Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 67.2% → 90.7%

Time: 7.3s

Alternatives: 24

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

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

Initial Program: 67.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

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

Alternative 1: 90.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -5.658749435392879 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8635204505841042 \cdot 10^{+125}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{a - z} \cdot y, t - x, \mathsf{fma}\left(\frac{z}{z - a}, t - x, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (- t (* (/ (- t x) z) (- y a)))))
  (if (<= z -5.658749435392879e+164)
    t_1
    (if (<= z 2.8635204505841042e+125)
      (fma
       (* (/ 1.0 (- a z)) y)
       (- t x)
       (fma (/ z (- z a)) (- t x) x))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (((t - x) / z) * (y - a));
	double tmp;
	if (z <= -5.658749435392879e+164) {
		tmp = t_1;
	} else if (z <= 2.8635204505841042e+125) {
		tmp = fma(((1.0 / (a - z)) * y), (t - x), fma((z / (z - a)), (t - x), x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)))
	tmp = 0.0
	if (z <= -5.658749435392879e+164)
		tmp = t_1;
	elseif (z <= 2.8635204505841042e+125)
		tmp = fma(Float64(Float64(1.0 / Float64(a - z)) * y), Float64(t - x), fma(Float64(z / Float64(z - a)), Float64(t - x), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.658749435392879e+164], t$95$1, If[LessEqual[z, 2.8635204505841042e+125], N[(N[(N[(1.0 / N[(a - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] * N[(t - x), $MachinePrecision] + N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = (t - (((t - x) / z) * (y - a))) IN
		LET tmp_1 = IF (z <= (286352045058410420490264139108340857458535947234372674413941038453343851907049852863794073629727222619566289550213153135001600)) THEN (((((1) / (a - z)) * y) * (t - x)) + (((z / (z - a)) * (t - x)) + x)) ELSE t_1 ENDIF IN
		LET tmp = IF (z <= (-565874943539287884914895127571820671345578588936487026250807561638448052822953565973623938846126855387457197767063212847655023772869254643913374663786366399026298880)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -5.6587494353928788e164 or 2.8635204505841042e125 < z

   1. Initial program 67.2%

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

   2. Taylor expanded in z around -inf

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

   4. Applied rewrites 46.8%

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

   6. Applied rewrites 52.7%

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

   if -5.6587494353928788e164 < z < 2.8635204505841042e125

   1. Initial program 67.2%

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

   3. Applied rewrites 87.8%

      \[\leadsto \mathsf{fma}\left(\frac{1}{a - z} \cdot y, t - x, \mathsf{fma}\left(\frac{z}{z - a}, t - x, x\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 88.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -5.658749435392879 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8635204505841042 \cdot 10^{+125}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{z}{z - a}, \mathsf{fma}\left(\frac{y}{a - z}, t - x, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (- t (* (/ (- t x) z) (- y a)))))
  (if (<= z -5.658749435392879e+164)
    t_1
    (if (<= z 2.8635204505841042e+125)
      (fma (- t x) (/ z (- z a)) (fma (/ y (- a z)) (- t x) x))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (((t - x) / z) * (y - a));
	double tmp;
	if (z <= -5.658749435392879e+164) {
		tmp = t_1;
	} else if (z <= 2.8635204505841042e+125) {
		tmp = fma((t - x), (z / (z - a)), fma((y / (a - z)), (t - x), x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)))
	tmp = 0.0
	if (z <= -5.658749435392879e+164)
		tmp = t_1;
	elseif (z <= 2.8635204505841042e+125)
		tmp = fma(Float64(t - x), Float64(z / Float64(z - a)), fma(Float64(y / Float64(a - z)), Float64(t - x), x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.658749435392879e+164], t$95$1, If[LessEqual[z, 2.8635204505841042e+125], N[(N[(t - x), $MachinePrecision] * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] + N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = (t - (((t - x) / z) * (y - a))) IN
		LET tmp_1 = IF (z <= (286352045058410420490264139108340857458535947234372674413941038453343851907049852863794073629727222619566289550213153135001600)) THEN (((t - x) * (z / (z - a))) + (((y / (a - z)) * (t - x)) + x)) ELSE t_1 ENDIF IN
		LET tmp = IF (z <= (-565874943539287884914895127571820671345578588936487026250807561638448052822953565973623938846126855387457197767063212847655023772869254643913374663786366399026298880)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -5.6587494353928788e164 or 2.8635204505841042e125 < z

   1. Initial program 67.2%

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

   2. Taylor expanded in z around -inf

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

   4. Applied rewrites 46.8%

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

   6. Applied rewrites 52.7%

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

   if -5.6587494353928788e164 < z < 2.8635204505841042e125

   1. Initial program 67.2%

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

   3. Applied rewrites 83.6%

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

Alternative 3: 88.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -5.658749435392879 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8635204505841042 \cdot 10^{+125}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{z - y}{z - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (- t (* (/ (- t x) z) (- y a)))))
  (if (<= z -5.658749435392879e+164)
    t_1
    (if (<= z 2.8635204505841042e+125)
      (fma (- t x) (/ (- z y) (- z a)) x)
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (((t - x) / z) * (y - a));
	double tmp;
	if (z <= -5.658749435392879e+164) {
		tmp = t_1;
	} else if (z <= 2.8635204505841042e+125) {
		tmp = fma((t - x), ((z - y) / (z - a)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)))
	tmp = 0.0
	if (z <= -5.658749435392879e+164)
		tmp = t_1;
	elseif (z <= 2.8635204505841042e+125)
		tmp = fma(Float64(t - x), Float64(Float64(z - y) / Float64(z - a)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.658749435392879e+164], t$95$1, If[LessEqual[z, 2.8635204505841042e+125], N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = (t - (((t - x) / z) * (y - a))) IN
		LET tmp_1 = IF (z <= (286352045058410420490264139108340857458535947234372674413941038453343851907049852863794073629727222619566289550213153135001600)) THEN (((t - x) * ((z - y) / (z - a))) + x) ELSE t_1 ENDIF IN
		LET tmp = IF (z <= (-565874943539287884914895127571820671345578588936487026250807561638448052822953565973623938846126855387457197767063212847655023772869254643913374663786366399026298880)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -5.6587494353928788e164 or 2.8635204505841042e125 < z

