
Time bar (total: 6.4s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 100% | 0% | 0% | 0% | 0% | 0 |
| 0% | 0% | 100% | 0% | 0% | 0% | 0% | 1 |
| 50% | 50% | 50% | 0% | 0% | 0% | 0% | 2 |
| 66.7% | 50% | 25% | 0% | 0% | 25% | 0% | 3 |
| 83.3% | 62.5% | 12.5% | 0% | 0% | 25% | 0% | 4 |
| 91.7% | 68.7% | 6.2% | 0% | 0% | 25% | 0% | 5 |
| 95.8% | 71.8% | 3.1% | 0% | 0% | 25% | 0% | 6 |
| 97.9% | 73.4% | 1.6% | 0% | 0% | 25% | 0% | 7 |
| 99% | 74.2% | 0.8% | 0% | 0% | 25% | 0% | 8 |
| 99.5% | 74.6% | 0.4% | 0% | 0% | 25% | 0% | 9 |
| 99.7% | 74.8% | 0.2% | 0% | 0% | 25% | 0% | 10 |
| 99.9% | 74.9% | 0.1% | 0% | 0% | 25% | 0% | 11 |
| 99.9% | 74.9% | 0% | 0% | 0% | 25% | 0% | 12 |
Compiled 10 to 8 computations (20% saved)
| 418.0ms | 8 254× | 0 | valid |
| 0.0ms | 2× | 2 | valid |
| 0.0ms | 3× | 0 | invalid |
ival-add: 135.0ms (49.9% of total)ival-sqrt: 65.0ms (24% of total)ival-div: 58.0ms (21.4% of total)ival-true: 6.0ms (2.2% of total)exact: 4.0ms (1.5% of total)ival-assert: 3.0ms (1.1% of total)adjust: 0.0ms (0% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 0 | 0 | - | 0 | - | (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
| 0 | 0 | - | 0 | - | (+.f64 x #s(literal 1 binary64)) |
| 0 | 0 | - | 0 | - | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
| 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 |
| 84.0ms | 512× | 0 | valid |
Compiled 59 to 22 computations (62.7% saved)
ival-add: 5.0ms (34.6% of total)ival-sqrt: 5.0ms (34.6% of total)ival-div: 3.0ms (20.8% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| 1× | egg-herbie |
| 44× | associate-*l* |
| 42× | distribute-lft-neg-in |
| 42× | times-frac |
| 38× | unsub-neg |
| 36× | sub-neg |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 21 |
| 1 | 23 | 17 |
| 2 | 51 | 16 |
| 3 | 110 | 16 |
| 4 | 221 | 16 |
| 5 | 333 | 16 |
| 6 | 361 | 16 |
| 7 | 377 | 16 |
| 8 | 390 | 16 |
| 0 | 6 | 8 |
| 0 | 10 | 8 |
| 1 | 14 | 8 |
| 0 | 14 | 8 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| Outputs |
|---|
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 9 to 6 computations (33.3% saved)
Compiled 1 to 1 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 99.7% | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 9 to 6 computations (33.3% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (+.f64 x #s(literal 1 binary64)) | |
| cost-diff | 0 | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) | |
| cost-diff | 0 | (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) | |
| cost-diff | 0 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 8× | lower-+.f32 |
| 4× | lift-+.f64 |
| 4× | lower-+.f64 |
| 4× | +-commutative |
| 2× | lift-sqrt.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 23 |
| 0 | 10 | 23 |
| 1 | 14 | 23 |
| 0 | 14 | 23 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
x |
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
#s(literal 1 binary64) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
| Outputs |
|---|
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
x |
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
#s(literal 1 binary64) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (+.f64 x #s(literal 1 binary64)) | |
| accuracy | 0.00390625 | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) | |
| accuracy | 0.0078125 | (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) | |
| accuracy | 0.16796875 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 14.0ms | 256× | 0 | valid |
Compiled 25 to 8 computations (68% saved)
ival-add: 4.0ms (47.9% of total)ival-div: 2.0ms (23.9% of total)ival-sqrt: 2.0ms (23.9% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ()) |
#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) (taylor 0 x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- (sqrt x) 1) (taylor inf x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) (taylor inf x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) (taylor inf x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (sqrt x)) (taylor -inf x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) (taylor -inf x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) (taylor -inf x) (#s(alt (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt 2 (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ 2 (* 1/2 x)) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ 2 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
12 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | -inf | (+ 1 (sqrt (+ x 1))) |
| 1.0ms | x | @ | -inf | (/ x (+ 1 (sqrt (+ x 1)))) |
| 1.0ms | x | @ | inf | (/ x (+ 1 (sqrt (+ x 1)))) |
| 0.0ms | x | @ | -inf | (sqrt (+ x 1)) |
| 0.0ms | x | @ | inf | (sqrt (+ x 1)) |
| 1× | egg-herbie |
| 18 662× | lower-fma.f64 |
| 18 662× | lower-fma.f32 |
| 3 776× | lower-*.f64 |
| 3 776× | lower-*.f32 |
| 2 642× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 161 | 600 |
| 1 | 485 | 505 |
| 2 | 1633 | 483 |
| 3 | 5433 | 474 |
| 0 | 8374 | 430 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(- (sqrt x) 1) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(* -1 (sqrt x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
2 |
(+ 2 (* 1/2 x)) |
(+ 2 (* x (+ 1/2 (* -1/8 x)))) |
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (/ 1 x))) |
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
1 |
(+ 1 x) |
(+ 1 x) |
(+ 1 x) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
| Outputs |
|---|
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(sqrt x) |
(sqrt.f64 x) |
(- (sqrt x) 1) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(+.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64))) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(+.f64 (sqrt.f64 x) (+.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))))) |
(* -1 (sqrt x)) |
(neg.f64 (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(-.f64 #s(literal -1 binary64) (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(-.f64 (neg.f64 (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) x) x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(-.f64 (neg.f64 (sqrt.f64 x)) (+.f64 (/.f64 (/.f64 (fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) x) x) #s(literal 1 binary64))) |
2 |
#s(literal 2 binary64) |
(+ 2 (* 1/2 x)) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 2 binary64)) |
(+ 2 (* x (+ 1/2 (* -1/8 x)))) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)) |
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (/ 1 x))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
(* x (+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x))))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) |
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(-.f64 (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))) |
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 x)) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 x (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal -1/16 binary64) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
1 |
#s(literal 1 binary64) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
| 3 950× | lower-fma.f64 |
| 3 950× | lower-fma.f32 |
| 3 308× | lower-/.f32 |
| 3 306× | lower-/.f64 |
| 2 908× | lower-*.f64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 21 |
| 0 | 10 | 21 |
| 1 | 46 | 21 |
| 2 | 315 | 20 |
| 3 | 3400 | 20 |
| 0 | 8278 | 20 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
| Outputs |
|---|
(+.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(+.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))))) |
(+.f64 (/.f64 x (neg.f64 x)) (*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (neg.f64 x)))) |
(+.f64 (*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64)) (*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(+.f64 (*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64))) |
(+.f64 (*.f64 (/.f64 x (neg.f64 x)) #s(literal 1 binary64)) (*.f64 (/.f64 x (neg.f64 x)) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(+.f64 (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))) |
(exp.f64 (*.f64 (neg.f64 (log.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))) #s(literal -1 binary64))) |
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(fma.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))))) |
(fma.f64 x (/.f64 #s(literal -1 binary64) x) (*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (neg.f64 x)))) |
(fma.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))))) |
(fma.f64 #s(literal 1 binary64) (/.f64 x (neg.f64 x)) (*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (neg.f64 x)))) |
(fma.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))) |
(fma.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64) (*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(fma.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (*.f64 (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) #s(literal 1 binary64))) |
(fma.f64 (/.f64 x (neg.f64 x)) #s(literal 1 binary64) (*.f64 (/.f64 x (neg.f64 x)) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(fma.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))))) |
(fma.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (fma.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)) (*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (neg.f64 x)))) |
(fma.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))) (+.f64 #s(literal 2 binary64) x) (*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (neg.f64 x)))) |
(fma.f64 (/.f64 x (fma.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 x (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))))) |
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x))) |
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x)) |
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(/.f64 (fabs.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (fabs.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (fabs.f64 (neg.f64 (fma.f64 (*.f64 x x) (neg.f64 x) #s(literal -1 binary64)))) (fabs.f64 (neg.f64 (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (fabs.f64 (neg.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))))) (fabs.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (fabs.f64 (-.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) (*.f64 (+.f64 x #s(literal -1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x #s(literal -1 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))) (fabs.f64 (fma.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (fma.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)) (*.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))))))) |
(/.f64 (fabs.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64)))) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))))) (fabs.f64 (fma.f64 x (/.f64 x (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))))) |
(/.f64 (fabs.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))))) (fabs.f64 (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))) |
