747140562290239e46

   1. Initial program 84.4%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 47.5%

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

   6. Applied rewrites 50.2%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 52.6%

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

   if 2.0747140562290239e46 < z

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 53.9%

      \[\leadsto x \cdot \frac{z}{z - t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 70.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -9.094776060740505 \cdot 10^{+194}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq -5.524060034400675 \cdot 10^{+35}:\\ \;\;\;\;\frac{x \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;z \leq 3.049736435618952 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 9.184600344503367 \cdot 10^{+168}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= z -9.094776060740505e+194)
  (* x 1.0)
  (if (<= z -5.524060034400675e+35)
    (/ (* x (- z y)) z)
    (if (<= z 3.049736435618952e-54)
      (* x (/ y (- t z)))
      (if (<= z 9.184600344503367e+168)
        (* z (/ x (- z t)))
        (* x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.094776060740505e+194) {
		tmp = x * 1.0;
	} else if (z <= -5.524060034400675e+35) {
		tmp = (x * (z - y)) / z;
	} else if (z <= 3.049736435618952e-54) {
		tmp = x * (y / (t - z));
	} else if (z <= 9.184600344503367e+168) {
		tmp = z * (x / (z - t));
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 <= (-9.094776060740505d+194)) then
        tmp = x * 1.0d0
    else if (z <= (-5.524060034400675d+35)) then
        tmp = (x * (z - y)) / z
    else if (z <= 3.049736435618952d-54) then
        tmp = x * (y / (t - z))
    else if (z <= 9.184600344503367d+168) then
        tmp = z * (x / (z - t))
    else
        tmp = x * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.094776060740505e+194) {
		tmp = x * 1.0;
	} else if (z <= -5.524060034400675e+35) {
		tmp = (x * (z - y)) / z;
	} else if (z <= 3.049736435618952e-54) {
		tmp = x * (y / (t - z));
	} else if (z <= 9.184600344503367e+168) {
		tmp = z * (x / (z - t));
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.094776060740505e+194:
		tmp = x * 1.0
	elif z <= -5.524060034400675e+35:
		tmp = (x * (z - y)) / z
	elif z <= 3.049736435618952e-54:
		tmp = x * (y / (t - z))
	elif z <= 9.184600344503367e+168:
		tmp = z * (x / (z - t))
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.094776060740505e+194)
		tmp = Float64(x * 1.0);
	elseif (z <= -5.524060034400675e+35)
		tmp = Float64(Float64(x * Float64(z - y)) / z);
	elseif (z <= 3.049736435618952e-54)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	elseif (z <= 9.184600344503367e+168)
		tmp = Float64(z * Float64(x / Float64(z - t)));
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.094776060740505e+194)
		tmp = x * 1.0;
	elseif (z <= -5.524060034400675e+35)
		tmp = (x * (z - y)) / z;
	elseif (z <= 3.049736435618952e-54)
		tmp = x * (y / (t - z));
	elseif (z <= 9.184600344503367e+168)
		tmp = z * (x / (z - t));
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.094776060740505e+194], N[(x * 1.0), $MachinePrecision], If[LessEqual[z, -5.524060034400675e+35], N[(N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3.049736435618952e-54], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.184600344503367e+168], N[(z * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_3 = IF (z <= (9184600344503366934818830123625607761855721826341687161204814402386485905370007435364046523440400354522285198730675499577529398201428772268434052453459105931996447113216)) THEN (z * (x / (z - t))) ELSE (x * (1)) ENDIF IN
	LET tmp_2 = IF (z <= (30497364356189517969252979243968149751591776223761867884329846740193425364128785200371790718222351583251997069754795077307905222565036391924042646905945730395615100860595703125e-229)) THEN (x * (y / (t - z))) ELSE tmp_3 ENDIF IN
	LET tmp_1 = IF (z <= (-552406003440067519028647541124104192)) THEN ((x * (z - y)) / z) ELSE tmp_2 ENDIF IN
	LET tmp = IF (z <= (-909477606074050469057443913226544836762448362855000122018796242195260235573212427180050593077088035611953897872984629961756845583457876674156804934372024748861409299101176977037141584220587556864)) THEN (x * (1)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if z < -9.0947760607405047e194 or 9.1846003445033669e168 < z

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around inf

      \[\leadsto x \cdot 1 \]
   5. Step-by-step derivation

   6. Applied rewrites 35.4%

      \[\leadsto x \cdot 1 \]

   if -9.0947760607405047e194 < z < -5.5240600344006752e35

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot \left(z - y\right)}{z} \]
   5. Step-by-step derivation