   1. Initial program 67.2%

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

   2. Taylor expanded in z around -inf

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

   4. Applied rewrites 46.8%

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

   6. Applied rewrites 52.7%

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

   if -5.6587494353928788e164 < z < 2.8635204505841042e125

   1. Initial program 67.2%

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

   3. Applied rewrites 83.6%

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

Alternative 4: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)\\ t_2 := t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -1.2741505191544434 \cdot 10^{+136}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -545376926289049900:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2147915323371495200:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 2.8635204505841042 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma (- y z) (/ t (- a z)) x))
       (t_2 (- t (* (/ (- t x) z) (- y a)))))
  (if (<= z -1.2741505191544434e+136)
    t_2
    (if (<= z -545376926289049900.0)
      t_1
      (if (<= z 2147915323371495200.0)
        (+ x (/ (* y (- t x)) (- a z)))
        (if (<= z 2.8635204505841042e+125) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), (t / (a - z)), x);
	double t_2 = t - (((t - x) / z) * (y - a));
	double tmp;
	if (z <= -1.2741505191544434e+136) {
		tmp = t_2;
	} else if (z <= -545376926289049900.0) {
		tmp = t_1;
	} else if (z <= 2147915323371495200.0) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else if (z <= 2.8635204505841042e+125) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(t / Float64(a - z)), x)
	t_2 = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)))
	tmp = 0.0
	if (z <= -1.2741505191544434e+136)
		tmp = t_2;
	elseif (z <= -545376926289049900.0)
		tmp = t_1;
	elseif (z <= 2147915323371495200.0)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / Float64(a - z)));
	elseif (z <= 2.8635204505841042e+125)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2741505191544434e+136], t$95$2, If[LessEqual[z, -545376926289049900.0], t$95$1, If[LessEqual[z, 2147915323371495200.0], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8635204505841042e+125], t$95$1, t$95$2]]]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = (((y - z) * (t / (a - z))) + x) IN
		LET t_2 = (t - (((t - x) / z) * (y - a))) IN
			LET tmp_3 = IF (z <= (286352045058410420490264139108340857458535947234372674413941038453343851907049852863794073629727222619566289550213153135001600)) THEN t_1 ELSE t_2 ENDIF IN
			LET tmp_2 = IF (z <= (2147915323371495168)) THEN (x + ((y * (t - x)) / (a - z))) ELSE tmp_3 ENDIF IN
			LET tmp_1 = IF (z <= (-545376926289049920)) THEN t_1 ELSE tmp_2 ENDIF IN
			LET tmp = IF (z <= (-12741505191544434138798212298585525816718934927061338383238253793165645243538563745135374503493190646874231931887207904125363968943325184)) THEN t_2 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if z < -1.2741505191544434e136 or 2.8635204505841042e125 < z

   1. Initial program 67.2%

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

   2. Taylor expanded in z around -inf

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

   4. Applied rewrites 46.8%

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

   6. Applied rewrites 52.7%

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

   if -1.2741505191544434e136 < z < -545376926289049920 or 2147915323371495200 < z < 2.8635204505841042e125

   1. Initial program 67.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.3%

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

   6. Applied rewrites 63.8%

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

   if -545376926289049920 < z < 2147915323371495200

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 53.7%

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

Alternative 5: 76.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)\\ \mathbf{if}\;a \leq -7.687419735420144 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.487838901741181 \cdot 10^{+36}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma (- y z) (/ t (- a z)) x)))
  (if (<= a -7.687419735420144e-49)
    t_1
    (if (<= a 2.487838901741181e+36)
      (- t (* (/ (- t x) z) (- y a)))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), (t / (a - z)), x);
	double tmp;
	if (a <= -7.687419735420144e-49) {
		tmp = t_1;
	} else if (a <= 2.487838901741181e+36) {
		tmp = t - (((t - x) / z) * (y - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(t / Float64(a - z)), x)
	tmp = 0.0
	if (a <= -7.687419735420144e-49)
		tmp = t_1;
	elseif (a <= 2.487838901741181e+36)
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -7.687419735420144e-49], t$95$1, If[LessEqual[a, 2.487838901741181e+36], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = (((y - z) * (t / (a - z))) + x) IN
		LET tmp_1 = IF (a <= (2487838901741181000058377429762179072)) THEN (t - (((t - x) / z) * (y - a))) ELSE t_1 ENDIF IN
		LET tmp = IF (a <= (-76874197354201443468878190866621739448950011961305486166313976877719205424160545233490484737687745375272430458326248026222453357814146102100494317710399627685546875e-212)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if a < -7.6874197354201443e-49 or 2.487838901741181e36 < a

   1. Initial program 67.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.3%

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

   6. Applied rewrites 63.8%

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

   if -7.6874197354201443e-49 < a < 2.487838901741181e36

   1. Initial program 67.2%

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

   2. Taylor expanded in z around -inf

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

   4. Applied rewrites 46.8%

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

   6. Applied rewrites 52.7%

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

Alternative 6: 68.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -1.4893273096096436 \cdot 10^{+143}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;y \leq -2832939490217844700:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{x}{z - a}, x\right)\\ \mathbf{elif}\;y \leq 5.96442232106266 \cdot 10^{+176}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x - t}{z - a} \cdot y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= y -1.4893273096096436e+143)
  (* (- t x) (/ y (- a z)))
  (if (<= y -2832939490217844700.0)
    (fma (- y z) (/ x (- z a)) x)
    (if (<= y 5.96442232106266e+176)
      (fma (- y z) (/ t (- a z)) x)
      (* (/ (- x t) (- z a)) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.4893273096096436e+143) {
		tmp = (t - x) * (y / (a - z));
	} else if (y <= -2832939490217844700.0) {
		tmp = fma((y - z), (x / (z - a)), x);
	} else if (y <= 5.96442232106266e+176) {
		tmp = fma((y - z), (t / (a - z)), x);
	} else {
		tmp = ((x - t) / (z - a)) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.4893273096096436e+143)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (y <= -2832939490217844700.0)
		tmp = fma(Float64(y - z), Float64(x / Float64(z - a)), x);
	elseif (y <= 5.96442232106266e+176)
		tmp = fma(Float64(y - z), Float64(t / Float64(a - z)), x);
	else
		tmp = Float64(Float64(Float64(x - t) / Float64(z - a)) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.4893273096096436e+143], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2832939490217844700.0], N[(N[(y - z), $MachinePrecision] * N[(x / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[y, 5.96442232106266e+176], N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET tmp_2 = IF (y <= (596442232106266046703090808774940667980434470852008378916902203653118243716827085281720300265885120812677278260032338373820893419292613774928152607955272384891314287548387295232)) THEN (((y - z) * (t / (a - z))) + x) ELSE (((x - t) / (z - a)) * y) ENDIF IN
	LET tmp_1 = IF (y <= (-2832939490217844736)) THEN (((y - z) * (x / (z - a))) + x) ELSE tmp_2 ENDIF IN
	LET tmp = IF (y <= (-148932730960964362900335620445351811441899357803820199677087104360100723366303485378347782073178356888942214689166578031849504058468306029379584)) THEN ((t - x) * (y / (a - z))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if y < -1.4893273096096436e143

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 41.7%

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

   6. Applied rewrites 43.4%

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

   if -1.4893273096096436e143 < y < -2832939490217844700

   1. Initial program 67.2%

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

   3. Applied rewrites 79.6%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 40.8%

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

   if -2832939490217844700 < y < 5.9644223210626605e176

   1. Initial program 67.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.3%

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

   6. Applied rewrites 63.8%

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

   if 5.9644223210626605e176 < y

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 41.7%

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

   6. Applied rewrites 42.1%

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

Alternative 7: 64.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -1.342528679294354 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.4106863261597303 \cdot 10^{-252}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 4.940723685083182 \cdot 10^{+69}:\\ \;\;\;\;\frac{x - t}{z - a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma t (/ (- y z) a) x)))
  (if (<= a -1.342528679294354e+42)
    t_1
    (if (<= a 3.4106863261597303e-252)
      (+ t (/ (* x (- y a)) z))
      (if (<= a 4.940723685083182e+69)
        (* (/ (- x t) (- z a)) y)
        t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(t, ((y - z) / a), x);
	double tmp;
	if (a <= -1.342528679294354e+42) {
		tmp = t_1;
	} else if (a <= 3.4106863261597303e-252) {
		tmp = t + ((x * (y - a)) / z);
	} else if (a <= 4.940723685083182e+69) {
		tmp = ((x - t) / (z - a)) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(t, Float64(Float64(y - z) / a), x)
	tmp = 0.0
	if (a <= -1.342528679294354e+42)
		tmp = t_1;
	elseif (a <= 3.4106863261597303e-252)
		tmp = Float64(t + Float64(Float64(x * Float64(y - a)) / z));
	elseif (a <= 4.940723685083182e+69)
		tmp = Float64(Float64(Float64(x - t) / Float64(z - a)) * y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.342528679294354e+42], t$95$1, If[LessEqual[a, 3.4106863261597303e-252], N[(t + N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.940723685083182e+69], N[(N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((t * ((y - z) / a)) + x) IN
		LET tmp_2 = IF (a <= (4940723685083182375395813866942042674666855107353422967943956665466880)) THEN (((x - t) / (z - a)) * y) ELSE t_1 ENDIF IN
		LET tmp_1 = IF (a <= (341068632615973025723217920796936957644020999046121383386672212755902878289262444954552748280503241248368280948661051205338231353527675461310854846574724035635570598804018735424583349349085547037272993136584026229550247535408980801419731085506229820520989734398279313069360935026894271043154891767358006519598928207441430943680290847611953949421737625085414992568885854773070650813067671676850015385838131353677628479950898731296472003962044028145236649031857595731912773757190409074372567274612377503667760837626016239418464371140521215539715478565527855232065570407990538340674893114697001470121684452152521771495230495929718017578125e-887)) THEN (t + ((x * (y - a)) / z)) ELSE tmp_2 ENDIF IN
		LET tmp = IF (a <= (-1342528679294354067913840620818205287383040)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if a < -1.3425286792943541e42 or 4.9407236850831824e69 < a