(/.f64 (fabs.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))) (fabs.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64))))) |
(/.f64 (fabs.f64 (sqrt.f64 (*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))) (fabs.f64 (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))) |
(/.f64 (fabs.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))) (fabs.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64))))) |
(/.f64 (fabs.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))) (fabs.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))))) |
(/.f64 (fabs.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))) (fabs.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64)))) |
(/.f64 (fabs.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))) (fabs.f64 (fma.f64 x (*.f64 x (*.f64 x x)) (fma.f64 x x #s(literal 1 binary64))))) |
(/.f64 (fabs.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))) (fabs.f64 (fma.f64 x x #s(literal 1 binary64)))) |
(/.f64 (-.f64 (neg.f64 (*.f64 x x)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x)) |
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) |
(pow.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) |
(pow.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal 2 binary64)) |
(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal 4 binary64)) |
(pow.f64 (*.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) #s(literal 1/4 binary64)) |
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64)) |
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log1p.f64 x)) |
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) (log1p.f64 x))) |
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (log1p.f64 x))) |
(*.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) |
(*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) |
(*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) |
(*.f64 (+.f64 x #s(literal 1 binary64)) (fabs.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (+.f64 x #s(literal 1 binary64)) (fabs.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))) |
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))) |
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)) (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (fma.f64 (*.f64 x x) (neg.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) |
(*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (fabs.f64 (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))) |
(*.f64 (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (*.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(*.f64 (*.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64))) |
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))) (fma.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x x)))) |
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (*.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (+.f64 (fma.f64 x x #s(literal -1 binary64)) x))) (+.f64 (fma.f64 x x #s(literal -1 binary64)) x)) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))) |
(*.f64 (exp.f64 (log1p.f64 (*.f64 x (*.f64 x x)))) (exp.f64 (neg.f64 (log1p.f64 (-.f64 (*.f64 x x) x))))) |
(*.f64 (exp.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64)))) (exp.f64 (neg.f64 (log.f64 (+.f64 x #s(literal -1 binary64)))))) |
(*.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (fabs.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (fabs.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) (fabs.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) |
(*.f64 (fabs.f64 (fma.f64 x x #s(literal -1 binary64))) (fabs.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (fabs.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))) (fabs.f64 (fma.f64 x x #s(literal -1 binary64)))) |
(*.f64 (fabs.f64 (fma.f64 (*.f64 x x) (neg.f64 x) #s(literal -1 binary64))) (fabs.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))) |
(*.f64 (fabs.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (fabs.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (fabs.f64 (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (fabs.f64 (*.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))) (fabs.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))) |
(*.f64 (fabs.f64 (*.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (fabs.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))) |
(*.f64 (fabs.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (+.f64 x #s(literal 1 binary64))) |
(*.f64 (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (+.f64 x #s(literal 1 binary64))) |
(*.f64 (fabs.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (*.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))) (fabs.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x x))))) |
(*.f64 (fabs.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (*.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (+.f64 (fma.f64 x x #s(literal -1 binary64)) x)))) (fabs.f64 (+.f64 (fma.f64 x x #s(literal -1 binary64)) x))) |
(*.f64 (fabs.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1 binary64)))) (fabs.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (fabs.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (fabs.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 091 to 2 091 computations (81.1% saved)
8 alts after pruning (7 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 513 | 7 | 520 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 513 | 8 | 521 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 99.7% | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 34.3% | (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) | |
| ▶ | 29.2% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
| 70.8% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) | |
| ▶ | 72.0% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| ▶ | 70.6% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
| ▶ | 72.0% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
| ▶ | 30.3% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
Compiled 121 to 78 computations (35.5% saved)
| 1× | egg-herbie |
Found 14 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) | |
| cost-diff | 0 | (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) | |
| cost-diff | 0 | (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) | |
| cost-diff | 0 | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) | |
| cost-diff | 0 | (sqrt.f64 x) | |
| cost-diff | 0 | (+.f64 (sqrt.f64 x) #s(literal -1 binary64)) | |
| cost-diff | 0 | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) | |
| cost-diff | 0 | (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) | |
| cost-diff | 0 | (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) | |
| cost-diff | 0 | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) | |
| cost-diff | 0 | (sqrt.f64 x) | |
| cost-diff | 0 | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) | |
| cost-diff | 0 | (*.f64 #s(literal 1/2 binary64) x) | |
| cost-diff | 0 | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
| 132× | lower-fma.f32 |
| 126× | lower-fma.f64 |
| 70× | lower-*.f32 |
| 64× | lower-*.f64 |
| 64× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 23 | 122 |
| 0 | 34 | 122 |
| 1 | 63 | 122 |
| 2 | 91 | 122 |
| 3 | 118 | 122 |
| 4 | 125 | 122 |
| 0 | 125 | 122 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(literal 1/2 binary64) |
x |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
(sqrt.f64 x) |
x |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
x |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
#s(literal -1/8 binary64) |
#s(literal 1/2 binary64) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(sqrt.f64 x) |
x |
#s(literal -1 binary64) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
x |
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) |
#s(literal 1/16 binary64) |
#s(literal -1/8 binary64) |
#s(literal 1/2 binary64) |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) |
(*.f64 #s(literal 1/2 binary64) x) |
(*.f64 x #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
x |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
(sqrt.f64 x) |
x |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
x |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
#s(literal -1/8 binary64) |
#s(literal 1/2 binary64) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(sqrt.f64 x) |
x |
#s(literal -1 binary64) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
x |
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) |
#s(literal 1/16 binary64) |
#s(literal -1/8 binary64) |
#s(literal 1/2 binary64) |
Found 14 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) | |
| accuracy | 0 | (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) | |
| accuracy | 0.02734375 | (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) | |
| accuracy | 17.85267094776417 | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) | |
| accuracy | 0 | (+.f64 (sqrt.f64 x) #s(literal -1 binary64)) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 23.78369224165954 | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) | |
| accuracy | 0 | (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) | |
| accuracy | 0 | (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) | |
| accuracy | 18.621542715964654 | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 23.093718392605656 | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) | |
| accuracy | 0 | (*.f64 #s(literal 1/2 binary64) x) | |
| accuracy | 17.608900901713156 | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
| 27.0ms | 170× | 0 | valid |
| 12.0ms | 86× | 0 | invalid |
Compiled 102 to 23 computations (77.5% saved)
ival-mult: 13.0ms (49.2% of total)ival-add: 7.0ms (26.5% of total)ival-sqrt: 3.0ms (11.4% of total)ival-div: 2.0ms (7.6% of total)exact: 1.0ms (3.8% of total)ival-true: 0.0ms (0% of total)ival-assert: 0.0ms (0% of total)| Inputs |
|---|
#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ()) |
#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ()) |
#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ()) |
#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ()) |
#s(alt (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) (patch (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (patch (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) #<representation binary64>) () ()) |
#s(alt (+.f64 (sqrt.f64 x) #s(literal -1 binary64)) (patch (+.f64 (sqrt.f64 x) #s(literal -1 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ()) |