   6. Applied rewrites 44.7%

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

   if -5.5240600344006752e35 < z < 3.0497364356189518e-54

   1. Initial program 84.4%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 47.5%

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

   6. Applied rewrites 50.2%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 52.6%

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

   if 3.0497364356189518e-54 < z < 9.1846003445033669e168

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 44.6%

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

   8. Applied rewrites 45.3%

      \[\leadsto z \cdot \frac{x}{z - t} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 9: 64.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -9.094776060740505 \cdot 10^{+194}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq -5.411280593452379 \cdot 10^{+34}:\\ \;\;\;\;\frac{x \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;z \leq 1.2459515935553126 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 9.184600344503367 \cdot 10^{+168}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= z -9.094776060740505e+194)
  (* x 1.0)
  (if (<= z -5.411280593452379e+34)
    (/ (* x (- z y)) z)
    (if (<= z 1.2459515935553126e-54)
      (* x (/ y t))
      (if (<= z 9.184600344503367e+168)
        (* z (/ x (- z t)))
        (* x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.094776060740505e+194) {
		tmp = x * 1.0;
	} else if (z <= -5.411280593452379e+34) {
		tmp = (x * (z - y)) / z;
	} else if (z <= 1.2459515935553126e-54) {
		tmp = x * (y / t);
	} else if (z <= 9.184600344503367e+168) {
		tmp = z * (x / (z - t));
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 <= (-9.094776060740505d+194)) then
        tmp = x * 1.0d0
    else if (z <= (-5.411280593452379d+34)) then
        tmp = (x * (z - y)) / z
    else if (z <= 1.2459515935553126d-54) then
        tmp = x * (y / t)
    else if (z <= 9.184600344503367d+168) then
        tmp = z * (x / (z - t))
    else
        tmp = x * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.094776060740505e+194) {
		tmp = x * 1.0;
	} else if (z <= -5.411280593452379e+34) {
		tmp = (x * (z - y)) / z;
	} else if (z <= 1.2459515935553126e-54) {
		tmp = x * (y / t);
	} else if (z <= 9.184600344503367e+168) {
		tmp = z * (x / (z - t));
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.094776060740505e+194:
		tmp = x * 1.0
	elif z <= -5.411280593452379e+34:
		tmp = (x * (z - y)) / z
	elif z <= 1.2459515935553126e-54:
		tmp = x * (y / t)
	elif z <= 9.184600344503367e+168:
		tmp = z * (x / (z - t))
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.094776060740505e+194)
		tmp = Float64(x * 1.0);
	elseif (z <= -5.411280593452379e+34)
		tmp = Float64(Float64(x * Float64(z - y)) / z);
	elseif (z <= 1.2459515935553126e-54)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= 9.184600344503367e+168)
		tmp = Float64(z * Float64(x / Float64(z - t)));
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.094776060740505e+194)
		tmp = x * 1.0;
	elseif (z <= -5.411280593452379e+34)
		tmp = (x * (z - y)) / z;
	elseif (z <= 1.2459515935553126e-54)
		tmp = x * (y / t);
	elseif (z <= 9.184600344503367e+168)
		tmp = z * (x / (z - t));
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.094776060740505e+194], N[(x * 1.0), $MachinePrecision], If[LessEqual[z, -5.411280593452379e+34], N[(N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.2459515935553126e-54], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.184600344503367e+168], N[(z * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_3 = IF (z <= (9184600344503366934818830123625607761855721826341687161204814402386485905370007435364046523440400354522285198730675499577529398201428772268434052453459105931996447113216)) THEN (z * (x / (z - t))) ELSE (x * (1)) ENDIF IN
	LET tmp_2 = IF (z <= (124595159355531258598916676684253027862470406863170184866517522269949485580925361677018831527558439812862714562958741963953999324257846011143602282800202374346554279327392578125e-230)) THEN (x * (y / t)) ELSE tmp_3 ENDIF IN
	LET tmp_1 = IF (z <= (-54112805934523789887965557740797952)) THEN ((x * (z - y)) / z) ELSE tmp_2 ENDIF IN
	LET tmp = IF (z <= (-909477606074050469057443913226544836762448362855000122018796242195260235573212427180050593077088035611953897872984629961756845583457876674156804934372024748861409299101176977037141584220587556864)) THEN (x * (1)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if z < -9.0947760607405047e194 or 9.1846003445033669e168 < z

