
Time bar (total: 6.5s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 25% | 75% | 0% | 0% | 0% | 0 |
| 0% | 0% | 25% | 75% | 0% | 0% | 0% | 1 |
| 50% | 12.5% | 12.5% | 75% | 0% | 0% | 0% | 2 |
| 75% | 18.7% | 6.2% | 75% | 0% | 0% | 0% | 3 |
| 87.5% | 21.9% | 3.1% | 75% | 0% | 0% | 0% | 4 |
| 93.8% | 23.4% | 1.6% | 75% | 0% | 0% | 0% | 5 |
| 96.9% | 24.2% | 0.8% | 75% | 0% | 0% | 0% | 6 |
| 98.4% | 24.6% | 0.4% | 75% | 0% | 0% | 0% | 7 |
| 99.2% | 24.8% | 0.2% | 75% | 0% | 0% | 0% | 8 |
| 99.6% | 24.9% | 0.1% | 75% | 0% | 0% | 0% | 9 |
| 99.8% | 24.9% | 0% | 75% | 0% | 0% | 0% | 10 |
| 99.9% | 25% | 0% | 75% | 0% | 0% | 0% | 11 |
| 100% | 25% | 0% | 75% | 0% | 0% | 0% | 12 |
Compiled 15 to 11 computations (26.7% saved)
| 1.2s | 7 995× | 1 | valid |
| 16.0ms | 261× | 0 | valid |
ival-sqrt: 251.0ms (26.5% of total)adjust: 185.0ms (19.5% of total)const: 148.0ms (15.6% of total)ival-add: 125.0ms (13.2% of total)ival-sub: 125.0ms (13.2% of total)ival-<: 49.0ms (5.2% of total)ival->: 44.0ms (4.6% of total)ival-and: 11.0ms (1.2% of total)exact: 6.0ms (0.6% of total)ival-assert: 3.0ms (0.3% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 256 | 0 | - | 0 | - | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 0 | 0 | - | 0 | - | (+.f64 x #s(literal 1 binary64)) |
| 0 | 0 | - | 0 | - | (sqrt.f64 x) |
| 0 | 0 | - | 0 | - | #s(literal 1 binary64) |
| 0 | 0 | - | 0 | - | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) | cancellation | 256 | 0 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 256 | 0 |
| - | 0 | 0 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 256 | 0 | 0 |
| - | 0 | 0 | 0 |
| number | freq |
|---|---|
| 1 | 256 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 76.0ms | 500× | 1 | valid |
| 1.0ms | 12× | 0 | valid |
Compiled 48 to 22 computations (54.2% saved)
ival-sqrt: 42.0ms (70.2% of total)adjust: 8.0ms (13.4% of total)ival-add: 5.0ms (8.4% of total)ival-sub: 4.0ms (6.7% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)exact: 0.0ms (0% of total)| 1× | egg-herbie |
| 80× | lower-fma.f64 |
| 80× | lower-fma.f32 |
| 48× | lower-*.f64 |
| 48× | lower-*.f32 |
| 46× | sub-neg |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 8 | 19 |
| 1 | 18 | 17 |
| 2 | 41 | 16 |
| 3 | 73 | 16 |
| 4 | 121 | 16 |
| 5 | 178 | 16 |
| 6 | 201 | 16 |
| 7 | 212 | 16 |
| 0 | 6 | 7 |
| 0 | 10 | 7 |
| 1 | 15 | 7 |
| 2 | 19 | 7 |
| 3 | 25 | 7 |
| 4 | 33 | 7 |
| 5 | 48 | 7 |
| 6 | 80 | 7 |
| 7 | 106 | 7 |
| 8 | 150 | 7 |
| 9 | 165 | 7 |
| 10 | 173 | 7 |
| 0 | 173 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Outputs |
|---|
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
Compiled 8 to 6 computations (25% saved)
Compiled 1 to 1 computations (0% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 6.0% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
Compiled 8 to 6 computations (25% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (sqrt.f64 x) | |
| 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))) (sqrt.f64 x)) |
| 80× | lower-fma.f64 |
| 80× | lower-fma.f32 |
| 48× | lower-*.f64 |
| 48× | lower-*.f32 |
| 36× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 18 |
| 0 | 10 | 18 |
| 1 | 15 | 18 |
| 2 | 19 | 18 |
| 3 | 25 | 18 |
| 4 | 33 | 18 |
| 5 | 48 | 18 |
| 6 | 80 | 18 |
| 7 | 106 | 18 |
| 8 | 150 | 18 |
| 9 | 165 | 18 |
| 10 | 173 | 18 |
| 0 | 173 | 18 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
x |
#s(literal 1 binary64) |
(sqrt.f64 x) |
| Outputs |
|---|
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 x #s(literal 1 binary64)) |
(+.f64 #s(literal 1 binary64) x) |
x |
#s(literal 1 binary64) |
(sqrt.f64 x) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (+.f64 x #s(literal 1 binary64)) | |
| accuracy | 0 | (sqrt.f64 (+.f64 x #s(literal 1 binary64))) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 60.13735659976297 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 23.0ms | 250× | 1 | valid |
| 0.0ms | 6× | 0 | valid |
Compiled 20 to 8 computations (60% saved)
ival-sqrt: 6.0ms (38.8% of total)adjust: 4.0ms (25.9% of total)ival-add: 3.0ms (19.4% of total)ival-sub: 2.0ms (12.9% 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))) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<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>) () ()) |
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (- 1 (sqrt x)) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* 1/2 x)) (sqrt x)) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<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 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 (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 (* 1/2 (sqrt (/ 1 x))) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<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 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 (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 (* -1/2 (sqrt (/ 1 x))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x)) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x)) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<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 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 (* -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>) () ())) ()) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 2.0ms | x | @ | -inf | ((- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ x 1) (sqrt x)) |
| 1.0ms | x | @ | inf | ((- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ x 1) (sqrt x)) |
| 1.0ms | x | @ | 0 | ((- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ x 1) (sqrt x)) |
| 1× | egg-herbie |
| 17 328× | lower-fma.f64 |
| 17 328× | lower-fma.f32 |
| 3 884× | lower-*.f64 |
| 3 884× | lower-*.f32 |
| 2 664× | lower--.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 113 | 498 |
| 1 | 299 | 446 |
| 2 | 804 | 442 |
| 3 | 2258 | 434 |
| 4 | 4617 | 434 |
| 0 | 8205 | 398 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(- 1 (sqrt x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
1 |
(+ 1 x) |
(+ 1 x) |
(+ 1 x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x) |