   1. Initial program 67.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.3%

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

   6. Applied rewrites 63.8%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 43.4%

      \[\leadsto \mathsf{fma}\left(y - z, \frac{t}{a}, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 45.0%

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

   if -1.3425286792943541e42 < a < 3.4106863261597303e-252

   1. Initial program 67.2%

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

   2. Taylor expanded in z around -inf

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

   4. Applied rewrites 46.8%

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

   5. Taylor expanded in x around -inf

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

   7. Applied rewrites 42.4%

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

   if 3.4106863261597303e-252 < a < 4.9407236850831824e69

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 41.7%

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

   6. Applied rewrites 42.1%

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

Alternative 8: 62.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -1.342528679294354 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.4106863261597303 \cdot 10^{-252}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;a \leq 4.940723685083182 \cdot 10^{+69}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma t (/ (- y z) a) x)))
  (if (<= a -1.342528679294354e+42)
    t_1
    (if (<= a 3.4106863261597303e-252)
      (+ t (/ (* x (- y a)) z))
      (if (<= a 4.940723685083182e+69)
        (* (- t x) (/ y (- a z)))
        t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(t, ((y - z) / a), x);
	double tmp;
	if (a <= -1.342528679294354e+42) {
		tmp = t_1;
	} else if (a <= 3.4106863261597303e-252) {
		tmp = t + ((x * (y - a)) / z);
	} else if (a <= 4.940723685083182e+69) {
		tmp = (t - x) * (y / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(t, Float64(Float64(y - z) / a), x)
	tmp = 0.0
	if (a <= -1.342528679294354e+42)
		tmp = t_1;
	elseif (a <= 3.4106863261597303e-252)
		tmp = Float64(t + Float64(Float64(x * Float64(y - a)) / z));
	elseif (a <= 4.940723685083182e+69)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.342528679294354e+42], t$95$1, If[LessEqual[a, 3.4106863261597303e-252], N[(t + N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.940723685083182e+69], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((t * ((y - z) / a)) + x) IN
		LET tmp_2 = IF (a <= (4940723685083182375395813866942042674666855107353422967943956665466880)) THEN ((t - x) * (y / (a - z))) ELSE t_1 ENDIF IN
		LET tmp_1 = IF (a <= (341068632615973025723217920796936957644020999046121383386672212755902878289262444954552748280503241248368280948661051205338231353527675461310854846574724035635570598804018735424583349349085547037272993136584026229550247535408980801419731085506229820520989734398279313069360935026894271043154891767358006519598928207441430943680290847611953949421737625085414992568885854773070650813067671676850015385838131353677628479950898731296472003962044028145236649031857595731912773757190409074372567274612377503667760837626016239418464371140521215539715478565527855232065570407990538340674893114697001470121684452152521771495230495929718017578125e-887)) THEN (t + ((x * (y - a)) / z)) ELSE tmp_2 ENDIF IN
		LET tmp = IF (a <= (-1342528679294354067913840620818205287383040)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if a < -1.3425286792943541e42 or 4.9407236850831824e69 < a

   1. Initial program 67.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.3%

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

   6. Applied rewrites 63.8%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 43.4%

      \[\leadsto \mathsf{fma}\left(y - z, \frac{t}{a}, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 45.0%

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

   if -1.3425286792943541e42 < a < 3.4106863261597303e-252

   1. Initial program 67.2%

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

   2. Taylor expanded in z around -inf

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

   4. Applied rewrites 46.8%

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

   5. Taylor expanded in x around -inf

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

   7. Applied rewrites 42.4%

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

   if 3.4106863261597303e-252 < a < 4.9407236850831824e69

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 41.7%

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

   6. Applied rewrites 43.4%

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

Alternative 9: 61.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -1.342528679294354 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.6849217979184506 \cdot 10^{+36}:\\ \;\;\;\;t + \frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma t (/ (- y z) a) x)))
  (if (<= a -1.342528679294354e+42)
    t_1
    (if (<= a 3.6849217979184506e+36) (+ t (/ (* x (- y a)) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(t, ((y - z) / a), x);
	double tmp;
	if (a <= -1.342528679294354e+42) {
		tmp = t_1;
	} else if (a <= 3.6849217979184506e+36) {
		tmp = t + ((x * (y - a)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(t, Float64(Float64(y - z) / a), x)
	tmp = 0.0
	if (a <= -1.342528679294354e+42)
		tmp = t_1;
	elseif (a <= 3.6849217979184506e+36)
		tmp = Float64(t + Float64(Float64(x * Float64(y - a)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.342528679294354e+42], t$95$1, If[LessEqual[a, 3.6849217979184506e+36], N[(t + N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((t * ((y - z) / a)) + x) IN
		LET tmp_1 = IF (a <= (3684921797918450552725767180865503232)) THEN (t + ((x * (y - a)) / z)) ELSE t_1 ENDIF IN
		LET tmp = IF (a <= (-1342528679294354067913840620818205287383040)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if a < -1.3425286792943541e42 or 3.6849217979184506e36 < a

   1. Initial program 67.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.3%

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

   6. Applied rewrites 63.8%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 43.4%

      \[\leadsto \mathsf{fma}\left(y - z, \frac{t}{a}, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 45.0%

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

   if -1.3425286792943541e42 < a < 3.6849217979184506e36

   1. Initial program 67.2%

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

   2. Taylor expanded in z around -inf

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

   4. Applied rewrites 46.8%

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

   5. Taylor expanded in x around -inf

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

   7. Applied rewrites 42.4%

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

Alternative 10: 61.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -7.152887946301167 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.957089289270708 \cdot 10^{-55}:\\ \;\;\;\;t \cdot \left(\frac{y}{a - z} - -1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma t (/ (- y z) a) x)))
  (if (<= a -7.152887946301167e+64)
    t_1
    (if (<= a 5.957089289270708e-55)
      (* t (- (/ y (- a z)) -1.0))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(t, ((y - z) / a), x);
	double tmp;
	if (a <= -7.152887946301167e+64) {
		tmp = t_1;
	} else if (a <= 5.957089289270708e-55) {
		tmp = t * ((y / (a - z)) - -1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(t, Float64(Float64(y - z) / a), x)
	tmp = 0.0
	if (a <= -7.152887946301167e+64)
		tmp = t_1;
	elseif (a <= 5.957089289270708e-55)
		tmp = Float64(t * Float64(Float64(y / Float64(a - z)) - -1.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -7.152887946301167e+64], t$95$1, If[LessEqual[a, 5.957089289270708e-55], N[(t * N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((t * ((y - z) / a)) + x) IN
		LET tmp_1 = IF (a <= (59570892892707079979069301957196834118909245116076858189167199508249055725509774575654245656897462056131983794607498970911173388681071985163717474875966217950917780399322509765625e-233)) THEN (t * ((y / (a - z)) - (-1))) ELSE t_1 ENDIF IN
		LET tmp = IF (a <= (-71528879463011672561405186213950320938318237317649560436689862656)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if a < -7.1528879463011673e64 or 5.957089289270708e-55 < a