#s(alt (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) (patch (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (patch (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (- (sqrt x) 1) (taylor inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) (taylor inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) (taylor inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (sqrt x)) (taylor -inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) (taylor -inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) (taylor -inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor -inf x) (#s(alt (*.f64 #s(literal 1/2 binary64) x) (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (- (sqrt x) 1) (taylor inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) (taylor inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) (taylor inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (sqrt x)) (taylor -inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) (taylor -inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) (taylor -inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- (sqrt x) 1) (taylor inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) (taylor inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) (taylor inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
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#s(alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) (taylor -inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) (patch (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) (patch (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) (patch (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) (patch (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/16 (pow x 3)) (taylor inf x) (#s(alt (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) (patch (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x)))) (taylor inf x) (#s(alt (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) (patch (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) (taylor inf x) (#s(alt (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) (patch (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) (taylor inf x) (#s(alt (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) (patch (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* 1/16 (pow x 3)) (taylor -inf x) (#s(alt (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) (patch (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16))) (taylor -inf x) (#s(alt (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) (patch (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16))) (taylor -inf x) (#s(alt (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) (patch (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16))) (taylor -inf x) (#s(alt (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) (patch (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 1/2 (taylor 0 x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/2 (* -1/8 x)) (taylor 0 x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/2 (* x (- (* 1/16 x) 1/8))) (taylor 0 x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1/2 (* x (- (* 1/16 x) 1/8))) (taylor 0 x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/16 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/16 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) (taylor -inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x)))) (taylor -inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x)))) (taylor -inf x) (#s(alt (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt -1/8 (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (patch (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (* 1/16 x) 1/8) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (patch (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (* 1/16 x) 1/8) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (patch (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (- (* 1/16 x) 1/8) (taylor 0 x) (#s(alt (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (patch (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/16 x) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (patch (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- 1/16 (* 1/8 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (patch (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- 1/16 (* 1/8 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (patch (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- 1/16 (* 1/8 (/ 1 x)))) (taylor inf x) (#s(alt (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (patch (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/16 x) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (patch (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/8 (/ 1 x)) 1/16))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (patch (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/8 (/ 1 x)) 1/16))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (patch (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* 1/8 (/ 1 x)) 1/16))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) (patch (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #<representation binary64>) () ())) ()) |
39 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | x | @ | -inf | (* x (+ (* x -1/8) 1/2)) |
| 1.0ms | x | @ | -inf | (* x (+ (* x (+ (* x 1/16) -1/8)) 1/2)) |
| 1.0ms | x | @ | inf | (* 1/2 x) |
| 0.0ms | x | @ | -inf | (sqrt x) |
| 0.0ms | x | @ | inf | (* x (+ (* x -1/8) 1/2)) |
| 1× | egg-herbie |
| 22 598× | lower-fma.f64 |
| 22 598× | lower-fma.f32 |
| 3 778× | lower-*.f64 |
| 3 778× | lower-*.f32 |
| 3 642× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 127 | 1477 |
| 1 | 375 | 1262 |
| 2 | 1258 | 1181 |
| 3 | 4155 | 1171 |
| 0 | 8370 | 1053 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(- (sqrt x) 1) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(* -1 (sqrt x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(- (sqrt x) 1) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(* -1 (sqrt x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(- (sqrt x) 1) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(* -1 (sqrt x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* -1/8 x))) |
(* -1/8 (pow x 2)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* -1/8 (pow x 2)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
1/2 |
(+ 1/2 (* -1/8 x)) |
(+ 1/2 (* -1/8 x)) |
(+ 1/2 (* -1/8 x)) |
(* -1/8 x) |
(* x (- (* 1/2 (/ 1 x)) 1/8)) |
(* x (- (* 1/2 (/ 1 x)) 1/8)) |
(* x (- (* 1/2 (/ 1 x)) 1/8)) |
(* -1/8 x) |
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) |
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) |
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(- (sqrt x) 1) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(* -1 (sqrt x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(- (sqrt x) 1) |
(- (sqrt x) 1) |
(- (sqrt x) 1) |
(- (sqrt x) 1) |
(sqrt x) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(- (sqrt x) 1) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(* -1 (sqrt x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* 1/16 (pow x 3)) |
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x)))) |
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(* 1/16 (pow x 3)) |
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16))) |
1/2 |
(+ 1/2 (* -1/8 x)) |
(+ 1/2 (* x (- (* 1/16 x) 1/8))) |
(+ 1/2 (* x (- (* 1/16 x) 1/8))) |
(* 1/16 (pow x 2)) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(* 1/16 (pow x 2)) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x)))) |
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x)))) |
-1/8 |
(- (* 1/16 x) 1/8) |
(- (* 1/16 x) 1/8) |
(- (* 1/16 x) 1/8) |
(* 1/16 x) |
(* x (- 1/16 (* 1/8 (/ 1 x)))) |
(* x (- 1/16 (* 1/8 (/ 1 x)))) |
(* x (- 1/16 (* 1/8 (/ 1 x)))) |
(* 1/16 x) |
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16))) |
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16))) |
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16))) |
| Outputs |
|---|
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(sqrt x) |
(sqrt.f64 x) |
(- (sqrt x) 1) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(+.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64))) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(+.f64 (sqrt.f64 x) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
(* -1 (sqrt x)) |
(neg.f64 (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(-.f64 #s(literal -1 binary64) (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(-.f64 (neg.f64 (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) x) x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(-.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) x) x)) (sqrt.f64 x)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(sqrt x) |
(sqrt.f64 x) |
(- (sqrt x) 1) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(+.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64))) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(+.f64 (sqrt.f64 x) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
(* -1 (sqrt x)) |
(neg.f64 (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(-.f64 #s(literal -1 binary64) (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(-.f64 (neg.f64 (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) x) x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(-.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) x) x)) (sqrt.f64 x)) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(sqrt x) |
(sqrt.f64 x) |
(- (sqrt x) 1) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(+.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64))) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(+.f64 (sqrt.f64 x) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
(* -1 (sqrt x)) |
(neg.f64 (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(-.f64 #s(literal -1 binary64) (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(-.f64 (neg.f64 (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) x) x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(-.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) x) x)) (sqrt.f64 x)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* -1/8 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/8 binary64))) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* -1/8 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal -1/8 binary64))) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8)) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* -1/8 x)) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(+ 1/2 (* -1/8 x)) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(+ 1/2 (* -1/8 x)) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(* -1/8 x) |
(*.f64 x #s(literal -1/8 binary64)) |
(* x (- (* 1/2 (/ 1 x)) 1/8)) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(* x (- (* 1/2 (/ 1 x)) 1/8)) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(* x (- (* 1/2 (/ 1 x)) 1/8)) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(* -1/8 x) |
(*.f64 x #s(literal -1/8 binary64)) |
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x))))) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(sqrt x) |
(sqrt.f64 x) |
(- (sqrt x) 1) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(+.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64))) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(+.f64 (sqrt.f64 x) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
(* -1 (sqrt x)) |
