
Time bar (total: 2.8s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 99.9% | 0.1% | 0% | 0% | 0% | 0 |
| 100% | 99.9% | 0% | 0.1% | 0% | 0% | 0% | 1 |
Compiled 11 to 11 computations (0% saved)
| 680.0ms | 8 256× | 0 | valid |
ival-div: 165.0ms (40.3% of total)ival-mult: 137.0ms (33.4% of total)ival-sub: 87.0ms (21.2% of total)exact: 10.0ms (2.4% of total)ival-true: 6.0ms (1.5% of total)adjust: 3.0ms (0.7% of total)ival-assert: 3.0ms (0.7% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 0 | 0 | - | 0 | - | #s(literal 8 binary64) |
| 0 | 0 | - | 0 | - | (/.f64 (*.f64 x y) #s(literal 2 binary64)) |
| 0 | 0 | - | 0 | - | z |
| 0 | 0 | - | 0 | - | (*.f64 x y) |
| 0 | 0 | - | 0 | - | (-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) |
| 0 | 0 | - | 0 | - | (/.f64 z #s(literal 8 binary64)) |
| 0 | 0 | - | 0 | - | #s(literal 2 binary64) |
| 0 | 0 | - | 0 | - | y |
| 0 | 0 | - | 0 | - | x |
| Predicted + | Predicted - | |
|---|---|---|
| + | 0 | 0 |
| - | 0 | 256 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 0 | 0 | 0 |
| - | 0 | 0 | 256 |
| number | freq |
|---|---|
| 0 | 256 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 0 | 0 | 0 |
| - | 0 | 0 | 1 |
| 52.0ms | 512× | 0 | valid |
Compiled 63 to 31 computations (50.8% saved)
ival-mult: 23.0ms (69.9% of total)ival-div: 6.0ms (18.2% of total)ival-sub: 2.0ms (6.1% of total)exact: 1.0ms (3% of total)ival-true: 0.0ms (0% of total)adjust: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 33 | 90 |
| 1 | 52 | 88 |
| 2 | 71 | 84 |
| 3 | 111 | 84 |
| 4 | 177 | 84 |
| 5 | 367 | 84 |
| 6 | 1725 | 84 |
| 7 | 5878 | 84 |
| 0 | 9 | 9 |
| 0 | 13 | 9 |
| 1 | 18 | 9 |
| 2 | 24 | 9 |
| 3 | 37 | 9 |
| 4 | 65 | 9 |
| 5 | 168 | 9 |
| 6 | 1047 | 9 |
| 7 | 5521 | 9 |
| 0 | 8425 | 9 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) |
| Outputs |
|---|
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) |
(-.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) |
(sort x y)
Compiled 9 to 9 computations (0% saved)
Compiled 0 to 3 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 100.0% | (-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) |
Compiled 9 to 9 computations (0% saved)
| Inputs |
|---|
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) |
(/.f64 (*.f64 x y) #s(literal 2 binary64)) |
(*.f64 x y) |
x |
y |
#s(literal 2 binary64) |
(/.f64 z #s(literal 8 binary64)) |
z |
#s(literal 8 binary64) |
| Outputs |
|---|
(* -1/8 z) |
(- (* 1/2 (* x y)) (* 1/8 z)) |
(* 1/2 (* x y)) |
(* x y) |
x |
(* x (+ (* -1/8 (/ z x)) (* 1/2 y))) |
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x))))) |
y |
(* y (+ (* -1/8 (/ z y)) (* 1/2 x))) |
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y))))) |
(+ (* -1/8 z) (* 1/2 (* x y))) |
(* 1/8 z) |
z |
(* z (- (* 1/2 (/ (* x y) z)) 1/8)) |
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z))))) |
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 4.0ms | x | @ | -inf | ((- (/ (* x y) 2) (/ z 8)) (/ (* x y) 2) (* x y) x y 2 (/ z 8) z 8) |
| 1.0ms | y | @ | inf | ((- (/ (* x y) 2) (/ z 8)) (/ (* x y) 2) (* x y) x y 2 (/ z 8) z 8) |
| 1.0ms | x | @ | 0 | ((- (/ (* x y) 2) (/ z 8)) (/ (* x y) 2) (* x y) x y 2 (/ z 8) z 8) |
| 1.0ms | y | @ | -inf | ((- (/ (* x y) 2) (/ z 8)) (/ (* x y) 2) (* x y) x y 2 (/ z 8) z 8) |
| 1.0ms | y | @ | 0 | ((- (/ (* x y) 2) (/ z 8)) (/ (* x y) 2) (* x y) x y 2 (/ z 8) z 8) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 42 | 89 |
| 1 | 128 | 89 |
| 2 | 444 | 89 |
| 3 | 1117 | 89 |
| 4 | 3311 | 89 |
| 5 | 6558 | 89 |
| 0 | 8590 | 81 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* -1/8 z) |
(- (* 1/2 (* x y)) (* 1/8 z)) |
(* 1/2 (* x y)) |
(* x y) |
x |
(* x (+ (* -1/8 (/ z x)) (* 1/2 y))) |