   1. Initial program 67.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.3%

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

   6. Applied rewrites 63.8%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 43.4%

      \[\leadsto \mathsf{fma}\left(y - z, \frac{t}{a}, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 45.0%

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

   if -7.1528879463011673e64 < a < 5.957089289270708e-55

   1. Initial program 67.2%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 52.9%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 42.8%

      \[\leadsto t \cdot \left(\frac{y}{a - z} - -1\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 58.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -2.3242574789394824 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.7290451020898444 \cdot 10^{-62}:\\ \;\;\;\;\mathsf{fma}\left(a - y, \frac{t}{z}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma t (/ (- y z) a) x)))
  (if (<= a -2.3242574789394824e-9)
    t_1
    (if (<= a 1.7290451020898444e-62) (fma (- a y) (/ t z) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(t, ((y - z) / a), x);
	double tmp;
	if (a <= -2.3242574789394824e-9) {
		tmp = t_1;
	} else if (a <= 1.7290451020898444e-62) {
		tmp = fma((a - y), (t / z), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(t, Float64(Float64(y - z) / a), x)
	tmp = 0.0
	if (a <= -2.3242574789394824e-9)
		tmp = t_1;
	elseif (a <= 1.7290451020898444e-62)
		tmp = fma(Float64(a - y), Float64(t / z), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2.3242574789394824e-9], t$95$1, If[LessEqual[a, 1.7290451020898444e-62], N[(N[(a - y), $MachinePrecision] * N[(t / z), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((t * ((y - z) / a)) + x) IN
		LET tmp_1 = IF (a <= (1729045102089844364551349015266822322110990415503331809115178825398771579519365463577275152978801958673922462765098699181285518692345890606227843899091851063987146375211523263715207576751708984375e-257)) THEN (((a - y) * (t / z)) + t) ELSE t_1 ENDIF IN
		LET tmp = IF (a <= (-2324257478939482426518321113591801496678357352720922790467739105224609375e-81)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if a < -2.3242574789394824e-9 or 1.7290451020898444e-62 < a

   1. Initial program 67.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.3%

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

   6. Applied rewrites 63.8%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 43.4%

      \[\leadsto \mathsf{fma}\left(y - z, \frac{t}{a}, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 45.0%

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

   if -2.3242574789394824e-9 < a < 1.7290451020898444e-62

   1. Initial program 67.2%

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

   2. Taylor expanded in z around -inf

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

   4. Applied rewrites 46.8%

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

   6. Applied rewrites 52.7%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 35.8%

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

   11. Applied rewrites 35.8%

       \[\leadsto \mathsf{fma}\left(a - y, \frac{t}{z}, t\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 53.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -8.462590972365703 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.149473746735766 \cdot 10^{-127}:\\ \;\;\;\;\frac{x - t}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma t (/ (- y z) a) x)))
  (if (<= a -8.462590972365703e-10)
    t_1
    (if (<= a 3.149473746735766e-127) (* (/ (- x t) z) y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(t, ((y - z) / a), x);
	double tmp;
	if (a <= -8.462590972365703e-10) {
		tmp = t_1;
	} else if (a <= 3.149473746735766e-127) {
		tmp = ((x - t) / z) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(t, Float64(Float64(y - z) / a), x)
	tmp = 0.0
	if (a <= -8.462590972365703e-10)
		tmp = t_1;
	elseif (a <= 3.149473746735766e-127)
		tmp = Float64(Float64(Float64(x - t) / z) * y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -8.462590972365703e-10], t$95$1, If[LessEqual[a, 3.149473746735766e-127], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((t * ((y - z) / a)) + x) IN
		LET tmp_1 = IF (a <= (31494737467357658268444477796974361579067834170414720370976473477713298356829114244590707881786666910164819687233347395935566712772752479427965311795545473663481400797737718816624189660368976568003445080953938357375729300133982132289902487772771646681038747067141219761818338453708675721326680035841761337404853815513661174918524920940399169921875e-473)) THEN (((x - t) / z) * y) ELSE t_1 ENDIF IN
		LET tmp = IF (a <= (-84625909723657026509241364057851801649956513529104995541274547576904296875e-83)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if a < -8.4625909723657027e-10 or 3.1494737467357658e-127 < a

   1. Initial program 67.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.3%

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

   6. Applied rewrites 63.8%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 43.4%

      \[\leadsto \mathsf{fma}\left(y - z, \frac{t}{a}, x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 45.0%

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

   if -8.4625909723657027e-10 < a < 3.1494737467357658e-127

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 41.7%

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

   6. Applied rewrites 42.1%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 25.5%

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

Alternative 13: 49.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -1.742608455713368 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.0604806497074427 \cdot 10^{-127}:\\ \;\;\;\;\frac{x - t}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (+ x (* t (/ y a)))))
  (if (<= a -1.742608455713368e-11)
    t_1
    (if (<= a 3.0604806497074427e-127) (* (/ (- x t) z) y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (a <= -1.742608455713368e-11) {
		tmp = t_1;
	} else if (a <= 3.0604806497074427e-127) {
		tmp = ((x - t) / z) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    if (a <= (-1.742608455713368d-11)) then
        tmp = t_1
    else if (a <= 3.0604806497074427d-127) then
        tmp = ((x - t) / z) * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (a <= -1.742608455713368e-11) {
		tmp = t_1;
	} else if (a <= 3.0604806497074427e-127) {
		tmp = ((x - t) / z) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if a <= -1.742608455713368e-11:
		tmp = t_1
	elif a <= 3.0604806497074427e-127:
		tmp = ((x - t) / z) * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -1.742608455713368e-11)
		tmp = t_1;
	elseif (a <= 3.0604806497074427e-127)
		tmp = Float64(Float64(Float64(x - t) / z) * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -1.742608455713368e-11)
		tmp = t_1;
	elseif (a <= 3.0604806497074427e-127)
		tmp = ((x - t) / z) * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.742608455713368e-11], t$95$1, If[LessEqual[a, 3.0604806497074427e-127], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = (x + (t * (y / a))) IN
		LET tmp_1 = IF (a <= (30604806497074426735615028169109732087552580892378732421906697401589379908245344447818287802755145229113300903734493679244444045183057649280889749440423501215584940943254009713681610459992278186671111414432611857364002217883230282204518003069811238273755092333875899229898696393300216395741207210025804801890869644154236084432341158390045166015625e-473)) THEN (((x - t) / z) * y) ELSE t_1 ENDIF IN
		LET tmp = IF (a <= (-174260845571336813338742060119432720870225050902035945910029113292694091796875e-88)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if a < -1.7426084557133681e-11 or 3.0604806497074427e-127 < a