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around inf

      \[\leadsto x \cdot 1 \]
   5. Step-by-step derivation

   6. Applied rewrites 35.4%

      \[\leadsto x \cdot 1 \]

   if -9.0947760607405047e194 < z < -5.411280593452379e34

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot \left(z - y\right)}{z} \]
   5. Step-by-step derivation

   6. Applied rewrites 44.7%

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

   if -5.411280593452379e34 < z < 1.2459515935553126e-54

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 39.5%

      \[\leadsto x \cdot \frac{y}{t} \]

   if 1.2459515935553126e-54 < z < 9.1846003445033669e168

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 44.6%

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

   8. Applied rewrites 45.3%

      \[\leadsto z \cdot \frac{x}{z - t} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 10: 63.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -6.608744827583972 \cdot 10^{+32}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq 1.2459515935553126 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 9.184600344503367 \cdot 10^{+168}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= z -6.608744827583972e+32)
  (* x 1.0)
  (if (<= z 1.2459515935553126e-54)
    (* x (/ y t))
    (if (<= z 9.184600344503367e+168) (* z (/ x (- z t))) (* x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.608744827583972e+32) {
		tmp = x * 1.0;
	} else if (z <= 1.2459515935553126e-54) {
		tmp = x * (y / t);
	} else if (z <= 9.184600344503367e+168) {
		tmp = z * (x / (z - t));
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 <= (-6.608744827583972d+32)) then
        tmp = x * 1.0d0
    else if (z <= 1.2459515935553126d-54) then
        tmp = x * (y / t)
    else if (z <= 9.184600344503367d+168) then
        tmp = z * (x / (z - t))
    else
        tmp = x * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.608744827583972e+32) {
		tmp = x * 1.0;
	} else if (z <= 1.2459515935553126e-54) {
		tmp = x * (y / t);
	} else if (z <= 9.184600344503367e+168) {
		tmp = z * (x / (z - t));
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.608744827583972e+32:
		tmp = x * 1.0
	elif z <= 1.2459515935553126e-54:
		tmp = x * (y / t)
	elif z <= 9.184600344503367e+168:
		tmp = z * (x / (z - t))
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.608744827583972e+32)
		tmp = Float64(x * 1.0);
	elseif (z <= 1.2459515935553126e-54)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= 9.184600344503367e+168)
		tmp = Float64(z * Float64(x / Float64(z - t)));
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.608744827583972e+32)
		tmp = x * 1.0;
	elseif (z <= 1.2459515935553126e-54)
		tmp = x * (y / t);
	elseif (z <= 9.184600344503367e+168)
		tmp = z * (x / (z - t));
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.608744827583972e+32], N[(x * 1.0), $MachinePrecision], If[LessEqual[z, 1.2459515935553126e-54], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.184600344503367e+168], N[(z * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_2 = IF (z <= (9184600344503366934818830123625607761855721826341687161204814402386485905370007435364046523440400354522285198730675499577529398201428772268434052453459105931996447113216)) THEN (z * (x / (z - t))) ELSE (x * (1)) ENDIF IN
	LET tmp_1 = IF (z <= (124595159355531258598916676684253027862470406863170184866517522269949485580925361677018831527558439812862714562958741963953999324257846011143602282800202374346554279327392578125e-230)) THEN (x * (y / t)) ELSE tmp_2 ENDIF IN
	LET tmp = IF (z <= (-660874482758397194530261691269120)) THEN (x * (1)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if z < -6.6087448275839719e32 or 9.1846003445033669e168 < z

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around inf

      \[\leadsto x \cdot 1 \]
   5. Step-by-step derivation

   6. Applied rewrites 35.4%

      \[\leadsto x \cdot 1 \]

   if -6.6087448275839719e32 < z < 1.2459515935553126e-54

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 39.5%

      \[\leadsto x \cdot \frac{y}{t} \]