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x))))) |
y |
(* y (+ (* -1/8 (/ z y)) (* 1/2 x))) |
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y))))) |
(+ (* -1/8 z) (* 1/2 (* x y))) |
(* 1/8 z) |
z |
(* z (- (* 1/2 (/ (* x y) z)) 1/8)) |
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z))))) |
| Outputs |
|---|
(* -1/8 z) |
(*.f64 #s(literal -1/8 binary64) z) |
(- (* 1/2 (* x y)) (* 1/8 z)) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)) |
(* 1/2 (* x y)) |
(*.f64 (*.f64 y x) #s(literal 1/2 binary64)) |
(* x y) |
(*.f64 y x) |
x |
(* x (+ (* -1/8 (/ z x)) (* 1/2 y))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)) |
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)) |
y |
(* y (+ (* -1/8 (/ z y)) (* 1/2 x))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)) |
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)) |
(+ (* -1/8 z) (* 1/2 (* x y))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)) |
(* 1/8 z) |
(*.f64 #s(literal 1/8 binary64) z) |
z |
(* z (- (* 1/2 (/ (* x y) z)) 1/8)) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)) |
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 9 | 25 |
| 0 | 13 | 25 |
| 1 | 45 | 25 |
| 0 | 319 | 25 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | unsound |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) |
(/.f64 (*.f64 x y) #s(literal 2 binary64)) |
(*.f64 x y) |
x |
y |
#s(literal 2 binary64) |
(/.f64 z #s(literal 8 binary64)) |
z |
#s(literal 8 binary64) |
| Outputs |
|---|
(/.f64 (/.f64 (fma.f64 #s(literal 8 binary64) (*.f64 y x) (*.f64 #s(literal -2 binary64) z)) #s(literal 2 binary64)) #s(literal 8 binary64)) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 2 binary64)))) (neg.f64 (fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal 8 binary64))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (/.f64 z #s(literal 8 binary64)) (fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal 8 binary64))) (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64))))) |
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (*.f64 y x) (*.f64 #s(literal -2 binary64) z))) #s(literal -16 binary64)) |
(/.f64 (-.f64 (*.f64 (*.f64 (neg.f64 x) y) #s(literal -8 binary64)) (*.f64 #s(literal -2 binary64) (neg.f64 z))) #s(literal 16 binary64)) |
(/.f64 (-.f64 (*.f64 (*.f64 (neg.f64 x) y) #s(literal 8 binary64)) (*.f64 #s(literal -2 binary64) z)) #s(literal -16 binary64)) |
(/.f64 (-.f64 (*.f64 (*.f64 y x) #s(literal -8 binary64)) (*.f64 #s(literal 2 binary64) (neg.f64 z))) #s(literal -16 binary64)) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 2 binary64))) (fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal 8 binary64)))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 z #s(literal 8 binary64)) (fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal 8 binary64))) (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)))) |
(/.f64 (fma.f64 #s(literal 8 binary64) (*.f64 y x) (*.f64 #s(literal -2 binary64) z)) #s(literal 16 binary64)) |
(-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)) (fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal 8 binary64)))) (/.f64 (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 2 binary64)) (fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal 8 binary64))))) |
(-.f64 (/.f64 (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 z #s(literal 8 binary64)) (fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal 8 binary64))) (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (/.f64 z #s(literal 8 binary64)) #s(literal 3 binary64)) (fma.f64 (/.f64 z #s(literal 8 binary64)) (fma.f64 (/.f64 y #s(literal 2 binary64)) x (/.f64 z #s(literal 8 binary64))) (pow.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) #s(literal 2 binary64))))) |