(neg.f64 (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(-.f64 #s(literal -1 binary64) (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(-.f64 (neg.f64 (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) x) x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(-.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) x) x)) (sqrt.f64 x)) |
(- (sqrt x) 1) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(- (sqrt x) 1) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(- (sqrt x) 1) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(- (sqrt x) 1) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(sqrt x) |
(sqrt.f64 x) |
(- (sqrt x) 1) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(+.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64))) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(+.f64 (sqrt.f64 x) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
(* -1 (sqrt x)) |
(neg.f64 (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(-.f64 #s(literal -1 binary64) (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(-.f64 (neg.f64 (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) x) x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(-.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) x) x)) (sqrt.f64 x)) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* 1/16 (pow x 3)) |
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/16 binary64)))) |
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x)))) |
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))) |
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* 1/16 (pow x 3)) |
(*.f64 x (*.f64 x (*.f64 x #s(literal 1/16 binary64)))) |
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16))) |
(*.f64 x (*.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* -1/8 x)) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(+ 1/2 (* x (- (* 1/16 x) 1/8))) |
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(+ 1/2 (* x (- (* 1/16 x) 1/8))) |
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(* 1/16 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/16 binary64))) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) |
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(* (pow x 2) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x)))) |
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(* 1/16 (pow x 2)) |
(*.f64 x (*.f64 x #s(literal 1/16 binary64))) |
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x)))) |
(*.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) |
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x)))) |
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(* (pow x 2) (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x)))) |
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
-1/8 |
#s(literal -1/8 binary64) |
(- (* 1/16 x) 1/8) |
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) |
(- (* 1/16 x) 1/8) |
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) |
(- (* 1/16 x) 1/8) |
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) |
(* 1/16 x) |
(*.f64 x #s(literal 1/16 binary64)) |
(* x (- 1/16 (* 1/8 (/ 1 x)))) |
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) |
(* x (- 1/16 (* 1/8 (/ 1 x)))) |
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) |
(* x (- 1/16 (* 1/8 (/ 1 x)))) |
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) |
(* 1/16 x) |
(*.f64 x #s(literal 1/16 binary64)) |
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16))) |
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) |
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16))) |
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) |
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16))) |
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) |
| 9 354× | lower-fma.f32 |
| 9 348× | lower-fma.f64 |
| 5 484× | lower-*.f32 |
| 5 478× | lower-*.f64 |
| 3 930× | lower-/.f64 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 23 | 108 |
| 0 | 34 | 108 |
| 1 | 145 | 108 |
| 2 | 966 | 103 |
| 0 | 8579 | 103 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
(*.f64 #s(literal 1/2 binary64) x) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
(sqrt.f64 x) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) |
(*.f64 x #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) |
(*.f64 #s(literal 1/2 binary64) x) |
(*.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
(*.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (sqrt.f64 x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))) |
(fabs.f64 (sqrt.f64 x)) |
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 x))) |
(sqrt.f64 x) |
(neg.f64 (neg.f64 (sqrt.f64 x))) |
(pow.f64 x #s(literal 1/2 binary64)) |
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(*.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(*.f64 (sqrt.f64 x) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64))) |
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x))) |
(*.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64)) |
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))) |
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
(+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x (*.f64 x #s(literal -1/8 binary64)))) |
(+.f64 (*.f64 x (*.f64 x #s(literal -1/8 binary64))) (*.f64 x #s(literal 1/2 binary64))) |
(-.f64 (/.f64 (*.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))) |
(fma.f64 x #s(literal 1/2 binary64) (*.f64 x (*.f64 x #s(literal -1/8 binary64)))) |
(fma.f64 x (*.f64 x #s(literal -1/8 binary64)) (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)) (*.f64 x (*.f64 x #s(literal -1/8 binary64)))) |
(fma.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/8 binary64))) (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 #s(literal 1/2 binary64) x (*.f64 x (*.f64 x #s(literal -1/8 binary64)))) |
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (*.f64 x (*.f64 x #s(literal -1/8 binary64)))) |
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 x (*.f64 x #s(literal -1/8 binary64)))) |
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (*.f64 x #s(literal -1/8 binary64))) (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 (*.f64 x #s(literal -1/8 binary64)) x (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 (*.f64 x x) #s(literal -1/8 binary64) (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 (*.f64 x (*.f64 x #s(literal -1/8 binary64))) #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x (*.f64 x #s(literal -1/8 binary64)))) |
(fma.f64 (*.f64 (*.f64 x #s(literal -1/8 binary64)) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x #s(literal 1/2 binary64))) |
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/16 binary64)))) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/512 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) (*.f64 (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/64 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/16 binary64)))) (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal -1/512 binary64)) #s(literal 1/8 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/64 binary64)) #s(literal -1/4 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (*.f64 x #s(literal 1/64 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/16 binary64)))) (*.f64 (fma.f64 x (*.f64 (*.f64 x x) #s(literal -1/512 binary64)) #s(literal 1/8 binary64)) x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) (*.f64 (fma.f64 x (*.f64 x #s(literal 1/64 binary64)) #s(literal -1/4 binary64)) x))) |
(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/512 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64))) (-.f64 (fma.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/16 binary64))))) |
(/.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)))) |
(/.f64 (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal -1/512 binary64)) #s(literal 1/8 binary64))) (fma.f64 x (*.f64 x #s(literal 1/64 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/16 binary64))))) |
(/.f64 (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal -1/512 binary64)) #s(literal 1/8 binary64))) (+.f64 #s(literal 1/4 binary64) (*.f64 x (-.f64 (*.f64 x #s(literal 1/64 binary64)) #s(literal -1/16 binary64))))) |
(/.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/64 binary64)) #s(literal -1/4 binary64))) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) |
(/.f64 (*.f64 (fma.f64 x (*.f64 (*.f64 x x) #s(literal -1/512 binary64)) #s(literal 1/8 binary64)) x) (fma.f64 x (*.f64 x #s(literal 1/64 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/16 binary64))))) |
(/.f64 (*.f64 (fma.f64 x (*.f64 x #s(literal 1/64 binary64)) #s(literal -1/4 binary64)) x) (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))) |
(/.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/512 binary64)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64)))) (neg.f64 (-.f64 (fma.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x))) (*.f64 (*.f64 x x) #s(literal 1/4 binary64))) (*.f64 (*.f64 x x) (*.f64 x #s(literal -1/16 binary64)))))) |
(/.f64 (neg.f64 (*.f64 (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))) (neg.f64 (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64))))) |
(/.f64 (neg.f64 (*.f64 x (fma.f64 x (*.f64 (*.f64 x x) #s(literal -1/512 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/64 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/16 binary64)))))) |
(/.f64 (neg.f64 (*.f64 x (fma.f64 x (*.f64 x #s(literal 1/64 binary64)) #s(literal -1/4 binary64)))) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))) |
(/.f64 (neg.f64 (*.f64 (fma.f64 x (*.f64 (*.f64 x x) #s(literal -1/512 binary64)) #s(literal 1/8 binary64)) x)) (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/64 binary64)) (+.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/16 binary64)))))) |
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(/.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/8 binary64) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) #s(literal -1/512 binary64)))) (fma.f64 (*.f64 x x) #s(literal 1/4 binary64) (-.f64 (*.f64 #s(literal 1/64 binary64) (*.f64 x (*.f64 x (*.f64 x x)))) (*.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x (*.f64 x #s(literal -1/8 binary64))))))) |
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(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/256 binary64)) #s(literal -1/64 binary64)))) (neg.f64 (fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64)))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) #s(literal 1/256 binary64)))) (neg.f64 (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64))))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/256 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/256 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/256 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) (fma.f64 (/.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/256 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/256 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/256 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64)))) (*.f64 (/.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))))) (+.f64 (/.f64 (*.f64 (*.f64 x x) #s(literal 1/256 binary64)) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64))))) |
