Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.6% → 95.7%

Time: 8.8s

Alternatives: 20

Speedup: 0.3×

Specification

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $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: 79.6% accurate, 1.0× speedup

Math

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

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(y - z) * Float64(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[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $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: 95.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{1}{a - z} \cdot y, \mathsf{fma}\left(\frac{-z}{a - z}, t - x, x\right)\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-261}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1
        (fma
         (- t x)
         (* (/ 1.0 (- a z)) y)
         (fma (/ (- z) (- a z)) (- t x) x)))
       (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
  (if (<= t_2 -1e-261)
    t_1
    (if (<= t_2 0.0) (- 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((t - x), ((1.0 / (a - z)) * y), fma((-z / (a - z)), (t - x), x));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -1e-261) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		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(t - x), Float64(Float64(1.0 / Float64(a - z)) * y), fma(Float64(Float64(-z) / Float64(a - z)), Float64(t - x), x))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -1e-261)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		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[(t - x), $MachinePrecision] * N[(N[(1.0 / N[(a - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] + N[(N[((-z) / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-261], t$95$1, If[LessEqual[t$95$2, 0.0], 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 = (((t - x) * (((1) / (a - z)) * y)) + ((((- z) / (a - z)) * (t - x)) + x)) IN
		LET t_2 = (x + ((y - z) * ((t - x) / (a - z)))) IN
			LET tmp_1 = IF (t_2 <= (0)) THEN (t - (((t - x) / z) * (y - a))) ELSE t_1 ENDIF IN
			LET tmp = IF (t_2 <= (-99999999999999998400751036348743394393736566782540462240318584996501362034842653096183707054359139876367227370071327202871347531113783761508048293906324058968258742835755829869406788748415695130440806600043856721180691093451748215661117451527599123708109603902481283306535476800046995014668697376533606531419034120508306348853236140136882670183896620029124843515417635830819897288932178098245590930051701145481582277078444137153901500403964469280488627472236140505428275419756957385794370175470927605091811150712639672177871184201768104247329678930918510840380610087023154663790550827981414572464666142574853625058233126676743296457061660476028919219970703125e-920)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999998e-262 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.6%

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

   3. Applied rewrites 87.8%

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

   if -9.9999999999999998e-262 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 79.6%

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

   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%

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

   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 2: 94.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot t\_1\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-261}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{z - y}{z - a}, x\right)\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t\_1, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- t x) (- a z))) (t_2 (+ x (* (- y z) t_1))))
  (if (<= t_2 -1e-261)
    (fma (- t x) (/ (- z y) (- z a)) x)
    (if (<= t_2 0.0)
      (- t (* (/ (- t x) z) (- y a)))
      (fma (- y z) t_1 x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) / (a - z);
	double t_2 = x + ((y - z) * t_1);
	double tmp;
	if (t_2 <= -1e-261) {
		tmp = fma((t - x), ((z - y) / (z - a)), x);
	} else if (t_2 <= 0.0) {
		tmp = t - (((t - x) / z) * (y - a));
	} else {
		tmp = fma((y - z), t_1, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) / Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * t_1))
	tmp = 0.0
	if (t_2 <= -1e-261)
		tmp = fma(Float64(t - x), Float64(Float64(z - y) / Float64(z - a)), x);
	elseif (t_2 <= 0.0)
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	else
		tmp = fma(Float64(y - z), t_1, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-261], N[(N[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t$95$1 + x), $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 = ((t - x) / (a - z)) IN
		LET t_2 = (x + ((y - z) * t_1)) IN
			LET tmp_1 = IF (t_2 <= (0)) THEN (t - (((t - x) / z) * (y - a))) ELSE (((y - z) * t_1) + x) ENDIF IN
			LET tmp = IF (t_2 <= (-99999999999999998400751036348743394393736566782540462240318584996501362034842653096183707054359139876367227370071327202871347531113783761508048293906324058968258742835755829869406788748415695130440806600043856721180691093451748215661117451527599123708109603902481283306535476800046995014668697376533606531419034120508306348853236140136882670183896620029124843515417635830819897288932178098245590930051701145481582277078444137153901500403964469280488627472236140505428275419756957385794370175470927605091811150712639672177871184201768104247329678930918510840380610087023154663790550827981414572464666142574853625058233126676743296457061660476028919219970703125e-920)) THEN (((t - x) * ((z - y) / (z - a))) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999998e-262

   1. Initial program 79.6%

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

   3. Applied rewrites 83.6%

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

   if -9.9999999999999998e-262 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 79.6%

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

   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%

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

   6. Applied rewrites 52.7%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.6%

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

   3. Applied rewrites 79.6%

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

Alternative 3: 92.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t - x, \frac{z - y}{z - a}, x\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-261}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma (- t x) (/ (- z y) (- z a)) x))
       (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
  (if (<= t_2 -1e-261)
    t_1
    (if (<= t_2 0.0) (- 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((t - x), ((z - y) / (z - a)), x);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -1e-261) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		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(t - x), Float64(Float64(z - y) / Float64(z - a)), x)
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -1e-261)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		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[(t - x), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-261], t$95$1, If[LessEqual[t$95$2, 0.0], 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 = (((t - x) * ((z - y) / (z - a))) + x) IN
		LET t_2 = (x + ((y - z) * ((t - x) / (a - z)))) IN
			LET tmp_1 = IF (t_2 <= (0)) THEN (t - (((t - x) / z) * (y - a))) ELSE t_1 ENDIF IN
			LET tmp = IF (t_2 <= (-99999999999999998400751036348743394393736566782540462240318584996501362034842653096183707054359139876367227370071327202871347531113783761508048293906324058968258742835755829869406788748415695130440806600043856721180691093451748215661117451527599123708109603902481283306535476800046995014668697376533606531419034120508306348853236140136882670183896620029124843515417635830819897288932178098245590930051701145481582277078444137153901500403964469280488627472236140505428275419756957385794370175470927605091811150712639672177871184201768104247329678930918510840380610087023154663790550827981414572464666142574853625058233126676743296457061660476028919219970703125e-920)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999998e-262 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.6%

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

   3. Applied rewrites 83.6%

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

   if -9.9999999999999998e-262 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 79.6%