(-.f64 (/.f64 (*.f64 #s(literal 8 binary64) (*.f64 y x)) #s(literal 16 binary64)) (/.f64 (*.f64 z #s(literal 2 binary64)) #s(literal 16 binary64))) |
(-.f64 (/.f64 (*.f64 y x) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) |
(*.f64 (/.f64 y #s(literal 2 binary64)) x) |
(*.f64 y (/.f64 x #s(literal 2 binary64))) |
(*.f64 x (/.f64 y #s(literal 2 binary64))) |
(/.f64 (neg.f64 (*.f64 (neg.f64 x) y)) #s(literal 2 binary64)) |
(/.f64 (*.f64 (neg.f64 x) y) #s(literal -2 binary64)) |
(/.f64 (*.f64 y x) #s(literal 2 binary64)) |
(neg.f64 (/.f64 (*.f64 (neg.f64 x) y) #s(literal 2 binary64))) |
(neg.f64 (/.f64 (*.f64 y x) #s(literal -2 binary64))) |
(*.f64 y x) |
(*.f64 x y) |
x |
y |
#s(literal 2 binary64) |
(/.f64 (neg.f64 (neg.f64 z)) #s(literal 8 binary64)) |
(/.f64 (neg.f64 z) #s(literal -8 binary64)) |
(/.f64 z #s(literal 8 binary64)) |
(neg.f64 (/.f64 (neg.f64 z) #s(literal 8 binary64))) |
(neg.f64 (/.f64 z #s(literal -8 binary64))) |
z |
#s(literal 8 binary64) |
Compiled 554 to 118 computations (78.7% saved)
2 alts after pruning (2 fresh and 0 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 37 | 2 | 39 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 0 | 1 |
| Done | 0 | 0 | 0 |
| Total | 38 | 2 | 40 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 100.0% | #s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))) |
| ▶ | 46.8% | #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)) |
Compiled 31 to 27 computations (12.9% saved)
| Inputs |
|---|
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)) |
(*.f64 #s(literal -1/8 binary64) z) |
#s(literal -1/8 binary64) |
z |
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
y |
| Outputs |
|---|
(* -1/8 z) |
(- (* 1/2 (* x y)) (* 1/8 z)) |
(+ (* -1/8 z) (* 1/2 (* x y))) |
(* 1/2 x) |
x |
(* 1/2 (* x y)) |
(* x (+ (* -1/8 (/ z x)) (* 1/2 y))) |
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x))))) |
y |
(* y (+ (* -1/8 (/ z y)) (* 1/2 x))) |
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y))))) |
z |
(* z (- (* 1/2 (/ (* x y) z)) 1/8)) |
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z))))) |
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 7.0ms | z | @ | inf | ((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) -1/8 z (- (/ (* x y) 2) (/ z 8)) (+ (* (* 1/2 x) y) (* -1/8 z)) (* 1/2 x) 1/2 x y) |
| 1.0ms | x | @ | -inf | ((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) -1/8 z (- (/ (* x y) 2) (/ z 8)) (+ (* (* 1/2 x) y) (* -1/8 z)) (* 1/2 x) 1/2 x y) |
| 1.0ms | z | @ | -inf | ((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) -1/8 z (- (/ (* x y) 2) (/ z 8)) (+ (* (* 1/2 x) y) (* -1/8 z)) (* 1/2 x) 1/2 x y) |
| 1.0ms | x | @ | inf | ((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) -1/8 z (- (/ (* x y) 2) (/ z 8)) (+ (* (* 1/2 x) y) (* -1/8 z)) (* 1/2 x) 1/2 x y) |
| 1.0ms | x | @ | 0 | ((- (/ (* x y) 2) (/ z 8)) (* -1/8 z) -1/8 z (- (/ (* x y) 2) (/ z 8)) (+ (* (* 1/2 x) y) (* -1/8 z)) (* 1/2 x) 1/2 x y) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 42 | 86 |
| 1 | 128 | 86 |
| 2 | 445 | 86 |
| 3 | 1119 | 86 |
| 4 | 3339 | 86 |
| 5 | 6605 | 86 |
| 0 | 8634 | 78 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* -1/8 z) |
(- (* 1/2 (* x y)) (* 1/8 z)) |
(+ (* -1/8 z) (* 1/2 (* x y))) |
(* 1/2 x) |
x |
(* 1/2 (* x y)) |
(* x (+ (* -1/8 (/ z x)) (* 1/2 y))) |
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x))))) |
y |
(* y (+ (* -1/8 (/ z y)) (* 1/2 x))) |
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y))))) |
z |
(* z (- (* 1/2 (/ (* x y) z)) 1/8)) |
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z))))) |
| Outputs |
|---|
(* -1/8 z) |