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))) |
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4096 binary64) #s(literal -1/512 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/128 binary64) (*.f64 (*.f64 x x) #s(literal 1/256 binary64)))))) |
(*.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4096 binary64) #s(literal -1/512 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (*.f64 x (-.f64 (*.f64 x #s(literal 1/256 binary64)) #s(literal -1/128 binary64)))))) |
(*.f64 (fma.f64 x (*.f64 x #s(literal 1/256 binary64)) #s(literal -1/64 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/16 binary64) #s(literal 1/8 binary64)))) |
(*.f64 (neg.f64 (fma.f64 (*.f64 x (*.f64 x x)) #s(literal 1/4096 binary64) #s(literal -1/512 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 #s(literal 1/64 binary64) (fma.f64 x #s(literal 1/128 binary64) (*.f64 (*.f64 x x) #s(literal 1/256 binary64))))))) |
(*.f64 (neg.f64 (fma.f64 x (*.f64 x #s(literal 1/256 binary64)) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/16 binary64) #s(literal -1/8 binary64)))) |
(*.f64 (-.f64 #s(literal 1/64 binary64) (*.f64 (*.f64 x x) #s(literal 1/256 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal -1/16 binary64))))) |
Compiled 10 572 to 1 212 computations (88.5% saved)
8 alts after pruning (2 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 590 | 0 | 590 |
| Fresh | 0 | 2 | 2 |
| Picked | 0 | 5 | 5 |
| Done | 0 | 1 | 1 |
| Total | 590 | 8 | 598 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 99.7% | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| ▶ | 34.3% | (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| ✓ | 29.2% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
| ▶ | 70.8% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| ✓ | 72.0% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| ✓ | 70.6% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
| ✓ | 72.0% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
| ✓ | 30.3% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
Compiled 65 to 42 computations (35.4% saved)
| 1× | egg-herbie |
Found 8 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (+.f64 x #s(literal 1 binary64)) | |
| cost-diff | 0 | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) | |
| cost-diff | 0 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) | |
| cost-diff | 128 | (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) | |
| cost-diff | 0 | (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) | |
| cost-diff | 0 | (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) | |
| cost-diff | 0 | (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) | |
| cost-diff | 0 | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| 5 920× | lower-fma.f32 |
| 5 914× | lower-fma.f64 |
| 1 488× | lower-*.f32 |
| 1 486× | lower-*.f64 |
| 1 420× | unsub-neg |
Useful iterations: 1 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 19 | 81 |
| 0 | 30 | 81 |
| 1 | 64 | 80 |
| 2 | 148 | 80 |
| 3 | 278 | 80 |
| 4 | 479 | 80 |
| 5 | 581 | 80 |
| 6 | 604 | 80 |
| 7 | 624 | 80 |
| 8 | 654 | 80 |
| 9 | 730 | 80 |
| 10 | 1194 | 80 |
| 11 | 3456 | 80 |
| 12 | 5203 | 80 |
| 13 | 5766 | 80 |
| 14 | 5780 | 80 |
| 15 | 5780 | 80 |
| 16 | 5803 | 80 |
| 17 | 5810 | 80 |
| 18 | 5810 | 80 |
| 19 | 5814 | 80 |
| 0 | 5814 | 80 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
x |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) |
(fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) |
#s(literal -5/128 binary64) |
#s(literal 1/16 binary64) |
#s(literal -1/8 binary64) |
#s(literal 1/2 binary64) |
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
#s(literal 1 binary64) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
x |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
x |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) |
(fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) |
#s(literal -5/128 binary64) |
#s(literal 1/16 binary64) |
#s(literal -1/8 binary64) |
#s(literal 1/2 binary64) |
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
#s(literal 1 binary64) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
x |
Found 8 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (+.f64 x #s(literal 1 binary64)) | |
| accuracy | 0 | (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) | |
| accuracy | 0.00390625 | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) | |
| accuracy | 42.03535065387235 | (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) | |
| accuracy | 0.0234375 | (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) | |
| accuracy | 0.03125 | (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) | |
| accuracy | 0.0390625 | (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) | |
| accuracy | 18.658017523149265 | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| 34.0ms | 69× | 2 | valid |
| 28.0ms | 112× | 1 | valid |
| 8.0ms | 75× | 0 | valid |
Compiled 79 to 21 computations (73.4% saved)
adjust: 9.0ms (21.7% of total)ival-add: 9.0ms (21.7% of total)ival-sub: 7.0ms (16.9% of total)ival-mult: 6.0ms (14.5% of total)ival-sqrt: 4.0ms (9.6% of total)ival-div: 3.0ms (7.2% of total)ival-neg: 2.0ms (4.8% of total)exact: 1.0ms (2.4% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ()) |
#s(alt (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) (patch (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ()) |
#s(alt (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (patch (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) (patch (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #<representation binary64>) () ()) |
#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- (sqrt x) 1) (taylor inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) (taylor inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) (taylor inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (sqrt x)) (taylor -inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) (taylor -inf x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ()) |
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#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) (taylor -inf x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ()) |
#s(alt (* -1/2 x) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (* 1/8 x) 1/2)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (* x (+ 1/8 (* -1/16 x))) 1/2)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (* x (+ 1/8 (* x (- (* 5/128 x) 1/16)))) 1/2)) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (sqrt x)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (/ 1 x) (sqrt (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)) (sqrt (/ 1 x)))) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (/ 1 x)) (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* (sqrt x) (pow (sqrt -1) 2)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1 (/ (+ 1 (* 1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (* -1 (/ (+ 1 (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
24 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 3.0ms | x | @ | 0 | (- 1 (sqrt (+ x 1))) |
| 0.0ms | x | @ | inf | (* x (+ (* x (+ (* x (+ (* x -5/128) 1/16)) -1/8)) 1/2)) |
| 0.0ms | x | @ | -inf | (- 1 (sqrt (+ x 1))) |
| 0.0ms | x | @ | -inf | (* x (+ (* x (+ (* x (+ (* x -5/128) 1/16)) -1/8)) 1/2)) |
| 0.0ms | x | @ | inf | (- 1 (sqrt (+ x 1))) |
| 1× | egg-herbie |
| 11 358× | lower-fma.f64 |
| 11 358× | lower-fma.f32 |
| 3 382× | lower-*.f64 |
| 3 382× | lower-*.f32 |
| 2 956× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 253 | 1154 |
| 1 | 766 | 1018 |
| 2 | 2621 | 980 |
| 3 | 7413 | 979 |
| 0 | 8383 | 908 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(- (sqrt x) 1) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(* -1 (sqrt x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(* -5/128 (pow x 4)) |
(* (pow x 4) (- (* 1/16 (/ 1 x)) 5/128)) |
(* (pow x 4) (- (* 1/16 (/ 1 x)) (+ 5/128 (/ 1/8 (pow x 2))))) |
(* (pow x 4) (- (+ (* 1/16 (/ 1 x)) (* 1/2 (/ 1 (pow x 3)))) (+ 5/128 (/ 1/8 (pow x 2))))) |
(* -5/128 (pow x 4)) |
(* (pow x 4) (- (* 1/16 (/ 1 x)) 5/128)) |
(* (pow x 4) (- (* -1 (/ (- (* 1/8 (/ 1 x)) 1/16) x)) 5/128)) |
(* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16) x)) 5/128)) |
1/2 |
(+ 1/2 (* -1/8 x)) |
(+ 1/2 (* x (- (* 1/16 x) 1/8))) |
(+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))) |
(* -5/128 (pow x 3)) |
(* (pow x 3) (- (* 1/16 (/ 1 x)) 5/128)) |
(* (pow x 3) (- (* 1/16 (/ 1 x)) (+ 5/128 (/ 1/8 (pow x 2))))) |
(* (pow x 3) (- (+ (* 1/16 (/ 1 x)) (* 1/2 (/ 1 (pow x 3)))) (+ 5/128 (/ 1/8 (pow x 2))))) |
(* -5/128 (pow x 3)) |
(* -1 (* (pow x 3) (- 5/128 (* 1/16 (/ 1 x))))) |
(* -1 (* (pow x 3) (+ 5/128 (* -1 (/ (- 1/16 (* 1/8 (/ 1 x))) x))))) |
(* -1 (* (pow x 3) (+ 5/128 (* -1 (/ (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))) x))))) |
-1/8 |
(- (* 1/16 x) 1/8) |
(- (* x (+ 1/16 (* -5/128 x))) 1/8) |
(- (* x (+ 1/16 (* -5/128 x))) 1/8) |
(* -5/128 (pow x 2)) |
(* (pow x 2) (- (* 1/16 (/ 1 x)) 5/128)) |
(* (pow x 2) (- (* 1/16 (/ 1 x)) (+ 5/128 (/ 1/8 (pow x 2))))) |
(* (pow x 2) (- (* 1/16 (/ 1 x)) (+ 5/128 (/ 1/8 (pow x 2))))) |
(* -5/128 (pow x 2)) |
(* (pow x 2) (- (* 1/16 (/ 1 x)) 5/128)) |
(* (pow x 2) (- (* -1 (/ (- (* 1/8 (/ 1 x)) 1/16) x)) 5/128)) |
(* (pow x 2) (- (* -1 (/ (- (* 1/8 (/ 1 x)) 1/16) x)) 5/128)) |
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x))) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1/2 x) |
(* x (- (* 1/8 x) 1/2)) |
(* x (- (* x (+ 1/8 (* -1/16 x))) 1/2)) |
(* x (- (* x (+ 1/8 (* x (- (* 5/128 x) 1/16)))) 1/2)) |
(* -1 (sqrt x)) |
(* x (- (/ 1 x) (sqrt (/ 1 x)))) |
(* x (- (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)) (sqrt (/ 1 x)))) |
(* x (- (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (/ 1 x)) (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* (sqrt x) (pow (sqrt -1) 2)) |
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))) |
(* -1 (* x (- (* -1 (/ (+ 1 (* 1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (- (* -1 (/ (+ 1 (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
1 |
(+ 1 x) |
(+ 1 x) |
(+ 1 x) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
| Outputs |
|---|
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(sqrt x) |
(sqrt.f64 x) |
(- (sqrt x) 1) |
(+.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1) |
(+.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64))) |
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x))))))) |
(+.f64 (sqrt.f64 x) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (*.f64 x (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal 1 binary64))))) |
(* -1 (sqrt x)) |
(neg.f64 (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) |
(-.f64 #s(literal -1 binary64) (sqrt.f64 x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) |