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

   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%

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

   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 4: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ t_2 := t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -1.2741505191544434 \cdot 10^{+136}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -30200722481522934000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8213517619784619 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 2.8635204505841042 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (+ x (* (- y z) (/ t (- a z)))))
       (t_2 (- t (* (/ (- t x) z) (- y a)))))
  (if (<= z -1.2741505191544434e+136)
    t_2
    (if (<= z -30200722481522934000.0)
      t_1
      (if (<= z 1.8213517619784619e+22)
        (+ 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 = x + ((y - z) * (t / (a - z)));
	double t_2 = t - (((t - x) / z) * (y - a));
	double tmp;
	if (z <= -1.2741505191544434e+136) {
		tmp = t_2;
	} else if (z <= -30200722481522934000.0) {
		tmp = t_1;
	} else if (z <= 1.8213517619784619e+22) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else if (z <= 2.8635204505841042e+125) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - z) * (t / (a - z)))
    t_2 = t - (((t - x) / z) * (y - a))
    if (z <= (-1.2741505191544434d+136)) then
        tmp = t_2
    else if (z <= (-30200722481522934000.0d0)) then
        tmp = t_1
    else if (z <= 1.8213517619784619d+22) then
        tmp = x + ((y * (t - x)) / (a - z))
    else if (z <= 2.8635204505841042d+125) then
        tmp = t_1
    else
        tmp = t_2
    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) * (t / (a - z)));
	double t_2 = t - (((t - x) / z) * (y - a));
	double tmp;
	if (z <= -1.2741505191544434e+136) {
		tmp = t_2;
	} else if (z <= -30200722481522934000.0) {
		tmp = t_1;
	} else if (z <= 1.8213517619784619e+22) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else if (z <= 2.8635204505841042e+125) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (t / (a - z)))
	t_2 = t - (((t - x) / z) * (y - a))
	tmp = 0
	if z <= -1.2741505191544434e+136:
		tmp = t_2
	elif z <= -30200722481522934000.0:
		tmp = t_1
	elif z <= 1.8213517619784619e+22:
		tmp = x + ((y * (t - x)) / (a - z))
	elif z <= 2.8635204505841042e+125:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))))
	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 <= -30200722481522934000.0)
		tmp = t_1;
	elseif (z <= 1.8213517619784619e+22)
		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

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (t / (a - z)));
	t_2 = t - (((t - x) / z) * (y - a));
	tmp = 0.0;
	if (z <= -1.2741505191544434e+136)
		tmp = t_2;
	elseif (z <= -30200722481522934000.0)
		tmp = t_1;
	elseif (z <= 1.8213517619784619e+22)
		tmp = x + ((y * (t - x)) / (a - z));
	elseif (z <= 2.8635204505841042e+125)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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, -30200722481522934000.0], t$95$1, If[LessEqual[z, 1.8213517619784619e+22], 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 = (x + ((y - z) * (t / (a - z)))) 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 <= (18213517619784618868736)) THEN (x + ((y * (t - x)) / (a - z))) ELSE tmp_3 ENDIF IN
			LET tmp_1 = IF (z <= (-30200722481522933760)) 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 79.6%

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

   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%

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

   6. Applied rewrites 52.7%

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

   if -1.2741505191544434e136 < z < -30200722481522934000 or 1.8213517619784619e22 < z < 2.8635204505841042e125

   1. Initial program 79.6%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 63.8%

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

   if -30200722481522934000 < z < 1.8213517619784619e22

   1. Initial program 79.6%

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

   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: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -4.307957662105071 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.9332468564022815 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;z \leq 1.459960935600874 \cdot 10^{+125}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (- t (* (/ (- t x) z) (- y a)))))
  (if (<= z -4.307957662105071e+135)
    t_1
    (if (<= z 1.9332468564022815e+22)
      (+ x (/ (* y (- t x)) (- a z)))
      (if (<= z 1.459960935600874e+125)
        (+ x (/ (* t (- y z)) (- a z)))
        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 <= -4.307957662105071e+135) {
		tmp = t_1;
	} else if (z <= 1.9332468564022815e+22) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else if (z <= 1.459960935600874e+125) {
		tmp = x + ((t * (y - z)) / (a - z));
	} 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 = t - (((t - x) / z) * (y - a))
    if (z <= (-4.307957662105071d+135)) then
        tmp = t_1
    else if (z <= 1.9332468564022815d+22) then
        tmp = x + ((y * (t - x)) / (a - z))
    else if (z <= 1.459960935600874d+125) then
        tmp = x + ((t * (y - z)) / (a - z))
    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 = t - (((t - x) / z) * (y - a));
	double tmp;
	if (z <= -4.307957662105071e+135) {
		tmp = t_1;
	} else if (z <= 1.9332468564022815e+22) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else if (z <= 1.459960935600874e+125) {
		tmp = x + ((t * (y - z)) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (((t - x) / z) * (y - a))
	tmp = 0
	if z <= -4.307957662105071e+135:
		tmp = t_1
	elif z <= 1.9332468564022815e+22:
		tmp = x + ((y * (t - x)) / (a - z))
	elif z <= 1.459960935600874e+125:
		tmp = x + ((t * (y - z)) / (a - z))
	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 <= -4.307957662105071e+135)
		tmp = t_1;
	elseif (z <= 1.9332468564022815e+22)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / Float64(a - z)));
	elseif (z <= 1.459960935600874e+125)
		tmp = Float64(x + Float64(Float64(t * Float64(y - z)) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (((t - x) / z) * (y - a));
	tmp = 0.0;
	if (z <= -4.307957662105071e+135)
		tmp = t_1;
	elseif (z <= 1.9332468564022815e+22)
		tmp = x + ((y * (t - x)) / (a - z));
	elseif (z <= 1.459960935600874e+125)
		tmp = x + ((t * (y - z)) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = 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, -4.307957662105071e+135], t$95$1, If[LessEqual[z, 1.9332468564022815e+22], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.459960935600874e+125], N[(x + N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / 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 - (((t - x) / z) * (y - a))) IN
		LET tmp_2 = IF (z <= (145996093560087393105480706117089014695186730063850957668521966056082241721537445123491329286094650338845049826750117468700672)) THEN (x + ((t * (y - z)) / (a - z))) ELSE t_1 ENDIF IN
		LET tmp_1 = IF (z <= (19332468564022815358976)) THEN (x + ((y * (t - x)) / (a - z))) ELSE tmp_2 ENDIF IN
		LET tmp = IF (z <= (-4307957662105071171991224618165330184853518091763414131994554857511853789092896061987932816330351670784626748306167443045443057328586752)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if z < -4.3079576621050712e135 or 1.4599609356008739e125 < z