(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)))))))) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(* -1/2 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x)) |
(* -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))))))) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 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))) |
| Outputs |
|---|
(- 1 (sqrt x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 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 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) |
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)) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -5/128 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) x) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) |
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) 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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x) |
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)) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(* -1/2 (sqrt (/ 1 x))) |
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x)) |
(/.f64 (fma.f64 (/.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) (*.f64 (*.f64 x x) x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x)) |
(/.f64 (fma.f64 (/.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) (*.f64 (*.f64 x x) x))) (fma.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (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 -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) 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 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) 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 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) 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 (/.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) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x) |
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)) |
(* -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) |
| 5 090× | lower-fma.f64 |
| 5 090× | lower-fma.f32 |
| 3 260× | lower-*.f64 |
| 3 260× | lower-*.f32 |
| 2 676× | lower-/.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 43 | 16 |
| 2 | 290 | 16 |
| 3 | 3385 | 16 |
| 0 | 8686 | 16 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(sqrt.f64 (+.f64 x #s(literal 1 binary64))) |
(+.f64 x #s(literal 1 binary64)) |
(sqrt.f64 x) |
| Outputs |
|---|
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))) (-.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))))) (-.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))) |
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))) (fma.f64 (*.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (fma.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (-.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) |
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))) |
(*.f64 (+.f64 (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) |
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) |
(*.f64 (neg.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(*.f64 (neg.f64 (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))))) |
(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) |
(*.f64 (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))))) |
(*.f64 (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))) (*.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))))) |
(*.f64 (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))))) |
(*.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64)) |
(/.f64 (*.f64 (*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (+.f64 (+.f64 #s(literal 1 binary64) x) x)) |
(/.f64 (*.f64 (fma.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (*.f64 x x) x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) x) x)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (*.f64 x x) x)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))))) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 (sqrt.f64 x) x) (*.f64 (*.f64 x x) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))))) (fma.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (fma.f64 (fma.f64 x x x) (sqrt.f64 (fma.f64 x x x)) (*.f64 (*.f64 x x) x)))) |
(/.f64 (-.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (*.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))) (/.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))))) (*.f64 (/.f64 (*.f64 (sqrt.f64 x) x) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))) (/.f64 (*.f64 (sqrt.f64 x) x) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))) (/.f64 (*.f64 (sqrt.f64 x) x) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))))) |
(/.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x)) (-.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (-.f64 (/.f64 (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (/.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) (fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (fma.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))))) |
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(/.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 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 x x #s(literal 1 binary64))) (-.f64 x #s(literal 1 binary64)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 x x) x #s(literal -1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (*.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))) (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))) |
(/.f64 (*.f64 (sqrt.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (*.f64 (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))) |
(/.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 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (*.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))) |
(/.f64 (fma.f64 (*.f64 x x) (*.f64 x x) #s(literal -1 binary64)) (*.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))) |