(-.f64 (neg.f64 (sqrt.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) x) x)) |
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) |
(-.f64 (neg.f64 (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (*.f64 (neg.f64 (sqrt.f64 (*.f64 x (*.f64 x x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1/2 binary64)))) x) x))) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* -5/128 (pow x 4)) |
(*.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 4 binary64))) |
(* (pow x 4) (- (* 1/16 (/ 1 x)) 5/128)) |
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal -5/128 binary64) (/.f64 #s(literal 1/16 binary64) x))) |
(* (pow x 4) (- (* 1/16 (/ 1 x)) (+ 5/128 (/ 1/8 (pow x 2))))) |
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal -5/128 binary64) (/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))) |
(* (pow x 4) (- (+ (* 1/16 (/ 1 x)) (* 1/2 (/ 1 (pow x 3)))) (+ 5/128 (/ 1/8 (pow x 2))))) |
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) x) (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x)) #s(literal -5/128 binary64)))) |
(* -5/128 (pow x 4)) |
(*.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 4 binary64))) |
(* (pow x 4) (- (* 1/16 (/ 1 x)) 5/128)) |
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal -5/128 binary64) (/.f64 #s(literal 1/16 binary64) x))) |
(* (pow x 4) (- (* -1 (/ (- (* 1/8 (/ 1 x)) 1/16) x)) 5/128)) |
(*.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal -5/128 binary64) (/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))) |
(* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16) x)) 5/128)) |
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal -5/128 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/2 binary64) x)) x) #s(literal -1/16 binary64)) x))) |
1/2 |
#s(literal 1/2 binary64) |
(+ 1/2 (* -1/8 x)) |
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) |
(+ 1/2 (* x (- (* 1/16 x) 1/8))) |
(fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(* -5/128 (pow x 3)) |
(*.f64 x (*.f64 #s(literal -5/128 binary64) (*.f64 x x))) |
(* (pow x 3) (- (* 1/16 (/ 1 x)) 5/128)) |
(*.f64 x (*.f64 x (*.f64 x (+.f64 #s(literal -5/128 binary64) (/.f64 #s(literal 1/16 binary64) x))))) |
(* (pow x 3) (- (* 1/16 (/ 1 x)) (+ 5/128 (/ 1/8 (pow x 2))))) |
(*.f64 x (*.f64 x (*.f64 x (+.f64 #s(literal -5/128 binary64) (/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))))) |
(* (pow x 3) (- (+ (* 1/16 (/ 1 x)) (* 1/2 (/ 1 (pow x 3)))) (+ 5/128 (/ 1/8 (pow x 2))))) |
(*.f64 (*.f64 x (*.f64 x x)) (+.f64 (/.f64 #s(literal 1/16 binary64) x) (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 x x)) #s(literal -5/128 binary64)))) |
(* -5/128 (pow x 3)) |
(*.f64 x (*.f64 #s(literal -5/128 binary64) (*.f64 x x))) |
(* -1 (* (pow x 3) (- 5/128 (* 1/16 (/ 1 x))))) |
(*.f64 (+.f64 #s(literal 5/128 binary64) (/.f64 #s(literal -1/16 binary64) x)) (neg.f64 (*.f64 x (*.f64 x x)))) |
(* -1 (* (pow x 3) (+ 5/128 (* -1 (/ (- 1/16 (* 1/8 (/ 1 x))) x))))) |
(*.f64 x (*.f64 x (*.f64 x (+.f64 #s(literal -5/128 binary64) (/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))))) |
(* -1 (* (pow x 3) (+ 5/128 (* -1 (/ (+ 1/16 (* -1 (/ (- 1/8 (* 1/2 (/ 1 x))) x))) x))))) |
(*.f64 (*.f64 x (*.f64 x x)) (-.f64 #s(literal -5/128 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/2 binary64) x)) x) #s(literal -1/16 binary64)) x))) |
-1/8 |
#s(literal -1/8 binary64) |
(- (* 1/16 x) 1/8) |
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) |
(- (* x (+ 1/16 (* -5/128 x))) 1/8) |
(fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) |
(- (* x (+ 1/16 (* -5/128 x))) 1/8) |
(fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) |
(* -5/128 (pow x 2)) |
(*.f64 #s(literal -5/128 binary64) (*.f64 x x)) |
(* (pow x 2) (- (* 1/16 (/ 1 x)) 5/128)) |
(*.f64 x (*.f64 x (+.f64 #s(literal -5/128 binary64) (/.f64 #s(literal 1/16 binary64) x)))) |
(* (pow x 2) (- (* 1/16 (/ 1 x)) (+ 5/128 (/ 1/8 (pow x 2))))) |
(*.f64 x (*.f64 x (+.f64 #s(literal -5/128 binary64) (/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))) |
(* (pow x 2) (- (* 1/16 (/ 1 x)) (+ 5/128 (/ 1/8 (pow x 2))))) |
(*.f64 x (*.f64 x (+.f64 #s(literal -5/128 binary64) (/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))) |
(* -5/128 (pow x 2)) |
(*.f64 #s(literal -5/128 binary64) (*.f64 x x)) |
(* (pow x 2) (- (* 1/16 (/ 1 x)) 5/128)) |
(*.f64 x (*.f64 x (+.f64 #s(literal -5/128 binary64) (/.f64 #s(literal 1/16 binary64) x)))) |
(* (pow x 2) (- (* -1 (/ (- (* 1/8 (/ 1 x)) 1/16) x)) 5/128)) |
(*.f64 x (*.f64 x (+.f64 #s(literal -5/128 binary64) (/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))) |
(* (pow x 2) (- (* -1 (/ (- (* 1/8 (/ 1 x)) 1/16) x)) 5/128)) |
(*.f64 x (*.f64 x (+.f64 #s(literal -5/128 binary64) (/.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))) |
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(sqrt x) |
(sqrt.f64 x) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(-.f64 (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (neg.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) #s(literal -1 binary64))) #s(literal 1 binary64))) |
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x))) |
(* -1/2 x) |
(*.f64 x #s(literal -1/2 binary64)) |
(* x (- (* 1/8 x) 1/2)) |
(*.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))) |
(* x (- (* x (+ 1/8 (* -1/16 x))) 1/2)) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal -1/16 binary64) #s(literal 1/8 binary64)) #s(literal -1/2 binary64))) |
(* x (- (* x (+ 1/8 (* x (- (* 5/128 x) 1/16)))) 1/2)) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 5/128 binary64) #s(literal -1/16 binary64)) #s(literal 1/8 binary64)) #s(literal -1/2 binary64))) |
(* -1 (sqrt x)) |
(neg.f64 (sqrt.f64 x)) |
(* x (- (/ 1 x) (sqrt (/ 1 x)))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 x) #s(literal 1 binary64)) |
(* x (- (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)) (sqrt (/ 1 x)))) |
(fma.f64 x (-.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) |
(* x (- (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (/ 1 x)) (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* (sqrt x) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 x)) |
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 x) #s(literal 1 binary64)) |
(* -1 (* x (- (* -1 (/ (+ 1 (* 1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 x (-.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* -1 (* x (- (* -1 (/ (+ 1 (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(-.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x)) (*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 x)) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(*.f64 x (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 x (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(neg.f64 (*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 (fma.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x)) |
1 |
#s(literal 1 binary64) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
| 4 362× | lower-*.f32 |
| 4 360× | lower-*.f64 |
| 4 352× | lower-/.f64 |
| 4 352× | lower-/.f32 |
| 3 676× | lower-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 19 | 70 |
| 0 | 30 | 70 |
| 1 | 141 | 69 |
| 2 | 1063 | 69 |
| 0 | 8367 | 68 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) |
(fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) |
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(+.f64 (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (*.f64 x #s(literal 1/2 binary64))) |
(+.f64 (*.f64 x #s(literal 1/2 binary64)) (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))) |
(-.f64 (/.f64 (*.f64 (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))) (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))) (fma.f64 (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) x))) (/.f64 (*.f64 (*.f64 x x) #s(literal 1/4 binary64)) (fma.f64 (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) (*.f64 x x) (*.f64 #s(literal -1/2 binary64) x)))) |
(fma.f64 x #s(literal 1/2 binary64) (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))) |
(fma.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) (*.f64 x x) (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 #s(literal 1/2 binary64) x (*.f64 x (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))))) |
(fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) x (*.f64 x #s(literal 1/2 binary64))) |
(fma.f64 (*.f64 x x) (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) (*.f64 x #s(literal 1/2 binary64))) |
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
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(/.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) |
(/.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) |
(/.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) x)))) |
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (+.f64 (neg.f64 x) #s(literal 1 binary64))) |
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x)) |
(/.f64 (-.f64 (*.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (*.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) |
(/.f64 (*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (*.f64 (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) |
(/.f64 (*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))) |
(/.f64 (*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (*.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64))) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) |
(/.f64 (*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64))) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))) |
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x))) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) |
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) |
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x x) (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal -1 binary64)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 x #s(literal -1 binary64)))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)))) |
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (-.f64 #s(literal 1 binary64) x))) |
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (*.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64)))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) (+.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) |
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) |
(pow.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 2 binary64)) |
(pow.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) |
(*.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) |
(*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) |
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) |
(*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) x)))) |
(*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) |
(*.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) |
(*.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 x) #s(literal 1 binary64)))) |
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(*.f64 (pow.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))) |