   1. Initial program 79.6%

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

   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%

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

   6. Applied rewrites 52.7%

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

   if -4.3079576621050712e135 < z < 1.9332468564022815e22

   1. Initial program 79.6%

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

   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%

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

   if 1.9332468564022815e22 < z < 1.4599609356008739e125

   1. Initial program 79.6%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.3%

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

Alternative 6: 71.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{if}\;z \leq -1.1102663521641867 \cdot 10^{+136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.459960935600874 \cdot 10^{+125}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (- t (* (/ (- t x) z) (- y a)))))
  (if (<= z -1.1102663521641867e+136)
    t_1
    (if (<= z 1.459960935600874e+125)
      (+ x (/ (* t (- y z)) (- a z)))
      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 <= -1.1102663521641867e+136) {
		tmp = t_1;
	} else if (z <= 1.459960935600874e+125) {
		tmp = x + ((t * (y - z)) / (a - z));
	} 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 = t - (((t - x) / z) * (y - a))
    if (z <= (-1.1102663521641867d+136)) then
        tmp = t_1
    else if (z <= 1.459960935600874d+125) then
        tmp = x + ((t * (y - z)) / (a - z))
    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 = t - (((t - x) / z) * (y - a));
	double tmp;
	if (z <= -1.1102663521641867e+136) {
		tmp = t_1;
	} else if (z <= 1.459960935600874e+125) {
		tmp = x + ((t * (y - z)) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (((t - x) / z) * (y - a))
	tmp = 0
	if z <= -1.1102663521641867e+136:
		tmp = t_1
	elif z <= 1.459960935600874e+125:
		tmp = x + ((t * (y - z)) / (a - z))
	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 <= -1.1102663521641867e+136)
		tmp = t_1;
	elseif (z <= 1.459960935600874e+125)
		tmp = Float64(x + Float64(Float64(t * Float64(y - z)) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (((t - x) / z) * (y - a));
	tmp = 0.0;
	if (z <= -1.1102663521641867e+136)
		tmp = t_1;
	elseif (z <= 1.459960935600874e+125)
		tmp = x + ((t * (y - z)) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = 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, -1.1102663521641867e+136], t$95$1, If[LessEqual[z, 1.459960935600874e+125], N[(x + N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / 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 - (((t - x) / z) * (y - a))) IN
		LET tmp_1 = IF (z <= (145996093560087393105480706117089014695186730063850957668521966056082241721537445123491329286094650338845049826750117468700672)) THEN (x + ((t * (y - z)) / (a - z))) ELSE t_1 ENDIF IN
		LET tmp = IF (z <= (-11102663521641867476697772095813985546036966459977122883291080384641239981409095535818086423571957916309628737125591422071904996413145088)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -1.1102663521641867e136 or 1.4599609356008739e125 < z

   1. Initial program 79.6%

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

   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%

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

   6. Applied rewrites 52.7%

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

   if -1.1102663521641867e136 < z < 1.4599609356008739e125

   1. Initial program 79.6%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.3%

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

Alternative 7: 70.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -5.078410752414052 \cdot 10^{+63}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 4.3066036097393237 \cdot 10^{+36}:\\ \;\;\;\;t - \frac{t - x}{z} \cdot \left(y - a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a}, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= a -5.078410752414052e+63)
  (+ x (* y (/ (- t x) a)))
  (if (<= a 4.3066036097393237e+36)
    (- t (* (/ (- t x) z) (- y a)))
    (fma (- y z) (/ t a) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.078410752414052e+63) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= 4.3066036097393237e+36) {
		tmp = t - (((t - x) / z) * (y - a));
	} else {
		tmp = fma((y - z), (t / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.078410752414052e+63)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= 4.3066036097393237e+36)
		tmp = Float64(t - Float64(Float64(Float64(t - x) / z) * Float64(y - a)));
	else
		tmp = fma(Float64(y - z), Float64(t / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.078410752414052e+63], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.3066036097393237e+36], N[(t - N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision] + x), $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 (a <= (4306603609739323683958692999323451392)) THEN (t - (((t - x) / z) * (y - a))) ELSE (((y - z) * (t / a)) + x) ENDIF IN
	LET tmp = IF (a <= (-5078410752414052130476961624678376730420663946848580088392318976)) THEN (x + (y * ((t - x) / a))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if a < -5.0784107524140521e63

   1. Initial program 79.6%

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

   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 47.0%

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

   if -5.0784107524140521e63 < a < 4.3066036097393237e36

   1. Initial program 79.6%

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

   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%

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

   6. Applied rewrites 52.7%

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

   if 4.3066036097393237e36 < a

   1. Initial program 79.6%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 51.1%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 43.4%