   1. Initial program 67.2%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 43.3%

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

   6. Applied rewrites 48.2%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 40.6%

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

   if -1.7426084557133681e-11 < a < 3.0604806497074427e-127

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 41.7%

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

   6. Applied rewrites 42.1%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 25.5%

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

Alternative 14: 44.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -1.6162588213476134 \cdot 10^{+64}:\\ \;\;\;\;\frac{a - y}{a} \cdot x\\ \mathbf{elif}\;a \leq 7.691691775103464 \cdot 10^{-20}:\\ \;\;\;\;\frac{x - t}{z} \cdot y\\ \mathbf{elif}\;a \leq 1.3319650690096113 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= a -1.6162588213476134e+64)
  (* (/ (- a y) a) x)
  (if (<= a 7.691691775103464e-20)
    (* (/ (- x t) z) y)
    (if (<= a 1.3319650690096113e+76)
      (* y (/ (- t x) a))
      (* x (- 1.0 (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6162588213476134e+64) {
		tmp = ((a - y) / a) * x;
	} else if (a <= 7.691691775103464e-20) {
		tmp = ((x - t) / z) * y;
	} else if (a <= 1.3319650690096113e+76) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.6162588213476134d+64)) then
        tmp = ((a - y) / a) * x
    else if (a <= 7.691691775103464d-20) then
        tmp = ((x - t) / z) * y
    else if (a <= 1.3319650690096113d+76) then
        tmp = y * ((t - x) / a)
    else
        tmp = x * (1.0d0 - (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6162588213476134e+64) {
		tmp = ((a - y) / a) * x;
	} else if (a <= 7.691691775103464e-20) {
		tmp = ((x - t) / z) * y;
	} else if (a <= 1.3319650690096113e+76) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = x * (1.0 - (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6162588213476134e+64:
		tmp = ((a - y) / a) * x
	elif a <= 7.691691775103464e-20:
		tmp = ((x - t) / z) * y
	elif a <= 1.3319650690096113e+76:
		tmp = y * ((t - x) / a)
	else:
		tmp = x * (1.0 - (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6162588213476134e+64)
		tmp = Float64(Float64(Float64(a - y) / a) * x);
	elseif (a <= 7.691691775103464e-20)
		tmp = Float64(Float64(Float64(x - t) / z) * y);
	elseif (a <= 1.3319650690096113e+76)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.6162588213476134e+64)
		tmp = ((a - y) / a) * x;
	elseif (a <= 7.691691775103464e-20)
		tmp = ((x - t) / z) * y;
	elseif (a <= 1.3319650690096113e+76)
		tmp = y * ((t - x) / a);
	else
		tmp = x * (1.0 - (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6162588213476134e+64], N[(N[(N[(a - y), $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[a, 7.691691775103464e-20], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[a, 1.3319650690096113e+76], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET tmp_2 = IF (a <= (13319650690096112914647441007280895669612208528097882334406670138178646573056)) THEN (y * ((t - x) / a)) ELSE (x * ((1) - (y / a))) ENDIF IN
	LET tmp_1 = IF (a <= (769169177510346389916173215380569980060763877987344764967925225818135004374198615550994873046875e-115)) THEN (((x - t) / z) * y) ELSE tmp_2 ENDIF IN
	LET tmp = IF (a <= (-16162588213476134179186745119895376560692215594803540075275616256)) THEN (((a - y) / a) * x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if a < -1.6162588213476134e64

   1. Initial program 67.2%

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

   3. Applied rewrites 77.5%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 50.6%

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

   7. Taylor expanded in z around 0

      \[\leadsto x \cdot \left(1 - \frac{y}{a}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 35.4%

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

   11. Applied rewrites 35.4%

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

   if -1.6162588213476134e64 < a < 7.6916917751034639e-20

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 41.7%

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

   6. Applied rewrites 42.1%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 25.5%

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

   if 7.6916917751034639e-20 < a < 1.3319650690096113e76

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 41.7%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 25.8%

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

   if 1.3319650690096113e76 < a

   1. Initial program 67.2%

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

   3. Applied rewrites 77.5%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 50.6%

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

   7. Taylor expanded in z around 0

      \[\leadsto x \cdot \left(1 - \frac{y}{a}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 35.4%

      \[\leadsto x \cdot \left(1 - \frac{y}{a}\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 15: 44.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \frac{a - y}{a} \cdot x\\ \mathbf{if}\;a \leq -1.6162588213476134 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.691691775103464 \cdot 10^{-20}:\\ \;\;\;\;\frac{x - t}{z} \cdot y\\ \mathbf{elif}\;a \leq 1.3319650690096113 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* (/ (- a y) a) x)))
  (if (<= a -1.6162588213476134e+64)
    t_1
    (if (<= a 7.691691775103464e-20)
      (* (/ (- x t) z) y)
      (if (<= a 1.3319650690096113e+76) (* y (/ (- t x) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((a - y) / a) * x;
	double tmp;
	if (a <= -1.6162588213476134e+64) {
		tmp = t_1;
	} else if (a <= 7.691691775103464e-20) {
		tmp = ((x - t) / z) * y;
	} else if (a <= 1.3319650690096113e+76) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((a - y) / a) * x
    if (a <= (-1.6162588213476134d+64)) then
        tmp = t_1
    else if (a <= 7.691691775103464d-20) then
        tmp = ((x - t) / z) * y
    else if (a <= 1.3319650690096113d+76) then
        tmp = y * ((t - x) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((a - y) / a) * x;
	double tmp;
	if (a <= -1.6162588213476134e+64) {
		tmp = t_1;
	} else if (a <= 7.691691775103464e-20) {
		tmp = ((x - t) / z) * y;
	} else if (a <= 1.3319650690096113e+76) {
		tmp = y * ((t - x) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((a - y) / a) * x
	tmp = 0
	if a <= -1.6162588213476134e+64:
		tmp = t_1
	elif a <= 7.691691775103464e-20:
		tmp = ((x - t) / z) * y
	elif a <= 1.3319650690096113e+76:
		tmp = y * ((t - x) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(a - y) / a) * x)
	tmp = 0.0
	if (a <= -1.6162588213476134e+64)
		tmp = t_1;
	elseif (a <= 7.691691775103464e-20)
		tmp = Float64(Float64(Float64(x - t) / z) * y);
	elseif (a <= 1.3319650690096113e+76)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((a - y) / a) * x;
	tmp = 0.0;
	if (a <= -1.6162588213476134e+64)
		tmp = t_1;
	elseif (a <= 7.691691775103464e-20)
		tmp = ((x - t) / z) * y;
	elseif (a <= 1.3319650690096113e+76)
		tmp = y * ((t - x) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(a - y), $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[a, -1.6162588213476134e+64], t$95$1, If[LessEqual[a, 7.691691775103464e-20], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[a, 1.3319650690096113e+76], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = (((a - y) / a) * x) IN
		LET tmp_2 = IF (a <= (13319650690096112914647441007280895669612208528097882334406670138178646573056)) THEN (y * ((t - x) / a)) ELSE t_1 ENDIF IN
		LET tmp_1 = IF (a <= (769169177510346389916173215380569980060763877987344764967925225818135004374198615550994873046875e-115)) THEN (((x - t) / z) * y) ELSE tmp_2 ENDIF IN
		LET tmp = IF (a <= (-16162588213476134179186745119895376560692215594803540075275616256)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if a < -1.6162588213476134e64 or 1.3319650690096113e76 < a

   1. Initial program 67.2%

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

   3. Applied rewrites 77.5%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 50.6%

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

   7. Taylor expanded in z around 0

      \[\leadsto x \cdot \left(1 - \frac{y}{a}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 35.4%

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

   11. Applied rewrites 35.4%

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

   if -1.6162588213476134e64 < a < 7.6916917751034639e-20

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 41.7%

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

   6. Applied rewrites 42.1%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 25.5%

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

   if 7.6916917751034639e-20 < a < 1.3319650690096113e76

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 41.7%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 25.8%