(*.f64 #s(literal -1/8 binary64) z) |
(- (* 1/2 (* x y)) (* 1/8 z)) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) (*.f64 #s(literal -1/8 binary64) z)) |
(+ (* -1/8 z) (* 1/2 (* x y))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) (*.f64 #s(literal -1/8 binary64) z)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
x |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 y x)) |
(* x (+ (* -1/8 (/ z x)) (* 1/2 y))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) (*.f64 #s(literal -1/8 binary64) z)) |
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x))))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) (*.f64 #s(literal -1/8 binary64) z)) |
y |
(* y (+ (* -1/8 (/ z y)) (* 1/2 x))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) (*.f64 #s(literal -1/8 binary64) z)) |
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y))))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) (*.f64 #s(literal -1/8 binary64) z)) |
z |
(* z (- (* 1/2 (/ (* x y) z)) 1/8)) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) (*.f64 #s(literal -1/8 binary64) z)) |
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z))))) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) (*.f64 #s(literal -1/8 binary64) z)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 16 | 50 |
| 0 | 20 | 50 |
| 1 | 73 | 50 |
| 0 | 533 | 50 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)) |
(*.f64 #s(literal -1/8 binary64) z) |
#s(literal -1/8 binary64) |
z |
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
y |
| Outputs |
|---|
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)) |
(*.f64 #s(literal -1/8 binary64) z) |
(*.f64 z #s(literal -1/8 binary64)) |
#s(literal -1/8 binary64) |
z |
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))) |
(/.f64 (-.f64 (pow.f64 (*.f64 #s(literal -1/8 binary64) z) #s(literal 2 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64))) (-.f64 (*.f64 #s(literal -1/8 binary64) z) (*.f64 (*.f64 #s(literal 1/2 binary64) x) y))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal 1/8 binary64) z) #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (fma.f64 #s(literal 1/64 binary64) (*.f64 z z) (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) (*.f64 #s(literal 1/8 binary64) z))))) |
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal -1/8 binary64) z) #s(literal 2 binary64)))) (neg.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x (*.f64 #s(literal 1/8 binary64) z)))) |
(/.f64 (neg.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 z #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) z) (-.f64 (*.f64 #s(literal -1/8 binary64) z) (*.f64 (*.f64 #s(literal 1/2 binary64) x) y)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64))))) |
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (pow.f64 (*.f64 #s(literal -1/8 binary64) z) #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x (*.f64 #s(literal 1/8 binary64) z))) |
(/.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 z #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 3 binary64))) (fma.f64 #s(literal 1/64 binary64) (*.f64 z z) (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (*.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal -1/8 binary64)) z)))) |
(/.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 z #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 3 binary64))) (fma.f64 (*.f64 #s(literal -1/8 binary64) z) (-.f64 (*.f64 #s(literal -1/8 binary64) z) (*.f64 (*.f64 #s(literal 1/2 binary64) x) y)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) y) x (*.f64 #s(literal -1/8 binary64) z)) |
(fma.f64 (*.f64 y #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/8 binary64) z)) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)) |