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

   9. Applied rewrites 43.4%

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

Alternative 8: 64.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -7.795703790764831 \cdot 10^{+59}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 3.553914174691604 \cdot 10^{-288}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{elif}\;a \leq 9.971581761024804 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a}, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= a -7.795703790764831e+59)
  (+ x (* y (/ (- t x) a)))
  (if (<= a 3.553914174691604e-288)
    (* t (/ (- z y) (- z a)))
    (if (<= a 9.971581761024804e+63)
      (* y (/ (- t x) (- a z)))
      (fma (- y z) (/ t a) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.795703790764831e+59) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= 3.553914174691604e-288) {
		tmp = t * ((z - y) / (z - a));
	} else if (a <= 9.971581761024804e+63) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = fma((y - z), (t / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.795703790764831e+59)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= 3.553914174691604e-288)
		tmp = Float64(t * Float64(Float64(z - y) / Float64(z - a)));
	elseif (a <= 9.971581761024804e+63)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = fma(Float64(y - z), Float64(t / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.795703790764831e+59], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.553914174691604e-288], N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.971581761024804e+63], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision] + x), $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 <= (9971581761024803980593985657038695275917116132339498499407085568)) THEN (y * ((t - x) / (a - z))) ELSE (((y - z) * (t / a)) + x) ENDIF IN
	LET tmp_1 = IF (a <= (355391417469160424723453651630824918658984300202794622207367834316453829360554124856035022924795105556216079225295514039868754245120283120209109117603468283578649506516636247696974151136848945639194314374409144115734969546762289199233093049294405154906641346891038777798948587961390454545778406118242166791528836801950786170683666032751412348638454755771629805977153463720069238292085958814048759511435698063618670072014488387433516519338052443955890031154174321896593414714950634103859503332337917917112930469377540813958745020483635695143119629736045843742461178649617670288059915935545898010736549787637855981424029318057141007800168617474204601160686848689167744946859018250438777553057434488437138497829437255859375e-1007)) THEN (t * ((z - y) / (z - a))) ELSE tmp_2 ENDIF IN
	LET tmp = IF (a <= (-779570379076483083113887747491956741142103796285330444779520)) THEN (x + (y * ((t - x) / a))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if a < -7.7957037907648308e59

   1. Initial program 79.6%

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

   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 47.0%

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

   if -7.7957037907648308e59 < a < 3.5539141746916042e-288

   1. Initial program 79.6%

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

   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. Step-by-step derivation

   6. Applied rewrites 52.9%

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

   if 3.5539141746916042e-288 < a < 9.971581761024804e63

   1. Initial program 79.6%

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

   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%

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

   if 9.971581761024804e63 < a

   1. Initial program 79.6%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 51.1%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 43.4%

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

   9. Applied rewrites 43.4%

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

Alternative 9: 62.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -7.795703790764831 \cdot 10^{+59}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;a \leq 6.408559906734058 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \frac{z - y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a}, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= a -7.795703790764831e+59)
  (+ x (* y (/ (- t x) a)))
  (if (<= a 6.408559906734058e+29)
    (* t (/ (- z y) (- z a)))
    (fma (- y z) (/ t a) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.795703790764831e+59) {
		tmp = x + (y * ((t - x) / a));
	} else if (a <= 6.408559906734058e+29) {
		tmp = t * ((z - y) / (z - a));
	} else {
		tmp = fma((y - z), (t / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.795703790764831e+59)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	elseif (a <= 6.408559906734058e+29)
		tmp = Float64(t * Float64(Float64(z - y) / Float64(z - a)));
	else
		tmp = fma(Float64(y - z), Float64(t / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.795703790764831e+59], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.408559906734058e+29], N[(t * N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision] + x), $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 (a <= (640855990673405790817804615680)) THEN (t * ((z - y) / (z - a))) ELSE (((y - z) * (t / a)) + x) ENDIF IN
	LET tmp = IF (a <= (-779570379076483083113887747491956741142103796285330444779520)) THEN (x + (y * ((t - x) / a))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if a < -7.7957037907648308e59

   1. Initial program 79.6%

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

   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 47.0%

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

   if -7.7957037907648308e59 < a < 6.4085599067340579e29

   1. Initial program 79.6%

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

   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. Step-by-step derivation

   6. Applied rewrites 52.9%

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

   if 6.4085599067340579e29 < a

   1. Initial program 79.6%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 51.1%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 43.4%

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

   9. Applied rewrites 43.4%

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

Alternative 10: 59.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t}{a}, x\right)\\ \mathbf{if}\;a \leq -5.617839962885588 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.611758196774356 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma (- y z) (/ t a) x)))
  (if (<= a -5.617839962885588e-9)
    t_1
    (if (<= a 5.611758196774356e-62) (* t (/ (- z y) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), (t / a), x);
	double tmp;
	if (a <= -5.617839962885588e-9) {
		tmp = t_1;
	} else if (a <= 5.611758196774356e-62) {
		tmp = t * ((z - y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(t / a), x)
	tmp = 0.0
	if (a <= -5.617839962885588e-9)
		tmp = t_1;
	elseif (a <= 5.611758196774356e-62)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	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 / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -5.617839962885588e-9], t$95$1, If[LessEqual[a, 5.611758196774356e-62], N[(t * N[(N[(z - y), $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 = (((y - z) * (t / a)) + x) IN
		LET tmp_1 = IF (a <= (561175819677435558749156612384132629178676607668429004106000322209413249479713835768795309053073643242151251958384697204441804254202850544898255978208852223776403889132780022919178009033203125e-253)) THEN (t * ((z - y) / z)) ELSE t_1 ENDIF IN
		LET tmp = IF (a <= (-561783996288558765571393330382106434672806472008232958614826202392578125e-80)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if a < -5.6178399628855877e-9 or 5.6117581967743556e-62 < a

   1. Initial program 79.6%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 51.1%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 43.4%