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

Alternative 16: 42.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := y \cdot \frac{t - x}{a}\\ \mathbf{if}\;a \leq -1.0573031963515148 \cdot 10^{+114}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;a \leq -6.125365941638943 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.691691775103464 \cdot 10^{-20}:\\ \;\;\;\;\frac{x - t}{z} \cdot y\\ \mathbf{elif}\;a \leq 4.147299749583203 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* y (/ (- t x) a))))
  (if (<= a -1.0573031963515148e+114)
    (* x 1.0)
    (if (<= a -6.125365941638943e-9)
      t_1
      (if (<= a 7.691691775103464e-20)
        (* (/ (- x t) z) y)
        (if (<= a 4.147299749583203e+147) t_1 (* x 1.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (a <= -1.0573031963515148e+114) {
		tmp = x * 1.0;
	} else if (a <= -6.125365941638943e-9) {
		tmp = t_1;
	} else if (a <= 7.691691775103464e-20) {
		tmp = ((x - t) / z) * y;
	} else if (a <= 4.147299749583203e+147) {
		tmp = t_1;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((t - x) / a)
    if (a <= (-1.0573031963515148d+114)) then
        tmp = x * 1.0d0
    else if (a <= (-6.125365941638943d-9)) then
        tmp = t_1
    else if (a <= 7.691691775103464d-20) then
        tmp = ((x - t) / z) * y
    else if (a <= 4.147299749583203d+147) then
        tmp = t_1
    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 a) {
	double t_1 = y * ((t - x) / a);
	double tmp;
	if (a <= -1.0573031963515148e+114) {
		tmp = x * 1.0;
	} else if (a <= -6.125365941638943e-9) {
		tmp = t_1;
	} else if (a <= 7.691691775103464e-20) {
		tmp = ((x - t) / z) * y;
	} else if (a <= 4.147299749583203e+147) {
		tmp = t_1;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((t - x) / a)
	tmp = 0
	if a <= -1.0573031963515148e+114:
		tmp = x * 1.0
	elif a <= -6.125365941638943e-9:
		tmp = t_1
	elif a <= 7.691691775103464e-20:
		tmp = ((x - t) / z) * y
	elif a <= 4.147299749583203e+147:
		tmp = t_1
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(t - x) / a))
	tmp = 0.0
	if (a <= -1.0573031963515148e+114)
		tmp = Float64(x * 1.0);
	elseif (a <= -6.125365941638943e-9)
		tmp = t_1;
	elseif (a <= 7.691691775103464e-20)
		tmp = Float64(Float64(Float64(x - t) / z) * y);
	elseif (a <= 4.147299749583203e+147)
		tmp = t_1;
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((t - x) / a);
	tmp = 0.0;
	if (a <= -1.0573031963515148e+114)
		tmp = x * 1.0;
	elseif (a <= -6.125365941638943e-9)
		tmp = t_1;
	elseif (a <= 7.691691775103464e-20)
		tmp = ((x - t) / z) * y;
	elseif (a <= 4.147299749583203e+147)
		tmp = t_1;
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.0573031963515148e+114], N[(x * 1.0), $MachinePrecision], If[LessEqual[a, -6.125365941638943e-9], t$95$1, If[LessEqual[a, 7.691691775103464e-20], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[a, 4.147299749583203e+147], t$95$1, N[(x * 1.0), $MachinePrecision]]]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = (y * ((t - x) / a)) IN
		LET tmp_3 = IF (a <= (4147299749583203120421558305448312751908181217847041342675424657963664869079392550372041680436277157852404702606899931198928844905910905953530675200)) THEN t_1 ELSE (x * (1)) ENDIF IN
		LET tmp_2 = IF (a <= (769169177510346389916173215380569980060763877987344764967925225818135004374198615550994873046875e-115)) THEN (((x - t) / z) * y) ELSE tmp_3 ENDIF IN
		LET tmp_1 = IF (a <= (-61253659416389430148460894351609973274008780208532698452472686767578125e-79)) THEN t_1 ELSE tmp_2 ENDIF IN
		LET tmp = IF (a <= (-1057303196351514839504633737173735911557564864036255200394503615696329522511043575844920885298117355544947678248960)) THEN (x * (1)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if a < -1.0573031963515148e114 or 4.1472997495832031e147 < a

   1. Initial program 67.2%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 46.1%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 24.6%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 24.4%

       \[\leadsto x \cdot 1 \]

   if -1.0573031963515148e114 < a < -6.125365941638943e-9 or 7.6916917751034639e-20 < a < 4.1472997495832031e147

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 41.7%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 25.8%

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

   if -6.125365941638943e-9 < a < 7.6916917751034639e-20

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 41.7%

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

   6. Applied rewrites 42.1%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 25.5%

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

Alternative 17: 41.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -1.531587912663493 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq 5.96442232106266 \cdot 10^{+176}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z - a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= y -1.531587912663493e+143)
  (* y (/ t (- a z)))
  (if (<= y 5.96442232106266e+176) (+ x t) (* x (/ y (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.531587912663493e+143) {
		tmp = y * (t / (a - z));
	} else if (y <= 5.96442232106266e+176) {
		tmp = x + t;
	} else {
		tmp = x * (y / (z - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.531587912663493d+143)) then
        tmp = y * (t / (a - z))
    else if (y <= 5.96442232106266d+176) then
        tmp = x + t
    else
        tmp = x * (y / (z - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.531587912663493e+143) {
		tmp = y * (t / (a - z));
	} else if (y <= 5.96442232106266e+176) {
		tmp = x + t;
	} else {
		tmp = x * (y / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.531587912663493e+143:
		tmp = y * (t / (a - z))
	elif y <= 5.96442232106266e+176:
		tmp = x + t
	else:
		tmp = x * (y / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.531587912663493e+143)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (y <= 5.96442232106266e+176)
		tmp = Float64(x + t);
	else
		tmp = Float64(x * Float64(y / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.531587912663493e+143)
		tmp = y * (t / (a - z));
	elseif (y <= 5.96442232106266e+176)
		tmp = x + t;
	else
		tmp = x * (y / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.531587912663493e+143], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.96442232106266e+176], N[(x + t), $MachinePrecision], N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET tmp_1 = IF (y <= (596442232106266046703090808774940667980434470852008378916902203653118243716827085281720300265885120812677278260032338373820893419292613774928152607955272384891314287548387295232)) THEN (x + t) ELSE (x * (y / (z - a))) ENDIF IN
	LET tmp = IF (y <= (-153158791266349302059067134646143137419441199017939972137454829263741356177562549975168567005190735022490714260833519588217537330168093707599872)) THEN (y * (t / (a - z))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if y < -1.531587912663493e143

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 41.7%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 23.5%

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

   if -1.531587912663493e143 < y < 5.9644223210626605e176

   1. Initial program 67.2%

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

   2. Taylor expanded in z around inf

      \[\leadsto x + \left(t - x\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 19.7%

      \[\leadsto x + \left(t - x\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto x + t \]

   if 5.9644223210626605e176 < y

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 41.7%

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

   6. Applied rewrites 42.1%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 21.1%

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

   11. Applied rewrites 24.1%

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

Alternative 18: 40.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -1.531587912663493 \cdot 10^{+143}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;y \leq 5.96442232106266 \cdot 10^{+176}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= y -1.531587912663493e+143)
  (* y (/ t (- a z)))
  (if (<= y 5.96442232106266e+176) (+ x t) (* x (/ y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.531587912663493e+143) {
		tmp = y * (t / (a - z));
	} else if (y <= 5.96442232106266e+176) {
		tmp = x + t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.531587912663493d+143)) then
        tmp = y * (t / (a - z))
    else if (y <= 5.96442232106266d+176) then
        tmp = x + t
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.531587912663493e+143) {
		tmp = y * (t / (a - z));
	} else if (y <= 5.96442232106266e+176) {
		tmp = x + t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.531587912663493e+143:
		tmp = y * (t / (a - z))
	elif y <= 5.96442232106266e+176:
		tmp = x + t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.531587912663493e+143)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (y <= 5.96442232106266e+176)
		tmp = Float64(x + t);
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.531587912663493e+143)
		tmp = y * (t / (a - z));
	elseif (y <= 5.96442232106266e+176)
		tmp = x + t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.531587912663493e+143], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.96442232106266e+176], N[(x + t), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET tmp_1 = IF (y <= (596442232106266046703090808774940667980434470852008378916902203653118243716827085281720300265885120812677278260032338373820893419292613774928152607955272384891314287548387295232)) THEN (x + t) ELSE (x * (y / z)) ENDIF IN
	LET tmp = IF (y <= (-153158791266349302059067134646143137419441199017939972137454829263741356177562549975168567005190735022490714260833519588217537330168093707599872)) THEN (y * (t / (a - z))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if y < -1.531587912663493e143