   if 1.2459515935553126e-54 < z < 9.1846003445033669e168

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 44.6%

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

   8. Applied rewrites 45.3%

      \[\leadsto z \cdot \frac{x}{z - t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 61.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -6.608744827583972 \cdot 10^{+32}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq 9.249845426392793 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= z -6.608744827583972e+32)
  (* x 1.0)
  (if (<= z 9.249845426392793e+47) (* x (/ y t)) (* x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.608744827583972e+32) {
		tmp = x * 1.0;
	} else if (z <= 9.249845426392793e+47) {
		tmp = x * (y / t);
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 <= (-6.608744827583972d+32)) then
        tmp = x * 1.0d0
    else if (z <= 9.249845426392793d+47) then
        tmp = x * (y / t)
    else
        tmp = x * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.608744827583972e+32) {
		tmp = x * 1.0;
	} else if (z <= 9.249845426392793e+47) {
		tmp = x * (y / t);
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.608744827583972e+32:
		tmp = x * 1.0
	elif z <= 9.249845426392793e+47:
		tmp = x * (y / t)
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.608744827583972e+32)
		tmp = Float64(x * 1.0);
	elseif (z <= 9.249845426392793e+47)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.608744827583972e+32)
		tmp = x * 1.0;
	elseif (z <= 9.249845426392793e+47)
		tmp = x * (y / t);
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.608744827583972e+32], N[(x * 1.0), $MachinePrecision], If[LessEqual[z, 9.249845426392793e+47], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_1 = IF (z <= (924984542639279314080535980226164398023059177472)) THEN (x * (y / t)) ELSE (x * (1)) ENDIF IN
	LET tmp = IF (z <= (-660874482758397194530261691269120)) THEN (x * (1)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -6.6087448275839719e32 or 9.2498454263927931e47 < z

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around inf

      \[\leadsto x \cdot 1 \]
   5. Step-by-step derivation

   6. Applied rewrites 35.4%

      \[\leadsto x \cdot 1 \]

   if -6.6087448275839719e32 < z < 9.2498454263927931e47

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 39.5%

      \[\leadsto x \cdot \frac{y}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 60.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -3.5314742303201063 \cdot 10^{+28}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq 9.249845426392793 \cdot 10^{+47}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= z -3.5314742303201063e+28)
  (* x 1.0)
  (if (<= z 9.249845426392793e+47) (/ (* x y) t) (* x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.5314742303201063e+28) {
		tmp = x * 1.0;
	} else if (z <= 9.249845426392793e+47) {
		tmp = (x * y) / t;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 <= (-3.5314742303201063d+28)) then
        tmp = x * 1.0d0
    else if (z <= 9.249845426392793d+47) then
        tmp = (x * y) / t
    else
        tmp = x * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.5314742303201063e+28) {
		tmp = x * 1.0;
	} else if (z <= 9.249845426392793e+47) {
		tmp = (x * y) / t;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.5314742303201063e+28:
		tmp = x * 1.0
	elif z <= 9.249845426392793e+47:
		tmp = (x * y) / t
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.5314742303201063e+28)
		tmp = Float64(x * 1.0);
	elseif (z <= 9.249845426392793e+47)
		tmp = Float64(Float64(x * y) / t);
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.5314742303201063e+28)
		tmp = x * 1.0;
	elseif (z <= 9.249845426392793e+47)
		tmp = (x * y) / t;
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.5314742303201063e+28], N[(x * 1.0), $MachinePrecision], If[LessEqual[z, 9.249845426392793e+47], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_1 = IF (z <= (924984542639279314080535980226164398023059177472)) THEN ((x * y) / t) ELSE (x * (1)) ENDIF IN
	LET tmp = IF (z <= (-35314742303201063355247755264)) THEN (x * (1)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -3.5314742303201063e28 or 9.2498454263927931e47 < z

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around inf

      \[\leadsto x \cdot 1 \]
   5. Step-by-step derivation

   6. Applied rewrites 35.4%

      \[\leadsto x \cdot 1 \]