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

   9. Applied rewrites 43.4%

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

   if -5.6178399628855877e-9 < a < 5.6117581967743556e-62

   1. Initial program 79.6%

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

   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. Step-by-step derivation

   6. Applied rewrites 52.9%

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

   7. Taylor expanded in a around 0

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

   9. Applied rewrites 37.2%

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

Alternative 11: 55.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -5.617839962885588 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.611758196774356 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (+ x (* y (/ t a)))))
  (if (<= a -5.617839962885588e-9)
    t_1
    (if (<= a 5.611758196774356e-62) (* t (/ (- z y) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double tmp;
	if (a <= -5.617839962885588e-9) {
		tmp = t_1;
	} else if (a <= 5.611758196774356e-62) {
		tmp = t * ((z - y) / z);
	} 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 * (t / a))
    if (a <= (-5.617839962885588d-9)) then
        tmp = t_1
    else if (a <= 5.611758196774356d-62) then
        tmp = t * ((z - y) / z)
    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 * (t / a));
	double tmp;
	if (a <= -5.617839962885588e-9) {
		tmp = t_1;
	} else if (a <= 5.611758196774356e-62) {
		tmp = t * ((z - y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (t / a))
	tmp = 0
	if a <= -5.617839962885588e-9:
		tmp = t_1
	elif a <= 5.611758196774356e-62:
		tmp = t * ((z - y) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(t / a)))
	tmp = 0.0
	if (a <= -5.617839962885588e-9)
		tmp = t_1;
	elseif (a <= 5.611758196774356e-62)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (t / a));
	tmp = 0.0;
	if (a <= -5.617839962885588e-9)
		tmp = t_1;
	elseif (a <= 5.611758196774356e-62)
		tmp = t * ((z - y) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.617839962885588e-9], t$95$1, If[LessEqual[a, 5.611758196774356e-62], N[(t * N[(N[(z - y), $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 = (x + (y * (t / a))) IN
		LET tmp_1 = IF (a <= (561175819677435558749156612384132629178676607668429004106000322209413249479713835768795309053073643242151251958384697204441804254202850544898255978208852223776403889132780022919178009033203125e-253)) THEN (t * ((z - y) / z)) ELSE t_1 ENDIF IN
		LET tmp = IF (a <= (-561783996288558765571393330382106434672806472008232958614826202392578125e-80)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if a < -5.6178399628855877e-9 or 5.6117581967743556e-62 < a

   1. Initial program 79.6%

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

   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 47.0%

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

   7. Taylor expanded in x around 0

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

   9. Applied rewrites 39.3%

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

   if -5.6178399628855877e-9 < a < 5.6117581967743556e-62

   1. Initial program 79.6%

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

   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. Step-by-step derivation

   6. Applied rewrites 52.9%

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

   7. Taylor expanded in a around 0

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

   9. Applied rewrites 37.2%

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

Alternative 12: 47.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := -1 \cdot \left(-x\right)\\ \mathbf{if}\;a \leq -7.521944471779783 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.611758196774356 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 4.147299749583203 \cdot 10^{+147}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* -1.0 (- x))))
  (if (<= a -7.521944471779783e+114)
    t_1
    (if (<= a 5.611758196774356e-62)
      (* t (/ (- z y) z))
      (if (<= a 4.147299749583203e+147) (/ (* t (- y z)) a) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -1.0 * -x;
	double tmp;
	if (a <= -7.521944471779783e+114) {
		tmp = t_1;
	} else if (a <= 5.611758196774356e-62) {
		tmp = t * ((z - y) / z);
	} else if (a <= 4.147299749583203e+147) {
		tmp = (t * (y - z)) / 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 = (-1.0d0) * -x
    if (a <= (-7.521944471779783d+114)) then
        tmp = t_1
    else if (a <= 5.611758196774356d-62) then
        tmp = t * ((z - y) / z)
    else if (a <= 4.147299749583203d+147) then
        tmp = (t * (y - z)) / 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 = -1.0 * -x;
	double tmp;
	if (a <= -7.521944471779783e+114) {
		tmp = t_1;
	} else if (a <= 5.611758196774356e-62) {
		tmp = t * ((z - y) / z);
	} else if (a <= 4.147299749583203e+147) {
		tmp = (t * (y - z)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -1.0 * -x
	tmp = 0
	if a <= -7.521944471779783e+114:
		tmp = t_1
	elif a <= 5.611758196774356e-62:
		tmp = t * ((z - y) / z)
	elif a <= 4.147299749583203e+147:
		tmp = (t * (y - z)) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-1.0 * Float64(-x))
	tmp = 0.0
	if (a <= -7.521944471779783e+114)
		tmp = t_1;
	elseif (a <= 5.611758196774356e-62)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	elseif (a <= 4.147299749583203e+147)
		tmp = Float64(Float64(t * Float64(y - z)) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -1.0 * -x;
	tmp = 0.0;
	if (a <= -7.521944471779783e+114)
		tmp = t_1;
	elseif (a <= 5.611758196774356e-62)
		tmp = t * ((z - y) / z);
	elseif (a <= 4.147299749583203e+147)
		tmp = (t * (y - z)) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-1.0 * (-x)), $MachinePrecision]}, If[LessEqual[a, -7.521944471779783e+114], t$95$1, If[LessEqual[a, 5.611758196774356e-62], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.147299749583203e+147], N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / a), $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 = ((-1) * (- x)) IN
		LET tmp_2 = IF (a <= (4147299749583203120421558305448312751908181217847041342675424657963664869079392550372041680436277157852404702606899931198928844905910905953530675200)) THEN ((t * (y - z)) / a) ELSE t_1 ENDIF IN
		LET tmp_1 = IF (a <= (561175819677435558749156612384132629178676607668429004106000322209413249479713835768795309053073643242151251958384697204441804254202850544898255978208852223776403889132780022919178009033203125e-253)) THEN (t * ((z - y) / z)) ELSE tmp_2 ENDIF IN
		LET tmp = IF (a <= (-7521944471779782746527472803051824667364982942406433249056080780382290106493121767074017930646290078135839522553856)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if a < -7.5219444717797827e114 or 4.1472997495832031e147 < a

   1. Initial program 79.6%

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

   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 z around 0

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

   7. Applied rewrites 35.4%

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

   8. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \left(x \cdot -1\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 24.4%

       \[\leadsto -1 \cdot \left(x \cdot -1\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 24.4%

       \[\leadsto -1 \cdot \left(-x\right) \]