Compiled 12 698 to 1 625 computations (87.2% saved)
8 alts after pruning (1 fresh and 7 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 469 | 1 | 470 |
| Fresh | 0 | 0 | 0 |
| Picked | 1 | 1 | 2 |
| Done | 0 | 6 | 6 |
| Total | 470 | 8 | 478 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 99.7% | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| ▶ | 34.3% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) |
| ✓ | 29.2% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
| ✓ | 70.8% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| ✓ | 72.0% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| ✓ | 70.6% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
| ✓ | 72.0% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
| ✓ | 30.3% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
Compiled 64 to 41 computations (35.9% saved)
| 1× | egg-herbie |
Found 3 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (+.f64 x #s(literal 1 binary64)) | |
| cost-diff | 0 | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) | |
| cost-diff | 0 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) |
| 8× | lower-+.f32 |
| 6× | lower-+.f64 |
| 4× | +-commutative |
| 2× | lift-sqrt.f64 |
| 2× | lift-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 5 | 15 |
| 0 | 8 | 15 |
| 1 | 14 | 15 |
| 2 | 15 | 15 |
| 0 | 15 | 15 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
x |
#s(literal 1 binary64) |
| Outputs |
|---|
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) |
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
x |
#s(literal 1 binary64) |
Found 3 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (+.f64 x #s(literal 1 binary64)) | |
| accuracy | 0.00390625 | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) | |
| accuracy | 42.03535065387235 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) |
| 92.0ms | 109× | 1 | valid |
| 8.0ms | 69× | 2 | valid |
| 3.0ms | 78× | 0 | valid |
Compiled 17 to 7 computations (58.8% saved)
ival-add: 85.0ms (89.3% of total)ival-sqrt: 4.0ms (4.2% of total)adjust: 3.0ms (3.2% of total)ival-sub: 2.0ms (2.1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| Inputs |
|---|
#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (sqrt (/ 1 x)) (/ 1 x))) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x))) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x))) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt x (taylor -inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
9 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 0.0ms | x | @ | 0 | (- (sqrt (+ x 1)) 1) |
| 0.0ms | x | @ | -inf | (- (sqrt (+ x 1)) 1) |
| 0.0ms | x | @ | inf | (- (sqrt (+ x 1)) 1) |
| 0.0ms | x | @ | -inf | (sqrt (+ x 1)) |
| 0.0ms | x | @ | inf | (sqrt (+ x 1)) |
| 1× | egg-herbie |
| 16 374× | lower-fma.f64 |
| 16 374× | lower-fma.f32 |
| 3 902× | lower-*.f64 |
| 3 902× | lower-*.f32 |
| 2 204× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 110 | 415 |
| 1 | 312 | 375 |
| 2 | 921 | 358 |
| 3 | 2747 | 347 |
| 4 | 6290 | 347 |
| 0 | 8163 | 312 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* 1/2 x) |
(* x (+ 1/2 (* -1/8 x))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(sqrt x) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x))) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
1 |
(+ 1 x) |
(+ 1 x) |
(+ 1 x) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
| Outputs |
|---|
(* 1/2 x) |
(*.f64 #s(literal 1/2 binary64) x) |
(* x (+ 1/2 (* -1/8 x))) |
(*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) |
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64))) |
(sqrt x) |
(sqrt.f64 x) |
(* x (- (sqrt (/ 1 x)) (/ 1 x))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) |
(* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (/ 1 x))) |
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) |
(* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(fma.f64 (neg.f64 x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x))) #s(literal -1 binary64)) |
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(fma.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x))) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 1/2 x)) |
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) |
(*.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
(* -1 (* (sqrt x) (pow (sqrt -1) 2))) |
(sqrt.f64 x) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(*.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) |
1 |
#s(literal 1 binary64) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
(+ 1 x) |
(+.f64 x #s(literal 1 binary64)) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
x |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
(* x (+ 1 (/ 1 x))) |
(+.f64 x #s(literal 1 binary64)) |
| 6 738× | lower-fma.f64 |
| 6 738× | lower-fma.f32 |
| 3 568× | lower-*.f64 |
| 3 568× | lower-*.f32 |
| 3 076× | lower-pow.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 5 | 13 |
| 0 | 8 | 13 |
| 1 | 39 | 13 |
| 2 | 260 | 13 |
| 3 | 3407 | 13 |
| 0 | 8287 | 12 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
| Outputs |
|---|
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) |
(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(+.f64 (/.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64)))))) |
(+.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))) |
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))) #s(literal -1 binary64))) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) |
(-.f64 (/.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64))))) |
(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(-.f64 (/.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 (+.f64 x #s(literal 2 binary64)) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 x #s(literal 2 binary64)) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))))) |
(expm1.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x))) |
(expm1.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)) #s(literal 1 binary64))) |
(expm1.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log1p.f64 x)) #s(literal 1/4 binary64))) |
(expm1.f64 (*.f64 (*.f64 (log1p.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64))) |
(expm1.f64 (-.f64 (log1p.f64 x) (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)))) |
(fma.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) |
(fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))) |
(fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64)))))) |
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64) #s(literal -1 binary64)) |
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (/.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))) |
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64)))))) |
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (pow.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (pow.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) #s(literal -1 binary64)) |
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) #s(literal -1 binary64)) |
(fma.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))) |
(fma.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64)))))) |
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))) |
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) #s(literal -1 binary64)) |
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1 binary64))) #s(literal -1 binary64)) |
(fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal -1 binary64)) |
(fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
(fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))) #s(literal -1 binary64)) |
(fma.f64 (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 2 binary64)))))) |
(fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64)) |
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)) (pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal 1/4 binary64)) #s(literal -1 binary64)) |
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/8 binary64)) (pow.f64 (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
(fma.f64 (pow.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/4 binary64)) #s(literal -1 binary64)) |
(fma.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64))) #s(literal 1/4 binary64)) #s(literal -1 binary64)) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64)) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)) |
(fma.f64 (sqrt.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
(fma.f64 (sqrt.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) #s(literal -1 binary64)) |
(fma.f64 (sqrt.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
(fma.f64 (sqrt.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) |
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) |
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) |
(fma.f64 (/.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))) |
(fma.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))) |
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(/.f64 (*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) |
(/.f64 (*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) (-.f64 (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x (*.f64 x x)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) |
(/.f64 (*.f64 (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (fma.f64 x (*.f64 x (*.f64 x x)) (fma.f64 x x #s(literal 1 binary64)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (fma.f64 x x #s(literal 1 binary64))) |
(/.f64 (exp.f64 (log1p.f64 (*.f64 x (*.f64 x x)))) (exp.f64 (log1p.f64 (-.f64 (*.f64 x x) x)))) |
(/.f64 (exp.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64)))) (exp.f64 (log.f64 (+.f64 x #s(literal -1 binary64))))) |
(/.f64 (exp.f64 (log.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))))) (exp.f64 (log.f64 (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))) |
(/.f64 (exp.f64 (log.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))))) (exp.f64 (log1p.f64 (neg.f64 x)))) |
(/.f64 (exp.f64 (log1p.f64 (*.f64 (neg.f64 x) x))) (exp.f64 (log1p.f64 (neg.f64 x)))) |
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) |
(pow.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) |
(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal 4 binary64)) |
(pow.f64 (*.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) #s(literal 1/4 binary64)) |
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64)) |
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log1p.f64 x)) |
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) (log1p.f64 x))) |
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (log1p.f64 x))) |
(*.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) |
(*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) |
(*.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) |
(*.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) |
(*.f64 (+.f64 x #s(literal 1 binary64)) (pow.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal 1 binary64))) |