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) #s(literal -1 binary64)) (*.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) (*.f64 x x) (fma.f64 x x #s(literal 1 binary64))))) |
(/.f64 (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) #s(literal -1 binary64)) (*.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (fma.f64 (*.f64 x x) x #s(literal -1 binary64)))) |
(/.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 x x) x)) (*.f64 (*.f64 x x) x) #s(literal 1 binary64)) (*.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (fma.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))))) |
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) x)) |
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1 binary64)) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (*.f64 (-.f64 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)) (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))) |
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 x #s(literal 1 binary64))) |
(/.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)) (*.f64 (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))) |
(/.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) |
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 #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 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) |
(neg.f64 (/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (-.f64 x #s(literal 1 binary64)))) |
(neg.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) |
(neg.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x))) |
(neg.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))) |
(fma.f64 (sqrt.f64 (*.f64 (sqrt.f64 x) x)) (sqrt.f64 (sqrt.f64 x)) #s(literal 1 binary64)) |
(fma.f64 (/.f64 (*.f64 x x) (fma.f64 (*.f64 x x) x #s(literal -1 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (/.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) x) (neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (*.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64)) (sqrt.f64 x) #s(literal 1 binary64)) |
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (*.f64 (sqrt.f64 x) x)) #s(literal 1 binary64)) |
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 x)) #s(literal 1 binary64)) |
(fma.f64 (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) #s(literal 1 binary64)) |
(fma.f64 #s(literal -1 binary64) (neg.f64 x) #s(literal 1 binary64)) |
(fma.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64)) |
(fma.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)) (neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))) |
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) #s(literal 1 binary64)) |
(fma.f64 #s(literal 1 binary64) x #s(literal 1 binary64)) |
(fma.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))) |
(fma.f64 x #s(literal 1 binary64) #s(literal 1 binary64)) |
(sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) |
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x))) |
(-.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))) |
(fabs.f64 (+.f64 #s(literal 1 binary64) x)) |
(hypot.f64 (neg.f64 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(hypot.f64 (sqrt.f64 (fma.f64 x x x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(hypot.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (fma.f64 x x x)))) |
(hypot.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (fma.f64 x x x))) |
(+.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))) |
(+.f64 #s(literal 1 binary64) x) |
(+.f64 x #s(literal 1 binary64)) |
(exp.f64 (*.f64 (neg.f64 (log1p.f64 x)) #s(literal -1 binary64))) |
(exp.f64 (log1p.f64 x)) |
(*.f64 (sqrt.f64 (*.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64))) (sqrt.f64 (sqrt.f64 x))) |
(*.f64 (sqrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x)))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 x))) |
(*.f64 (sqrt.f64 (neg.f64 (sqrt.f64 x))) (sqrt.f64 (neg.f64 (sqrt.f64 x)))) |
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 x)))) |
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))) |
(*.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 x)) |
(pow.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/8 binary64)) |
(pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64)) |
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(pow.f64 x #s(literal 1/2 binary64)) |
(sqrt.f64 x) |
(fabs.f64 (sqrt.f64 x)) |
(exp.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 x)) #s(literal 2 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/4 binary64))) |
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 1 binary64))) |
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64))) |
Compiled 8 826 to 1 369 computations (84.5% saved)
9 alts after pruning (8 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 395 | 8 | 403 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 395 | 9 | 404 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 7.2% | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
| ✓ | 6.0% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 4.3% | (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) | |
| ▶ | 3.8% | (-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) |
| ▶ | 1.6% | (-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
| ▶ | 5.1% | (*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))) |
| ▶ | 99.3% | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)) |
| 99.0% | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) | |
| 98.4% | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
Compiled 234 to 140 computations (40.2% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (+.f64 #s(literal 1 binary64) x) | |
| cost-diff | 0 | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) | |
| cost-diff | 320 | (*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))) | |
| cost-diff | 384 | (-.f64 (+.f64 #s(literal 1 binary64) x) x) | |
| cost-diff | 0 | (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) | |
| cost-diff | 0 | (+.f64 #s(literal 1 binary64) x) | |
| cost-diff | 0 | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) | |