(fma.f64 #s(literal 1/2 binary64) (*.f64 y x) (*.f64 #s(literal -1/8 binary64) z)) |
(fma.f64 #s(literal -1/8 binary64) z (*.f64 (*.f64 #s(literal 1/2 binary64) x) y)) |
(fma.f64 z #s(literal -1/8 binary64) (*.f64 (*.f64 #s(literal 1/2 binary64) x) y)) |
(fma.f64 (*.f64 y x) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) z)) |
(fma.f64 y (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal -1/8 binary64) z)) |
(fma.f64 x (*.f64 #s(literal 1/2 binary64) y) (*.f64 #s(literal -1/8 binary64) z)) |
(-.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x (*.f64 #s(literal 1/8 binary64) z))) (/.f64 (pow.f64 (*.f64 #s(literal -1/8 binary64) z) #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) y) x (*.f64 #s(literal 1/8 binary64) z)))) |
(-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) (*.f64 (neg.f64 z) #s(literal -1/8 binary64))) |
(-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) (*.f64 #s(literal 1/8 binary64) z)) |
(-.f64 (*.f64 #s(literal -1/8 binary64) z) (*.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) x)) y)) |
(-.f64 (*.f64 #s(literal -1/8 binary64) z) (*.f64 #s(literal -1/2 binary64) (*.f64 y x))) |
(-.f64 (*.f64 #s(literal -1/8 binary64) z) (*.f64 (neg.f64 y) (*.f64 #s(literal 1/2 binary64) x))) |
(+.f64 (/.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal -1/8 binary64) z) (-.f64 (*.f64 #s(literal -1/8 binary64) z) (*.f64 (*.f64 #s(literal 1/2 binary64) x) y)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)))) (/.f64 (pow.f64 (*.f64 #s(literal -1/8 binary64) z) #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal -1/8 binary64) z) (-.f64 (*.f64 #s(literal -1/8 binary64) z) (*.f64 (*.f64 #s(literal 1/2 binary64) x) y)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64))))) |
(+.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) x) y) (*.f64 #s(literal -1/8 binary64) z)) |
(+.f64 (*.f64 #s(literal -1/8 binary64) z) (*.f64 (*.f64 #s(literal 1/2 binary64) x) y)) |
(*.f64 #s(literal 1/2 binary64) x) |
(*.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
x |
y |
Compiled 1 010 to 131 computations (87% saved)
3 alts after pruning (1 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 43 | 1 | 44 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 2 | 2 |
| Done | 0 | 0 | 0 |
| Total | 43 | 3 | 46 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | #s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))) |
| ▶ | 54.7% | #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) |
| ✓ | 46.8% | #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)) |
Compiled 46 to 40 computations (13% saved)
| Inputs |
|---|
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 y x)) |
#s(literal 1/2 binary64) |
(*.f64 y x) |
y |
x |
| Outputs |
|---|
(* -1/8 z) |
(- (* 1/2 (* x y)) (* 1/8 z)) |
(* 1/2 (* x y)) |
(* x y) |
x |
(* x (+ (* -1/8 (/ z x)) (* 1/2 y))) |
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x))))) |
y |
(* y (+ (* -1/8 (/ z y)) (* 1/2 x))) |
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y))))) |
(+ (* -1/8 z) (* 1/2 (* x y))) |
(* z (- (* 1/2 (/ (* x y) z)) 1/8)) |
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z))))) |
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | ((- (/ (* x y) 2) (/ z 8)) (* 1/2 (* y x)) 1/2 (* y x) y x) |
| 1.0ms | y | @ | -inf | ((- (/ (* x y) 2) (/ z 8)) (* 1/2 (* y x)) 1/2 (* y x) y x) |
| 1.0ms | x | @ | inf | ((- (/ (* x y) 2) (/ z 8)) (* 1/2 (* y x)) 1/2 (* y x) y x) |
| 1.0ms | y | @ | inf | ((- (/ (* x y) 2) (/ z 8)) (* 1/2 (* y x)) 1/2 (* y x) y x) |
| 0.0ms | x | @ | 0 | ((- (/ (* x y) 2) (/ z 8)) (* 1/2 (* y x)) 1/2 (* y x) y x) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 42 | 85 |