   if -7.5219444717797827e114 < a < 5.6117581967743556e-62

   1. Initial program 79.6%

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

   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. Step-by-step derivation

   6. Applied rewrites 52.9%

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

   7. Taylor expanded in a around 0

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

   9. Applied rewrites 37.2%

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

   if 5.6117581967743556e-62 < a < 4.1472997495832031e147

   1. Initial program 79.6%

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

   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%

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

   6. Applied rewrites 40.3%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 20.0%

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

Alternative 13: 47.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := -1 \cdot \left(-x\right)\\ \mathbf{if}\;a \leq -7.521944471779783 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.611758196774356 \cdot 10^{-62}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;a \leq 4.147299749583203 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* -1.0 (- x))))
  (if (<= a -7.521944471779783e+114)
    t_1
    (if (<= a 5.611758196774356e-62)
      (* t (/ (- z y) z))
      (if (<= a 4.147299749583203e+147) (* t (/ (- y z) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -1.0 * -x;
	double tmp;
	if (a <= -7.521944471779783e+114) {
		tmp = t_1;
	} else if (a <= 5.611758196774356e-62) {
		tmp = t * ((z - y) / z);
	} else if (a <= 4.147299749583203e+147) {
		tmp = t * ((y - z) / 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 = (-1.0d0) * -x
    if (a <= (-7.521944471779783d+114)) then
        tmp = t_1
    else if (a <= 5.611758196774356d-62) then
        tmp = t * ((z - y) / z)
    else if (a <= 4.147299749583203d+147) then
        tmp = t * ((y - z) / 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 = -1.0 * -x;
	double tmp;
	if (a <= -7.521944471779783e+114) {
		tmp = t_1;
	} else if (a <= 5.611758196774356e-62) {
		tmp = t * ((z - y) / z);
	} else if (a <= 4.147299749583203e+147) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -1.0 * -x
	tmp = 0
	if a <= -7.521944471779783e+114:
		tmp = t_1
	elif a <= 5.611758196774356e-62:
		tmp = t * ((z - y) / z)
	elif a <= 4.147299749583203e+147:
		tmp = t * ((y - z) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-1.0 * Float64(-x))
	tmp = 0.0
	if (a <= -7.521944471779783e+114)
		tmp = t_1;
	elseif (a <= 5.611758196774356e-62)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	elseif (a <= 4.147299749583203e+147)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -1.0 * -x;
	tmp = 0.0;
	if (a <= -7.521944471779783e+114)
		tmp = t_1;
	elseif (a <= 5.611758196774356e-62)
		tmp = t * ((z - y) / z);
	elseif (a <= 4.147299749583203e+147)
		tmp = t * ((y - z) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-1.0 * (-x)), $MachinePrecision]}, If[LessEqual[a, -7.521944471779783e+114], t$95$1, If[LessEqual[a, 5.611758196774356e-62], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.147299749583203e+147], N[(t * N[(N[(y - z), $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 = ((-1) * (- x)) IN
		LET tmp_2 = IF (a <= (4147299749583203120421558305448312751908181217847041342675424657963664869079392550372041680436277157852404702606899931198928844905910905953530675200)) THEN (t * ((y - z) / a)) ELSE t_1 ENDIF IN
		LET tmp_1 = IF (a <= (561175819677435558749156612384132629178676607668429004106000322209413249479713835768795309053073643242151251958384697204441804254202850544898255978208852223776403889132780022919178009033203125e-253)) THEN (t * ((z - y) / z)) ELSE tmp_2 ENDIF IN
		LET tmp = IF (a <= (-7521944471779782746527472803051824667364982942406433249056080780382290106493121767074017930646290078135839522553856)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if a < -7.5219444717797827e114 or 4.1472997495832031e147 < a

   1. Initial program 79.6%

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

   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 z around 0

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

   7. Applied rewrites 35.4%

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

   8. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \left(x \cdot -1\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 24.4%

       \[\leadsto -1 \cdot \left(x \cdot -1\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 24.4%

       \[\leadsto -1 \cdot \left(-x\right) \]

   if -7.5219444717797827e114 < a < 5.6117581967743556e-62

   1. Initial program 79.6%

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

   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. Step-by-step derivation

   6. Applied rewrites 52.9%

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

   7. Taylor expanded in a around 0

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

   9. Applied rewrites 37.2%

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

   if 5.6117581967743556e-62 < a < 4.1472997495832031e147

   1. Initial program 79.6%

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

   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 a around inf

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

   7. Applied rewrites 23.6%

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

Alternative 14: 40.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+306}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-132}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-261}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-227}:\\ \;\;\;\;\frac{a}{z} \cdot \left(-x\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+27}:\\ \;\;\;\;-1 \cdot \left(-x\right)\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
  (if (<= t_1 -1e+306)
    (* x (/ y z))
    (if (<= t_1 -5e-132)
      (+ x t)
      (if (<= t_1 -1e-261)
        (* t (/ (- y z) a))
        (if (<= t_1 5e-227)
          (* (/ a z) (- x))
          (if (<= t_1 2e+27)
            (* -1.0 (- x))
            (if (<= t_1 INFINITY) (+ x t) (/ (* t (- z y)) z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e+306) {
		tmp = x * (y / z);
	} else if (t_1 <= -5e-132) {
		tmp = x + t;
	} else if (t_1 <= -1e-261) {
		tmp = t * ((y - z) / a);
	} else if (t_1 <= 5e-227) {
		tmp = (a / z) * -x;
	} else if (t_1 <= 2e+27) {
		tmp = -1.0 * -x;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = x + t;
	} else {
		tmp = (t * (z - y)) / z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e+306) {
		tmp = x * (y / z);
	} else if (t_1 <= -5e-132) {
		tmp = x + t;
	} else if (t_1 <= -1e-261) {
		tmp = t * ((y - z) / a);
	} else if (t_1 <= 5e-227) {
		tmp = (a / z) * -x;
	} else if (t_1 <= 2e+27) {
		tmp = -1.0 * -x;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = x + t;
	} else {
		tmp = (t * (z - y)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -1e+306:
		tmp = x * (y / z)
	elif t_1 <= -5e-132:
		tmp = x + t
	elif t_1 <= -1e-261:
		tmp = t * ((y - z) / a)
	elif t_1 <= 5e-227:
		tmp = (a / z) * -x
	elif t_1 <= 2e+27:
		tmp = -1.0 * -x
	elif t_1 <= math.inf:
		tmp = x + t
	else:
		tmp = (t * (z - y)) / z
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e+306)
		tmp = Float64(x * Float64(y / z));
	elseif (t_1 <= -5e-132)
		tmp = Float64(x + t);
	elseif (t_1 <= -1e-261)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (t_1 <= 5e-227)
		tmp = Float64(Float64(a / z) * Float64(-x));
	elseif (t_1 <= 2e+27)
		tmp = Float64(-1.0 * Float64(-x));
	elseif (t_1 <= Inf)
		tmp = Float64(x + t);
	else
		tmp = Float64(Float64(t * Float64(z - y)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -1e+306)
		tmp = x * (y / z);
	elseif (t_1 <= -5e-132)
		tmp = x + t;
	elseif (t_1 <= -1e-261)
		tmp = t * ((y - z) / a);
	elseif (t_1 <= 5e-227)
		tmp = (a / z) * -x;
	elseif (t_1 <= 2e+27)
		tmp = -1.0 * -x;
	elseif (t_1 <= Inf)
		tmp = x + t;
	else
		tmp = (t * (z - y)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+306], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-132], N[(x + t), $MachinePrecision], If[LessEqual[t$95$1, -1e-261], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-227], N[(N[(a / z), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[t$95$1, 2e+27], N[(-1.0 * (-x)), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(x + t), $MachinePrecision], N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1e306