   if -3.5314742303201063e28 < z < 9.2498454263927931e47

   1. Initial program 84.4%

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

   2. Taylor expanded in z around 0

      \[\leadsto \frac{x \cdot y}{t} \]
   3. Step-by-step derivation

   4. Applied rewrites 37.7%

      \[\leadsto \frac{x \cdot y}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 60.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -2.425334922953195 \cdot 10^{+32}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;z \leq 7.752928718639661 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= z -2.425334922953195e+32)
  (* x 1.0)
  (if (<= z 7.752928718639661e-18) (* y (/ x t)) (* x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.425334922953195e+32) {
		tmp = x * 1.0;
	} else if (z <= 7.752928718639661e-18) {
		tmp = y * (x / t);
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 <= (-2.425334922953195d+32)) then
        tmp = x * 1.0d0
    else if (z <= 7.752928718639661d-18) then
        tmp = y * (x / t)
    else
        tmp = x * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.425334922953195e+32) {
		tmp = x * 1.0;
	} else if (z <= 7.752928718639661e-18) {
		tmp = y * (x / t);
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.425334922953195e+32:
		tmp = x * 1.0
	elif z <= 7.752928718639661e-18:
		tmp = y * (x / t)
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.425334922953195e+32)
		tmp = Float64(x * 1.0);
	elseif (z <= 7.752928718639661e-18)
		tmp = Float64(y * Float64(x / t));
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.425334922953195e+32)
		tmp = x * 1.0;
	elseif (z <= 7.752928718639661e-18)
		tmp = y * (x / t);
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.425334922953195e+32], N[(x * 1.0), $MachinePrecision], If[LessEqual[z, 7.752928718639661e-18], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp_1 = IF (z <= (77529287186396613225468185128554410806283969000694301920706408282057964242994785308837890625e-109)) THEN (y * (x / t)) ELSE (x * (1)) ENDIF IN
	LET tmp = IF (z <= (-242533492295319504218637545242624)) THEN (x * (1)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -2.425334922953195e32 or 7.7529287186396613e-18 < z

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around inf

      \[\leadsto x \cdot 1 \]
   5. Step-by-step derivation

   6. Applied rewrites 35.4%

      \[\leadsto x \cdot 1 \]

   if -2.425334922953195e32 < z < 7.7529287186396613e-18

   1. Initial program 84.4%

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

   2. Taylor expanded in z around 0

      \[\leadsto \frac{x \cdot y}{t} \]
   3. Step-by-step derivation

   4. Applied rewrites 37.7%

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

   6. Applied rewrites 37.7%

      \[\leadsto y \cdot \frac{x}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 44.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{\left|x\right| \cdot \left(y - z\right)}{t - z}\\ \mathsf{copysign}\left(1, x\right) \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq 4 \cdot 10^{-321}:\\ \;\;\;\;0 \cdot 1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+231}:\\ \;\;\;\;\left|x\right| \cdot 1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{\left|x\right|}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (* (fabs x) (- y z)) (- t z))))
  (*
   (copysign 1.0 x)
   (if (<= t_1 4e-321)
     (* 0.0 1.0)
     (if (<= t_1 5e+231) (* (fabs x) 1.0) (* z (/ (fabs x) z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (fabs(x) * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= 4e-321) {
		tmp = 0.0 * 1.0;
	} else if (t_1 <= 5e+231) {
		tmp = fabs(x) * 1.0;
	} else {
		tmp = z * (fabs(x) / z);
	}
	return copysign(1.0, x) * tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (Math.abs(x) * (y - z)) / (t - z);
	double tmp;
	if (t_1 <= 4e-321) {
		tmp = 0.0 * 1.0;
	} else if (t_1 <= 5e+231) {
		tmp = Math.abs(x) * 1.0;
	} else {
		tmp = z * (Math.abs(x) / z);
	}
	return Math.copySign(1.0, x) * tmp;
}

Python

def code(x, y, z, t):
	t_1 = (math.fabs(x) * (y - z)) / (t - z)
	tmp = 0
	if t_1 <= 4e-321:
		tmp = 0.0 * 1.0
	elif t_1 <= 5e+231:
		tmp = math.fabs(x) * 1.0
	else:
		tmp = z * (math.fabs(x) / z)
	return math.copysign(1.0, x) * tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(abs(x) * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if (t_1 <= 4e-321)
		tmp = Float64(0.0 * 1.0);
	elseif (t_1 <= 5e+231)
		tmp = Float64(abs(x) * 1.0);
	else
		tmp = Float64(z * Float64(abs(x) / z));
	end
	return Float64(copysign(1.0, x) * tmp)
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (abs(x) * (y - z)) / (t - z);
	tmp = 0.0;
	if (t_1 <= 4e-321)
		tmp = 0.0 * 1.0;
	elseif (t_1 <= 5e+231)
		tmp = abs(x) * 1.0;
	else
		tmp = z * (abs(x) / z);
	end
	tmp_2 = (sign(x) * abs(1.0)) * tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[Abs[x], $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$1, 4e-321], N[(0.0 * 1.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+231], N[(N[Abs[x], $MachinePrecision] * 1.0), $MachinePrecision], N[(z * N[(N[Abs[x], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 4.001931731314097e-321

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around inf

      \[\leadsto x \cdot 1 \]
   5. Step-by-step derivation

   6. Applied rewrites 35.4%

      \[\leadsto x \cdot 1 \]