| 1 | 128 | 85 |
| 2 | 444 | 85 |
| 3 | 1115 | 85 |
| 4 | 3320 | 85 |
| 5 | 6556 | 85 |
| 0 | 8587 | 77 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* -1/8 z) |
(- (* 1/2 (* x y)) (* 1/8 z)) |
(* 1/2 (* x y)) |
(* x y) |
x |
(* x (+ (* -1/8 (/ z x)) (* 1/2 y))) |
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x))))) |
y |
(* y (+ (* -1/8 (/ z y)) (* 1/2 x))) |
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y))))) |
(+ (* -1/8 z) (* 1/2 (* x y))) |
(* z (- (* 1/2 (/ (* x y) z)) 1/8)) |
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z))))) |
| Outputs |
|---|
(* -1/8 z) |
(*.f64 #s(literal -1/8 binary64) z) |
(- (* 1/2 (* x y)) (* 1/8 z)) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)) |
(* 1/2 (* x y)) |
(*.f64 #s(literal 1/2 binary64) (*.f64 y x)) |
(* x y) |
(*.f64 y x) |
x |
(* x (+ (* -1/8 (/ z x)) (* 1/2 y))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)) |
(* -1 (* x (+ (* -1/2 y) (* 1/8 (/ z x))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)) |
y |
(* y (+ (* -1/8 (/ z y)) (* 1/2 x))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)) |
(* -1 (* y (+ (* -1/2 x) (* 1/8 (/ z y))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)) |
(+ (* -1/8 z) (* 1/2 (* x y))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)) |
(* z (- (* 1/2 (/ (* x y) z)) 1/8)) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)) |
(* -1 (* z (+ 1/8 (* -1/2 (/ (* x y) z))))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 13 | 26 |
| 0 | 15 | 26 |
| 1 | 51 | 26 |
| 0 | 332 | 26 |
| 1× | iter limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | unsound |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) |
(*.f64 #s(literal 1/2 binary64) (*.f64 y x)) |
#s(literal 1/2 binary64) |
(*.f64 y x) |
y |
x |
| Outputs |
|---|
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) x) y) |
(*.f64 (*.f64 #s(literal 1/2 binary64) y) x) |
(*.f64 #s(literal 1/2 binary64) (*.f64 y x)) |
(*.f64 (*.f64 y x) #s(literal 1/2 binary64)) |
(*.f64 y (*.f64 x #s(literal 1/2 binary64))) |
(*.f64 x (*.f64 #s(literal 1/2 binary64) y)) |
#s(literal 1/2 binary64) |
(*.f64 y x) |
(*.f64 x y) |
y |
x |
Compiled 251 to 42 computations (83.3% saved)
3 alts after pruning (0 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 16 | 0 | 16 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 2 | 2 |
| Total | 16 | 3 | 19 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 100.0% | #s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))) |
| ✓ | 54.7% | #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) |
| ✓ | 46.8% | #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)) |
Compiled 101 to 65 computations (35.6% saved)
| Inputs |
|---|
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)) |
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) |
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))) |
(-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) |
| Outputs |
|---|
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))) |
7 calls:
| 5.0ms | (-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) |
| 2.0ms | z |
| 2.0ms | (/.f64 z #s(literal 8 binary64)) |
| 2.0ms | x |
| 2.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 1 | (/.f64 z #s(literal 8 binary64)) |
| 100.0% | 1 | (*.f64 x y) |
| 100.0% | 1 | (/.f64 (*.f64 x y) #s(literal 2 binary64)) |
| 100.0% | 1 | (-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) |
| 100.0% | 1 | x |
| 100.0% | 1 | y |
| 100.0% | 1 | z |
Compiled 23 to 33 computations (-43.5% saved)
| Inputs |
|---|
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)) |
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) |
| Outputs |
|---|