| cost-diff | 384 | (-.f64 (+.f64 #s(literal 1 binary64) x) x) | |
| cost-diff | 0 | (sqrt.f64 x) | |
| cost-diff | 0 | #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) | |
| cost-diff | 0 | (-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) | |
| cost-diff | 0 | (sqrt.f64 x) | |
| cost-diff | 0 | #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) | |
| cost-diff | 0 | (-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) | |
| cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) | |
| cost-diff | 0 | (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) | |
| cost-diff | 0 | (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x) | |
| cost-diff | 0 | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)) |
| 29 824× | lower-fma.f32 |
| 29 816× | lower-fma.f64 |
| 3 178× | lower-+.f32 |
| 3 172× | lower-+.f64 |
| 3 090× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 38 | 307 |
| 0 | 67 | 299 |
| 1 | 120 | 275 |
| 2 | 227 | 273 |
| 3 | 445 | 273 |
| 4 | 1435 | 273 |
| 5 | 5201 | 273 |
| 0 | 8271 | 270 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) |
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) |
#s(literal 1 binary64) |
(*.f64 (*.f64 x x) x) |
(*.f64 x x) |
x |
#s(literal 1/16 binary64) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
#s(literal -1/8 binary64) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
#s(literal 1/2 binary64) |
(sqrt.f64 x) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(sqrt.f64 x) |
x |
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) |
#s(approx (sqrt (+ x 1)) (sqrt.f64 x)) |
(sqrt.f64 x) |
x |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(-.f64 (+.f64 #s(literal 1 binary64) x) x) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 x) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) |
(-.f64 (+.f64 #s(literal 1 binary64) x) x) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 x) |
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))) |
(+.f64 (+.f64 #s(literal 1 binary64) x) x) |
(sqrt.f64 (fma.f64 x x x)) |
(fma.f64 x x x) |
| Outputs |
|---|
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) x)) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x) |
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) x) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) |
(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) |
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) |
#s(literal 1 binary64) |
(*.f64 (*.f64 x x) x) |
(*.f64 x x) |
x |
#s(literal 1/16 binary64) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
#s(literal -1/8 binary64) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
(sqrt.f64 x) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(sqrt.f64 x) |
x |
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) |
#s(approx (sqrt (+ x 1)) (sqrt.f64 x)) |
(sqrt.f64 x) |
x |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) |
(-.f64 (+.f64 #s(literal 1 binary64) x) x) |
#s(literal 1 binary64) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(sqrt.f64 x) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))) |
(/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x x))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x))) |
(-.f64 (+.f64 #s(literal 1 binary64) x) x) |
#s(literal 1 binary64) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))) |
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)) |
(sqrt.f64 x) |
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))) |
(-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x x))) |
(+.f64 (+.f64 #s(literal 1 binary64) x) x) |
(fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) |
(sqrt.f64 (fma.f64 x x x)) |
(fma.f64 x x x) |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 1.2972886601722866 | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) | |
| accuracy | 20.120523304212785 | (*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))) | |
| accuracy | 29.772995479991767 | (sqrt.f64 (fma.f64 x x x)) | |
| accuracy | 59.81895248494932 | (-.f64 (+.f64 #s(literal 1 binary64) x) x) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 0.01171875 | (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) | |
| accuracy | 0.265625 | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) | |
| accuracy | 59.81895248494932 | (-.f64 (+.f64 #s(literal 1 binary64) x) x) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 0.9736115000708662 | #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) | |
| accuracy | 60.13735659976297 | (-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 59.64018466011672 | #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) | |
| accuracy | 60.13735659976297 | (-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) | |
| accuracy | 0.19790143039475586 | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)) | |
| accuracy | 0.23828125 | (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x) | |
| accuracy | 0.6554880426181869 | (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) | |
| accuracy | 19.283908611253587 | (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) |
| 120.0ms | 249× | 1 | valid |
| 2.0ms | 7× | 0 | valid |
Compiled 288 to 37 computations (87.2% saved)
adjust: 20.0ms (22.1% of total)ival-sqrt: 18.0ms (19.9% of total)ival-mult: 17.0ms (18.8% of total)ival-add: 16.0ms (17.7% of total)ival-div: 13.0ms (14.4% of total)ival-sub: 6.0ms (6.6% 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 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)) (patch #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)) #<representation binary64>) () ()) |
#s(alt (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x) (patch (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x) #<representation binary64>) () ()) |
#s(alt (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) (patch (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) (patch (-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) #<representation binary64>) () ()) |
#s(alt #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ()) |