   1. Initial program 79.6%

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

   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 -1e306 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.9999999999999999e-132 or 2e27 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < +inf.0

   1. Initial program 79.6%

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

   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 -4.9999999999999999e-132 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999998e-262

   1. Initial program 79.6%

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

   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 a around inf

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

   7. Applied rewrites 23.6%

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

   if -9.9999999999999998e-262 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999996e-227

   1. Initial program 79.6%

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

   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 z around -inf

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

   7. Applied rewrites 23.3%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 8.8%

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

   12. Applied rewrites 8.8%

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

   if 4.9999999999999996e-227 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2e27

   1. Initial program 79.6%

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

   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 z around 0

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

   7. Applied rewrites 35.4%

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

   8. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \left(x \cdot -1\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 24.4%

       \[\leadsto -1 \cdot \left(x \cdot -1\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 24.4%

       \[\leadsto -1 \cdot \left(-x\right) \]

   if +inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.6%

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

   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. Step-by-step derivation

   6. Applied rewrites 52.9%

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

   7. Taylor expanded in a around 0

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

   9. Applied rewrites 27.8%

      \[\leadsto \frac{t \cdot \left(z - y\right)}{z} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 15: 38.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+306}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-261}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-227}:\\ \;\;\;\;\frac{a}{z} \cdot \left(-x\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+27}:\\ \;\;\;\;-1 \cdot \left(-x\right)\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
  (if (<= t_1 -1e+306)
    (* x (/ y z))
    (if (<= t_1 -1e-261)
      (+ x t)
      (if (<= t_1 5e-227)
        (* (/ a z) (- x))
        (if (<= t_1 2e+27)
          (* -1.0 (- x))
          (if (<= t_1 INFINITY) (+ x t) (/ (* t (- z y)) z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e+306) {
		tmp = x * (y / z);
	} else if (t_1 <= -1e-261) {
		tmp = x + t;
	} else if (t_1 <= 5e-227) {
		tmp = (a / z) * -x;
	} else if (t_1 <= 2e+27) {
		tmp = -1.0 * -x;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = x + t;
	} else {
		tmp = (t * (z - y)) / z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -1e+306) {
		tmp = x * (y / z);
	} else if (t_1 <= -1e-261) {
		tmp = x + t;
	} else if (t_1 <= 5e-227) {
		tmp = (a / z) * -x;
	} else if (t_1 <= 2e+27) {
		tmp = -1.0 * -x;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = x + t;
	} else {
		tmp = (t * (z - y)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -1e+306:
		tmp = x * (y / z)
	elif t_1 <= -1e-261:
		tmp = x + t
	elif t_1 <= 5e-227:
		tmp = (a / z) * -x
	elif t_1 <= 2e+27:
		tmp = -1.0 * -x
	elif t_1 <= math.inf:
		tmp = x + t
	else:
		tmp = (t * (z - y)) / z
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= -1e+306)
		tmp = Float64(x * Float64(y / z));
	elseif (t_1 <= -1e-261)
		tmp = Float64(x + t);
	elseif (t_1 <= 5e-227)
		tmp = Float64(Float64(a / z) * Float64(-x));
	elseif (t_1 <= 2e+27)
		tmp = Float64(-1.0 * Float64(-x));
	elseif (t_1 <= Inf)
		tmp = Float64(x + t);
	else
		tmp = Float64(Float64(t * Float64(z - y)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -1e+306)
		tmp = x * (y / z);
	elseif (t_1 <= -1e-261)
		tmp = x + t;
	elseif (t_1 <= 5e-227)
		tmp = (a / z) * -x;
	elseif (t_1 <= 2e+27)
		tmp = -1.0 * -x;
	elseif (t_1 <= Inf)
		tmp = x + t;
	else
		tmp = (t * (z - y)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+306], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-261], N[(x + t), $MachinePrecision], If[LessEqual[t$95$1, 5e-227], N[(N[(a / z), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[t$95$1, 2e+27], N[(-1.0 * (-x)), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(x + t), $MachinePrecision], N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1e306

   1. Initial program 79.6%

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

   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 -1e306 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999998e-262 or 2e27 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < +inf.0

   1. Initial program 79.6%

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

   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 -9.9999999999999998e-262 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999996e-227

   1. Initial program 79.6%

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

   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 z around -inf

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

   7. Applied rewrites 23.3%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 8.8%

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

   12. Applied rewrites 8.8%

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

   if 4.9999999999999996e-227 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2e27

   1. Initial program 79.6%

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

   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 z around 0

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

   7. Applied rewrites 35.4%

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

   8. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \left(x \cdot -1\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 24.4%

       \[\leadsto -1 \cdot \left(x \cdot -1\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 24.4%

       \[\leadsto -1 \cdot \left(-x\right) \]

   if +inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.6%

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

   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. Step-by-step derivation

   6. Applied rewrites 52.9%

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

   7. Taylor expanded in a around 0

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

   9. Applied rewrites 27.8%

      \[\leadsto \frac{t \cdot \left(z - y\right)}{z} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 16: 38.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -1.531587912663493 \cdot 10^{+143}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 6.321199852404313 \cdot 10^{+176}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= y -1.531587912663493e+143)
  (* t (/ y a))
  (if (<= y 6.321199852404313e+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);
	} else if (y <= 6.321199852404313e+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)
    else if (y <= 6.321199852404313d+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);
	} else if (y <= 6.321199852404313e+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)
	elif y <= 6.321199852404313e+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(t * Float64(y / a));
	elseif (y <= 6.321199852404313e+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);
	elseif (y <= 6.321199852404313e+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[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.321199852404313e+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 <= (632119985240431316968680360387599552899987257465620308425558145664231807380398542829250119150816483907411616685029944181093450556693925446760155798298331835757772673507777314816)) THEN (x + t) ELSE (x * (y / z)) ENDIF IN
	LET tmp = IF (y <= (-153158791266349302059067134646143137419441199017939972137454829263741356177562549975168567005190735022490714260833519588217537330168093707599872)) THEN (t * (y / a)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if y < -1.531587912663493e143