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) |
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)) |
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) |
7 calls:
| 8.0ms | (/.f64 z #s(literal 8 binary64)) |
| 1.0ms | (-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) |
| 1.0ms | z |
| 1.0ms | x |
| 1.0ms | y |
| Accuracy | Segments | Branch |
|---|---|---|
| 71.6% | 3 | (/.f64 z #s(literal 8 binary64)) |
| 82.7% | 3 | (*.f64 x y) |
| 82.7% | 3 | (/.f64 (*.f64 x y) #s(literal 2 binary64)) |
| 73.2% | 7 | (-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) |
| 80.1% | 3 | x |
| 75.6% | 3 | y |
| 71.6% | 3 | z |
Compiled 23 to 33 computations (-43.5% saved)
Total 0.0b remaining (0%)
Threshold costs 0b (0%)
| Inputs |
|---|
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)) |
| Outputs |
|---|
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)) |
7 calls:
| 1.0ms | (/.f64 z #s(literal 8 binary64)) |
| 1.0ms | (/.f64 (*.f64 x y) #s(literal 2 binary64)) |
| 1.0ms | (-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) |
| 1.0ms | z |
| 1.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 46.8% | 1 | (-.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) (/.f64 z #s(literal 8 binary64))) |
| 46.8% | 1 | (/.f64 z #s(literal 8 binary64)) |
| 46.8% | 1 | z |
| 46.8% | 1 | y |
| 46.8% | 1 | x |
| 46.8% | 1 | (*.f64 x y) |
| 46.8% | 1 | (/.f64 (*.f64 x y) #s(literal 2 binary64)) |
Compiled 23 to 33 computations (-43.5% saved)
| 2× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.935661504659047e-25 | 3.1924317173137033e-25 |
| 0.0ms | -1.4459489187182815e-55 | -3.481194635533033e-57 |
Compiled 12 to 15 computations (-25% saved)
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 27 | 76 |
| 1 | 35 | 76 |
| 2 | 41 | 76 |
| 3 | 55 | 76 |
| 4 | 95 | 76 |
| 5 | 433 | 76 |
| 6 | 3639 | 76 |
| 1× | node limit |
| Inputs |
|---|
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))) |
(if (<=.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) #s(literal -5521397077432451/55213970774324510299478046898216203619608871777363092441300193790394368 binary64)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) (if (<=.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) #s(literal 8711228593176025/43556142965880123323311949751266331066368 binary64)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))))) |
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)) |
| Outputs |
|---|
#s(approx (- (/ (* x y) 2) (/ z 8)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) y (*.f64 #s(literal -1/8 binary64) z))) |
(if (<=.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) #s(literal -5521397077432451/55213970774324510299478046898216203619608871777363092441300193790394368 binary64)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) (if (<=.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) #s(literal 8711228593176025/43556142965880123323311949751266331066368 binary64)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))))) |
(if (or (<=.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) #s(literal -5521397077432451/55213970774324510299478046898216203619608871777363092441300193790394368 binary64)) (not (<=.f64 (/.f64 (*.f64 x y) #s(literal 2 binary64)) #s(literal 8711228593176025/43556142965880123323311949751266331066368 binary64)))) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal 1/2 binary64) (*.f64 y x))) #s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z))) |
#s(approx (- (/ (* x y) 2) (/ z 8)) (*.f64 #s(literal -1/8 binary64) z)) |
| 1× | done |
Compiled 76 to 29 computations (61.8% saved)
(sort x y)
Compiled 206 to 106 computations (48.5% saved)
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