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 41.7%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 23.5%

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

   if -1.531587912663493e143 < y < 5.9644223210626605e176

   1. Initial program 67.2%

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

   2. Taylor expanded in z around inf

      \[\leadsto x + \left(t - x\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 19.7%

      \[\leadsto x + \left(t - x\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto x + t \]

   if 5.9644223210626605e176 < y

   1. Initial program 67.2%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 46.1%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 16.5%

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

   9. Applied rewrites 18.9%

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

Alternative 19: 40.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -1.531587912663493 \cdot 10^{+143}:\\ \;\;\;\;\frac{t \cdot y}{a - z}\\ \mathbf{elif}\;y \leq 5.96442232106266 \cdot 10^{+176}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= y -1.531587912663493e+143)
  (/ (* t y) (- a z))
  (if (<= y 5.96442232106266e+176) (+ x t) (* x (/ y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.531587912663493e+143) {
		tmp = (t * y) / (a - z);
	} else if (y <= 5.96442232106266e+176) {
		tmp = x + t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.531587912663493d+143)) then
        tmp = (t * y) / (a - z)
    else if (y <= 5.96442232106266d+176) then
        tmp = x + t
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.531587912663493e+143) {
		tmp = (t * y) / (a - z);
	} else if (y <= 5.96442232106266e+176) {
		tmp = x + t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.531587912663493e+143:
		tmp = (t * y) / (a - z)
	elif y <= 5.96442232106266e+176:
		tmp = x + t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.531587912663493e+143)
		tmp = Float64(Float64(t * y) / Float64(a - z));
	elseif (y <= 5.96442232106266e+176)
		tmp = Float64(x + t);
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.531587912663493e+143)
		tmp = (t * y) / (a - z);
	elseif (y <= 5.96442232106266e+176)
		tmp = x + t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.531587912663493e+143], N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.96442232106266e+176], N[(x + t), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET tmp_1 = IF (y <= (596442232106266046703090808774940667980434470852008378916902203653118243716827085281720300265885120812677278260032338373820893419292613774928152607955272384891314287548387295232)) THEN (x + t) ELSE (x * (y / z)) ENDIF IN
	LET tmp = IF (y <= (-153158791266349302059067134646143137419441199017939972137454829263741356177562549975168567005190735022490714260833519588217537330168093707599872)) THEN ((t * y) / (a - z)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if y < -1.531587912663493e143

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 41.7%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 21.5%

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

   if -1.531587912663493e143 < y < 5.9644223210626605e176

   1. Initial program 67.2%

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

   2. Taylor expanded in z around inf

      \[\leadsto x + \left(t - x\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 19.7%

      \[\leadsto x + \left(t - x\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto x + t \]

   if 5.9644223210626605e176 < y

   1. Initial program 67.2%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 46.1%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 16.5%

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

   9. Applied rewrites 18.9%

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

Alternative 20: 38.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -1.4893273096096436 \cdot 10^{+143}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 5.96442232106266 \cdot 10^{+176}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= y -1.4893273096096436e+143)
  (* t (/ y a))
  (if (<= y 5.96442232106266e+176) (+ x t) (* x (/ y z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.4893273096096436e+143) {
		tmp = t * (y / a);
	} else if (y <= 5.96442232106266e+176) {
		tmp = x + t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.4893273096096436d+143)) then
        tmp = t * (y / a)
    else if (y <= 5.96442232106266d+176) then
        tmp = x + t
    else
        tmp = x * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.4893273096096436e+143) {
		tmp = t * (y / a);
	} else if (y <= 5.96442232106266e+176) {
		tmp = x + t;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.4893273096096436e+143:
		tmp = t * (y / a)
	elif y <= 5.96442232106266e+176:
		tmp = x + t
	else:
		tmp = x * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.4893273096096436e+143)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= 5.96442232106266e+176)
		tmp = Float64(x + t);
	else
		tmp = Float64(x * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.4893273096096436e+143)
		tmp = t * (y / a);
	elseif (y <= 5.96442232106266e+176)
		tmp = x + t;
	else
		tmp = x * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.4893273096096436e+143], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.96442232106266e+176], N[(x + t), $MachinePrecision], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET tmp_1 = IF (y <= (596442232106266046703090808774940667980434470852008378916902203653118243716827085281720300265885120812677278260032338373820893419292613774928152607955272384891314287548387295232)) THEN (x + t) ELSE (x * (y / z)) ENDIF IN
	LET tmp = IF (y <= (-148932730960964362900335620445351811441899357803820199677087104360100723366303485378347782073178356888942214689166578031849504058468306029379584)) THEN (t * (y / a)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if y < -1.4893273096096436e143

   1. Initial program 67.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 41.7%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 21.5%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 16.6%

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

   12. Applied rewrites 19.3%

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

   if -1.4893273096096436e143 < y < 5.9644223210626605e176

   1. Initial program 67.2%

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

   2. Taylor expanded in z around inf

      \[\leadsto x + \left(t - x\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 19.7%

      \[\leadsto x + \left(t - x\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto x + t \]

   if 5.9644223210626605e176 < y

   1. Initial program 67.2%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 46.1%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 16.5%

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

   9. Applied rewrites 18.9%

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

Alternative 21: 38.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -2.526723922218976 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.96442232106266 \cdot 10^{+176}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* x (/ y z))))
  (if (<= y -2.526723922218976e+59)
    t_1
    (if (<= y 5.96442232106266e+176) (+ x t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / z);
	double tmp;
	if (y <= -2.526723922218976e+59) {
		tmp = t_1;
	} else if (y <= 5.96442232106266e+176) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / z)
    if (y <= (-2.526723922218976d+59)) then
        tmp = t_1
    else if (y <= 5.96442232106266d+176) then
        tmp = x + 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 a) {
	double t_1 = x * (y / z);
	double tmp;
	if (y <= -2.526723922218976e+59) {
		tmp = t_1;
	} else if (y <= 5.96442232106266e+176) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / z)
	tmp = 0
	if y <= -2.526723922218976e+59:
		tmp = t_1
	elif y <= 5.96442232106266e+176:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (y <= -2.526723922218976e+59)
		tmp = t_1;
	elseif (y <= 5.96442232106266e+176)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / z);
	tmp = 0.0;
	if (y <= -2.526723922218976e+59)
		tmp = t_1;
	elseif (y <= 5.96442232106266e+176)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.526723922218976e+59], t$95$1, If[LessEqual[y, 5.96442232106266e+176], N[(x + t), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = (x * (y / z)) IN
		LET tmp_1 = IF (y <= (596442232106266046703090808774940667980434470852008378916902203653118243716827085281720300265885120812677278260032338373820893419292613774928152607955272384891314287548387295232)) THEN (x + t) ELSE t_1 ENDIF IN
		LET tmp = IF (y <= (-252672392221897583665082411349755371582910713339517750738944)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -2.5267239222189758e59 or 5.9644223210626605e176 < y

   1. Initial program 67.2%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 46.1%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 16.5%