(*.f64 (+.f64 x #s(literal 1 binary64)) (pow.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) |
(*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1 binary64))) |
(*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #s(literal 1 binary64))) |
(*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) #s(literal 2 binary64))) |
(*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) #s(literal 1/2 binary64))) |
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) |
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))) |
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64))) |
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal 2 binary64))) |
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) |
(*.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64))) |
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(*.f64 (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (pow.f64 (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 1 binary64))) |
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(*.f64 (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) |
(*.f64 (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64))) |
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))))) (fma.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x x)))) |
(*.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (*.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x) (+.f64 (fma.f64 x x #s(literal -1 binary64)) x))) (+.f64 (fma.f64 x x #s(literal -1 binary64)) x)) |
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) (+.f64 #s(literal 1 binary64) (fma.f64 x x x))) |
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64))) |
(*.f64 (pow.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 1 binary64)) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (*.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x) (+.f64 (fma.f64 x x #s(literal -1 binary64)) x))) #s(literal 1 binary64)) (pow.f64 (+.f64 (fma.f64 x x #s(literal -1 binary64)) x) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)) #s(literal 1 binary64))) |
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) |
(*.f64 (pow.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x x) (*.f64 (*.f64 x x) (*.f64 x x))) #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x (*.f64 (*.f64 x (*.f64 x x)) (*.f64 x x)) #s(literal 1 binary64)) (*.f64 x (*.f64 x x))))) |
(*.f64 (pow.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) #s(literal -1 binary64)))) |
(*.f64 (pow.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 (*.f64 x (*.f64 x x)) (*.f64 x (*.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x (*.f64 x x)) (fma.f64 x x #s(literal 1 binary64))))) |
(*.f64 (pow.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) |
(*.f64 (exp.f64 (log1p.f64 (*.f64 x (*.f64 x x)))) (exp.f64 (neg.f64 (log1p.f64 (-.f64 (*.f64 x x) x))))) |
(*.f64 (exp.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64)))) (exp.f64 (neg.f64 (log.f64 (+.f64 x #s(literal -1 binary64)))))) |
(*.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))) |
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))) |
(*.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) |
(*.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) |
Compiled 8 266 to 1 240 computations (85% saved)
10 alts after pruning (2 fresh and 8 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 400 | 2 | 402 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 7 | 7 |
| Total | 400 | 10 | 410 |
| Status | Accuracy | Program |
|---|---|---|
| ✓ | 99.7% | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| ✓ | 34.3% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) |
| 5.1% | (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) | |
| 4.7% | (-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64)) | |
| ✓ | 29.2% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
| ✓ | 70.8% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| ✓ | 72.0% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| ✓ | 70.6% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
| ✓ | 72.0% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
| ✓ | 30.3% | #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
Compiled 158 to 80 computations (49.4% saved)
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| Outputs |
|---|
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
2 calls:
| 29.0ms | x |
| 4.0ms | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.7% | 1 | x |
| 99.7% | 1 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 to 7 computations (36.4% saved)
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) |
2 calls:
| 4.0ms | x |
| 4.0ms | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 100.0% | 2 | x |
| 100.0% | 2 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 to 7 computations (36.4% saved)
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) |
2 calls:
| 5.0ms | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 3.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 2 | x |
| 99.9% | 2 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 to 7 computations (36.4% saved)
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)) |
2 calls:
| 3.0ms | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 3.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.7% | 2 | x |
| 99.7% | 2 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 to 7 computations (36.4% saved)
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)) |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
2 calls:
| 4.0ms | x |
| 3.0ms | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.8% | 2 | x |
| 98.8% | 2 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 to 7 computations (36.4% saved)
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
2 calls:
| 2.0ms | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 2.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.3% | 2 | x |
| 98.3% | 2 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 to 7 computations (36.4% saved)
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) |
2 calls:
| 2.0ms | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 2.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 97.8% | 2 | x |
| 97.8% | 2 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 to 7 computations (36.4% saved)
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
| Outputs |
|---|
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
2 calls:
| 3.0ms | x |
| 2.0ms | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| Accuracy | Segments | Branch |
|---|---|---|
| 72.0% | 1 | x |
| 72.0% | 1 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 to 7 computations (36.4% saved)
Total 0.0b remaining (0%)
Threshold costs 0b (0%)
| Inputs |
|---|
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
| Outputs |
|---|
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
2 calls:
| 1.0ms | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
| 1.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 4.7% | 1 | x |
| 4.7% | 1 | (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
Compiled 11 to 7 computations (36.4% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.4519624090459216e-9 | 2.341973808868717 |
Compiled 12 to 10 computations (16.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.4519624090459216e-9 | 2.341973808868717 |
Compiled 12 to 10 computations (16.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.4519624090459216e-9 | 2.341973808868717 |
Compiled 12 to 10 computations (16.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.4519624090459216e-9 | 2.341973808868717 |
Compiled 12 to 10 computations (16.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.4519624090459216e-9 | 2.341973808868717 |
Compiled 12 to 10 computations (16.7% saved)
| 1× | left-value |
| Time | Left | Right |
|---|---|---|
| 0.0ms | 1.4519624090459216e-9 | 2.341973808868717 |
Compiled 12 to 10 computations (16.7% saved)
| 1× | egg-herbie |
| 12× | +-commutative_binary64 |
| 10× | *-commutative_binary64 |
| 6× | sub-neg_binary64 |
| 2× | mul-1-neg_binary64 |
| 2× | 1-exp_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 44 | 243 |
| 1 | 57 | 243 |
| 2 | 61 | 243 |
| 3 | 66 | 243 |
| 1× | saturated |
| Inputs |
|---|
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4835703278458517/2417851639229258349412352 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4835703278458517/2417851639229258349412352 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4835703278458517/2417851639229258349412352 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4835703278458517/2417851639229258349412352 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4835703278458517/2417851639229258349412352 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4835703278458517/2417851639229258349412352 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
| Outputs |
|---|
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4835703278458517/2417851639229258349412352 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4835703278458517/2417851639229258349412352 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/128 binary64) #s(literal 1/16 binary64)) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4835703278458517/2417851639229258349412352 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4835703278458517/2417851639229258349412352 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4835703278458517/2417851639229258349412352 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4835703278458517/2417851639229258349412352 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4835703278458517/2417851639229258349412352 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) #s(literal -1 binary64)))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4835703278458517/2417851639229258349412352 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4835703278458517/2417851639229258349412352 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))) |
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 4835703278458517/2417851639229258349412352 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) |
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal 1 binary64)) |
(+.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
| 18 662× | lower-fma.f64 |
| 18 662× | lower-fma.f32 |
| 16 374× | lower-fma.f64 |
| 16 374× | lower-fma.f32 |
| 4 362× | lower-*.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 21 |
| 0 | 10 | 21 |
| 1 | 46 | 21 |
| 2 | 315 | 20 |
| 3 | 3400 | 20 |
| 0 | 8278 | 20 |
| 0 | 110 | 415 |
| 1 | 312 | 375 |
| 2 | 921 | 358 |
| 3 | 2747 | 347 |
| 4 | 6290 | 347 |
| 0 | 8163 | 312 |
| 0 | 19 | 70 |
| 0 | 30 | 70 |
| 1 | 141 | 69 |
| 2 | 1063 | 69 |
| 0 | 8367 | 68 |
| 0 | 161 | 600 |
| 1 | 485 | 505 |
| 2 | 1633 | 483 |
| 3 | 5433 | 474 |
| 0 | 8374 | 430 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
Compiled 347 to 141 computations (59.4% saved)
Compiled 338 to 78 computations (76.9% saved)
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