   1. Initial program 79.6%

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

   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 -1.531587912663493e143 < y < 6.3211998524043132e176

   1. Initial program 79.6%

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

   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 6.3211998524043132e176 < y

   1. Initial program 79.6%

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

   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 17: 38.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := x \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -2.526723922218976 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.321199852404313 \cdot 10^{+176}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

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 6.321199852404313e+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 <= 6.321199852404313e+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 <= 6.321199852404313d+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 <= 6.321199852404313e+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 <= 6.321199852404313e+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 <= 6.321199852404313e+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 <= 6.321199852404313e+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, 6.321199852404313e+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 <= (632119985240431316968680360387599552899987257465620308425558145664231807380398542829250119150816483907411616685029944181093450556693925446760155798298331835757772673507777314816)) 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 6.3211998524043132e176 < y

   1. Initial program 79.6%

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

   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 < 6.3211998524043132e176

   1. Initial program 79.6%

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

   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 18: 38.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := -1 \cdot \left(-x\right)\\ \mathbf{if}\;a \leq -2.9579371790710295 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.1105346300770184 \cdot 10^{-101}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 7239434900.004449:\\ \;\;\;\;0 + t\\ \mathbf{elif}\;a \leq 4.988986641920986 \cdot 10^{+183}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* -1.0 (- x))))
  (if (<= a -2.9579371790710295e+152)
    t_1
    (if (<= a -1.1105346300770184e-101)
      (+ x t)
      (if (<= a 7239434900.004449)
        (+ 0.0 t)
        (if (<= a 4.988986641920986e+183) (+ x t) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -1.0 * -x;
	double tmp;
	if (a <= -2.9579371790710295e+152) {
		tmp = t_1;
	} else if (a <= -1.1105346300770184e-101) {
		tmp = x + t;
	} else if (a <= 7239434900.004449) {
		tmp = 0.0 + t;
	} else if (a <= 4.988986641920986e+183) {
		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 = (-1.0d0) * -x
    if (a <= (-2.9579371790710295d+152)) then
        tmp = t_1
    else if (a <= (-1.1105346300770184d-101)) then
        tmp = x + t
    else if (a <= 7239434900.004449d0) then
        tmp = 0.0d0 + t
    else if (a <= 4.988986641920986d+183) 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 = -1.0 * -x;
	double tmp;
	if (a <= -2.9579371790710295e+152) {
		tmp = t_1;
	} else if (a <= -1.1105346300770184e-101) {
		tmp = x + t;
	} else if (a <= 7239434900.004449) {
		tmp = 0.0 + t;
	} else if (a <= 4.988986641920986e+183) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -1.0 * -x
	tmp = 0
	if a <= -2.9579371790710295e+152:
		tmp = t_1
	elif a <= -1.1105346300770184e-101:
		tmp = x + t
	elif a <= 7239434900.004449:
		tmp = 0.0 + t
	elif a <= 4.988986641920986e+183:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-1.0 * Float64(-x))
	tmp = 0.0
	if (a <= -2.9579371790710295e+152)
		tmp = t_1;
	elseif (a <= -1.1105346300770184e-101)
		tmp = Float64(x + t);
	elseif (a <= 7239434900.004449)
		tmp = Float64(0.0 + t);
	elseif (a <= 4.988986641920986e+183)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -1.0 * -x;
	tmp = 0.0;
	if (a <= -2.9579371790710295e+152)
		tmp = t_1;
	elseif (a <= -1.1105346300770184e-101)
		tmp = x + t;
	elseif (a <= 7239434900.004449)
		tmp = 0.0 + t;
	elseif (a <= 4.988986641920986e+183)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-1.0 * (-x)), $MachinePrecision]}, If[LessEqual[a, -2.9579371790710295e+152], t$95$1, If[LessEqual[a, -1.1105346300770184e-101], N[(x + t), $MachinePrecision], If[LessEqual[a, 7239434900.004449], N[(0.0 + t), $MachinePrecision], If[LessEqual[a, 4.988986641920986e+183], 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 = ((-1) * (- x)) IN
		LET tmp_3 = IF (a <= (4988986641920985938466169792183497807102416866876192698782647024627962002160565666281005102475733907571230562088197220108179102431293681718902830624553373639852957329260899405322518528)) THEN (x + t) ELSE t_1 ENDIF IN
		LET tmp_2 = IF (a <= (723943490000444889068603515625e-20)) THEN ((0) + t) ELSE tmp_3 ENDIF IN
		LET tmp_1 = IF (a <= (-111053463007701843730552725821292599310442190275310195449970179863145277763372916443673244872995869802021744130812577113463667157983357960687243172208385547593580707899178450572610314797807950600961231841432061080304126669523918161412264661236305902936027933947116252966225147247314453125e-388)) THEN (x + t) ELSE tmp_2 ENDIF IN
		LET tmp = IF (a <= (-295793717907102950942297275270299850829896158262799795073949506919917419466943960899258100554196387677659290202273981465052871660511299133272666362871808)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if a < -2.9579371790710295e152 or 4.9889866419209859e183 < a

   1. Initial program 79.6%

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

   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 z around 0

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

   7. Applied rewrites 35.4%

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

   8. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \left(x \cdot -1\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 24.4%

       \[\leadsto -1 \cdot \left(x \cdot -1\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 24.4%

       \[\leadsto -1 \cdot \left(-x\right) \]

   if -2.9579371790710295e152 < a < -1.1105346300770184e-101 or 7239434900.0044489 < a < 4.9889866419209859e183

   1. Initial program 79.6%

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

   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 -1.1105346300770184e-101 < a < 7239434900.0044489

   1. Initial program 79.6%

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

   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 19: 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 79.6%

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

   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 79.6%

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

   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 20: 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 79.6%

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

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 "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))