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

   9. Applied rewrites 18.9%

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

   if -2.5267239222189758e59 < y < 5.9644223210626605e176

   1. Initial program 67.2%

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

   2. Taylor expanded in z around inf

      \[\leadsto x + \left(t - x\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 19.7%

      \[\leadsto x + \left(t - x\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

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

Alternative 22: 38.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -2.341161945684198 \cdot 10^{+153}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;a \leq -1.039988862863241 \cdot 10^{-101}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 8402868895.534154:\\ \;\;\;\;0 + t\\ \mathbf{elif}\;a \leq 4.988986641920986 \cdot 10^{+183}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= a -2.341161945684198e+153)
  (* x 1.0)
  (if (<= a -1.039988862863241e-101)
    (+ x t)
    (if (<= a 8402868895.534154)
      (+ 0.0 t)
      (if (<= a 4.988986641920986e+183) (+ x t) (* x 1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.341161945684198e+153) {
		tmp = x * 1.0;
	} else if (a <= -1.039988862863241e-101) {
		tmp = x + t;
	} else if (a <= 8402868895.534154) {
		tmp = 0.0 + t;
	} else if (a <= 4.988986641920986e+183) {
		tmp = x + t;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.341161945684198d+153)) then
        tmp = x * 1.0d0
    else if (a <= (-1.039988862863241d-101)) then
        tmp = x + t
    else if (a <= 8402868895.534154d0) then
        tmp = 0.0d0 + t
    else if (a <= 4.988986641920986d+183) then
        tmp = 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 a) {
	double tmp;
	if (a <= -2.341161945684198e+153) {
		tmp = x * 1.0;
	} else if (a <= -1.039988862863241e-101) {
		tmp = x + t;
	} else if (a <= 8402868895.534154) {
		tmp = 0.0 + t;
	} else if (a <= 4.988986641920986e+183) {
		tmp = x + t;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.341161945684198e+153:
		tmp = x * 1.0
	elif a <= -1.039988862863241e-101:
		tmp = x + t
	elif a <= 8402868895.534154:
		tmp = 0.0 + t
	elif a <= 4.988986641920986e+183:
		tmp = x + t
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.341161945684198e+153)
		tmp = Float64(x * 1.0);
	elseif (a <= -1.039988862863241e-101)
		tmp = Float64(x + t);
	elseif (a <= 8402868895.534154)
		tmp = Float64(0.0 + t);
	elseif (a <= 4.988986641920986e+183)
		tmp = Float64(x + t);
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.341161945684198e+153)
		tmp = x * 1.0;
	elseif (a <= -1.039988862863241e-101)
		tmp = x + t;
	elseif (a <= 8402868895.534154)
		tmp = 0.0 + t;
	elseif (a <= 4.988986641920986e+183)
		tmp = x + t;
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.341161945684198e+153], N[(x * 1.0), $MachinePrecision], If[LessEqual[a, -1.039988862863241e-101], N[(x + t), $MachinePrecision], If[LessEqual[a, 8402868895.534154], N[(0.0 + t), $MachinePrecision], If[LessEqual[a, 4.988986641920986e+183], N[(x + t), $MachinePrecision], N[(x * 1.0), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET tmp_3 = IF (a <= (4988986641920985938466169792183497807102416866876192698782647024627962002160565666281005102475733907571230562088197220108179102431293681718902830624553373639852957329260899405322518528)) THEN (x + t) ELSE (x * (1)) ENDIF IN
	LET tmp_2 = IF (a <= (840286889553415393829345703125e-20)) THEN ((0) + t) ELSE tmp_3 ENDIF IN
	LET tmp_1 = IF (a <= (-103998886286324096396014723484231794918150178365210296000781026572266507480319731384801198869559923777271079603950905362200614476269008844415567789001940796075467231960517531925487962212360476810965543664932513376714020253487516109179315482860593393421577701474234345369040966033935546875e-388)) THEN (x + t) ELSE tmp_2 ENDIF IN
	LET tmp = IF (a <= (-2341161945684198056985905611943324662441538948709578558390974389295927845329843157210782360839368571083746172865952575306102646513767044165016005002657792)) THEN (x * (1)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if a < -2.3411619456841981e153 or 4.9889866419209859e183 < a

   1. Initial program 67.2%

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

   2. Taylor expanded in x around -inf

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

   4. Applied rewrites 46.1%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 24.6%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 24.4%

       \[\leadsto x \cdot 1 \]

   if -2.3411619456841981e153 < a < -1.039988862863241e-101 or 8402868895.5341539 < a < 4.9889866419209859e183

   1. Initial program 67.2%

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

   2. Taylor expanded in z around inf

      \[\leadsto x + \left(t - x\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 19.7%

      \[\leadsto x + \left(t - x\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto x + t \]

   if -1.039988862863241e-101 < a < 8402868895.5341539

   1. Initial program 67.2%

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

   2. Taylor expanded in z around inf

      \[\leadsto x + \left(t - x\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 19.7%

      \[\leadsto x + \left(t - x\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto x + t \]

   8. Taylor expanded in undef-var around zero

      \[\leadsto 0 + t \]
   9. Step-by-step derivation

   10. Applied rewrites 26.0%

       \[\leadsto 0 + t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 23: 35.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq 2.127004327879293 \cdot 10^{+113}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;0 + t\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= z 2.127004327879293e+113) (+ x t) (+ 0.0 t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 2.127004327879293e+113) {
		tmp = x + t;
	} else {
		tmp = 0.0 + t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    real(8) :: tmp
    if (z <= 2.127004327879293d+113) then
        tmp = x + t
    else
        tmp = 0.0d0 + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 2.127004327879293e+113) {
		tmp = x + t;
	} else {
		tmp = 0.0 + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 2.127004327879293e+113:
		tmp = x + t
	else:
		tmp = 0.0 + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 2.127004327879293e+113)
		tmp = Float64(x + t);
	else
		tmp = Float64(0.0 + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 2.127004327879293e+113)
		tmp = x + t;
	else
		tmp = 0.0 + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 2.127004327879293e+113], N[(x + t), $MachinePrecision], N[(0.0 + t), $MachinePrecision]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET tmp = IF (z <= (212700432787929294832000289643583090219385354854104189939713924049364038204167172433658223278500981986288023371776)) THEN (x + t) ELSE ((0) + t) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < 2.1270043278792929e113

   1. Initial program 67.2%

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

   2. Taylor expanded in z around inf

      \[\leadsto x + \left(t - x\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 19.7%

      \[\leadsto x + \left(t - x\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto x + t \]

   if 2.1270043278792929e113 < z

   1. Initial program 67.2%

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

   2. Taylor expanded in z around inf

      \[\leadsto x + \left(t - x\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 19.7%

      \[\leadsto x + \left(t - x\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto x + t \]
   6. Step-by-step derivation

   7. Applied rewrites 33.6%

      \[\leadsto x + t \]

   8. Taylor expanded in undef-var around zero

      \[\leadsto 0 + t \]
   9. Step-by-step derivation

   10. Applied rewrites 26.0%

       \[\leadsto 0 + t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 24: 33.6% accurate, 5.1× speedup

Math

\[x + t \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (+ x t))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + t), $MachinePrecision]

ReFlow

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

Derivation

1. Initial program 67.2%

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

2. Taylor expanded in z around inf

   \[\leadsto x + \left(t - x\right) \]
3. Step-by-step derivation

4. Applied rewrites 19.7%

   \[\leadsto x + \left(t - x\right) \]

5. Taylor expanded in x around 0

   \[\leadsto x + t \]
6. Step-by-step derivation

7. Applied rewrites 33.6%

   \[\leadsto x + t \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64
  (+ x (/ (* (- y z) (- t x)) (- a z))))