   7. Taylor expanded in undef-var around zero

      \[\leadsto 0 \cdot 1 \]
   8. Step-by-step derivation

   9. Applied rewrites 10.8%

      \[\leadsto 0 \cdot 1 \]

   if 4.001931731314097e-321 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 5.0000000000000003e231

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around inf

      \[\leadsto x \cdot 1 \]
   5. Step-by-step derivation

   6. Applied rewrites 35.4%

      \[\leadsto x \cdot 1 \]

   if 5.0000000000000003e231 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot \left(z - y\right)}{z} \]
   5. Step-by-step derivation

   6. Applied rewrites 44.7%

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

   7. Taylor expanded in y around 0

      \[\leadsto \frac{x \cdot z}{z} \]
   8. Step-by-step derivation

   9. Applied rewrites 30.3%

      \[\leadsto \frac{x \cdot z}{z} \]
   10. Step-by-step derivation

   11. Applied rewrites 29.2%

       \[\leadsto z \cdot \frac{x}{z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 42.5% accurate, 0.5× speedup

Math

\[\mathsf{copysign}\left(1, x\right) \cdot \begin{array}{l} \mathbf{if}\;\frac{\left|x\right| \cdot \left(y - z\right)}{t - z} \leq 4 \cdot 10^{-321}:\\ \;\;\;\;0 \cdot 1\\ \mathbf{else}:\\ \;\;\;\;\left|x\right| \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (*
 (copysign 1.0 x)
 (if (<= (/ (* (fabs x) (- y z)) (- t z)) 4e-321)
   (* 0.0 1.0)
   (* (fabs x) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((fabs(x) * (y - z)) / (t - z)) <= 4e-321) {
		tmp = 0.0 * 1.0;
	} else {
		tmp = fabs(x) * 1.0;
	}
	return copysign(1.0, x) * tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((Math.abs(x) * (y - z)) / (t - z)) <= 4e-321) {
		tmp = 0.0 * 1.0;
	} else {
		tmp = Math.abs(x) * 1.0;
	}
	return Math.copySign(1.0, x) * tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((math.fabs(x) * (y - z)) / (t - z)) <= 4e-321:
		tmp = 0.0 * 1.0
	else:
		tmp = math.fabs(x) * 1.0
	return math.copysign(1.0, x) * tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(abs(x) * Float64(y - z)) / Float64(t - z)) <= 4e-321)
		tmp = Float64(0.0 * 1.0);
	else
		tmp = Float64(abs(x) * 1.0);
	end
	return Float64(copysign(1.0, x) * tmp)
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((abs(x) * (y - z)) / (t - z)) <= 4e-321)
		tmp = 0.0 * 1.0;
	else
		tmp = abs(x) * 1.0;
	end
	tmp_2 = (sign(x) * abs(1.0)) * tmp;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[(N[(N[Abs[x], $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], 4e-321], N[(0.0 * 1.0), $MachinePrecision], N[(N[Abs[x], $MachinePrecision] * 1.0), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 4.001931731314097e-321

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around inf

      \[\leadsto x \cdot 1 \]
   5. Step-by-step derivation

   6. Applied rewrites 35.4%

      \[\leadsto x \cdot 1 \]

   7. Taylor expanded in undef-var around zero

      \[\leadsto 0 \cdot 1 \]
   8. Step-by-step derivation

   9. Applied rewrites 10.8%

      \[\leadsto 0 \cdot 1 \]

   if 4.001931731314097e-321 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 84.4%

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

   3. Applied rewrites 97.0%

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

   4. Taylor expanded in z around inf

      \[\leadsto x \cdot 1 \]
   5. Step-by-step derivation

   6. Applied rewrites 35.4%

      \[\leadsto x \cdot 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 35.4% accurate, 3.3× speedup

Math

\[x \cdot 1 \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (* x 1.0))

C

double code(double x, double y, double z, double t) {
	return x * 1.0;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * 1.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * 1.0;
}

Python

def code(x, y, z, t):
	return x * 1.0

Julia

function code(x, y, z, t)
	return Float64(x * 1.0)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * 1.0;
end

Wolfram

code[x_, y_, z_, t_] := N[(x * 1.0), $MachinePrecision]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	x * (1)
END code

Derivation

1. Initial program 84.4%

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

3. Applied rewrites 97.0%

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

4. Taylor expanded in z around inf

   \[\leadsto x \cdot 1 \]
5. Step-by-step derivation

6. Applied rewrites 35.4%

   \[\leadsto x \cdot 1 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64
  (/ (* x (- y z)) (- t z)))