#s(alt (-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) (patch (-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ()) |
#s(alt #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (patch #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) #<representation binary64>) () ()) |
#s(alt (-.f64 (+.f64 #s(literal 1 binary64) x) x) (patch (-.f64 (+.f64 #s(literal 1 binary64) x) x) #<representation binary64>) () ()) |
#s(alt (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ()) |
#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ()) |
#s(alt (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ()) |
#s(alt (*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))) (patch (*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))) #<representation binary64>) () ()) |
#s(alt (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) (patch (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (- 1 (sqrt x)) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)) (patch #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* 1/2 x)) (sqrt x)) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)) (patch #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)) (patch #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)) (patch #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/16 (sqrt (/ 1 (pow x 5)))) (taylor 0 x) (#s(alt (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x) (patch (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3)) (taylor 0 x) (#s(alt (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x) (patch (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3)) (taylor 0 x) (#s(alt (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x) (patch (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3)) (taylor 0 x) (#s(alt (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x) (patch (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x) #<representation binary64>) () ())) ()) |
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3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 6.0ms | x | @ | -inf | ((- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 (* (* x x) x))) 1/16) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x)))) x) (+ (* (sqrt (/ 1 (* (* x x) x))) 1/16) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x)))) (sqrt (/ 1 (* (* x x) x))) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (- (+ 1 x) x) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (+ 1 x) (+ (sqrt x) (sqrt (+ 1 x))) (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (/ 1 (* (* x x) x)) (sqrt (+ (* x x) x))) |
| 4.0ms | x | @ | inf | ((- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 (* (* x x) x))) 1/16) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x)))) x) (+ (* (sqrt (/ 1 (* (* x x) x))) 1/16) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x)))) (sqrt (/ 1 (* (* x x) x))) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (- (+ 1 x) x) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (+ 1 x) (+ (sqrt x) (sqrt (+ 1 x))) (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (/ 1 (* (* x x) x)) (sqrt (+ (* x x) x))) |
| 4.0ms | x | @ | 0 | ((- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 (* (* x x) x))) 1/16) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x)))) x) (+ (* (sqrt (/ 1 (* (* x x) x))) 1/16) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x)))) (sqrt (/ 1 (* (* x x) x))) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (- (+ 1 x) x) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (+ 1 x) (+ (sqrt x) (sqrt (+ 1 x))) (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (/ 1 (* (* x x) x)) (sqrt (+ (* x x) x))) |
| 1× | egg-herbie |
| 9 310× | lower-fma.f64 |
| 9 310× | lower-fma.f32 |
| 5 068× | lower-*.f64 |
| 5 068× | lower-*.f32 |
| 2 750× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 465 | 3478 |
| 1 | 1442 | 2884 |
| 2 | 5004 | 2830 |
| 0 | 8208 | 2626 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(- 1 (sqrt x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
(* 1/16 (sqrt (/ 1 (pow x 5)))) |
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3)) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 2)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2)) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(- 1 (sqrt x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(- 1 (sqrt x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
1 |
1 |
1 |
1 |
(/ 1 (+ 1 (sqrt x))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
1 |
(+ 1 x) |
(+ 1 x) |
(+ 1 x) |
(+ 1 (sqrt x)) |
(+ 1 (+ (sqrt x) (* 1/2 x))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x))))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))) |
(- 1 (sqrt x)) |
(- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x)) |
(- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x)) |
(- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x)) |
1 |
(+ 1 (* -1 (* x (+ 3/2 (sqrt x))))) |
(+ 1 (* x (- (* -1 (* x (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x))))) |
(+ 1 (* x (- (* x (- (* x (- 1/16 (+ (* -1 (* (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))) (+ 3/2 (sqrt x)))) (* -3/8 (+ 3/2 (sqrt x)))))) (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x))))) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(sqrt x) |
(+ (sqrt x) (* 1/2 (sqrt (pow x 3)))) |
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x)))))))) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x) |
(* 1/2 (sqrt (/ 1 x))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) |
(* 1/2 (sqrt x)) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(sqrt (/ 1 (pow x 3))) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x) |
(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)))))))) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x) |
(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 |
1 |
1 |
1 |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x) |
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* 2 (sqrt x)) |
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x) |
(/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) x) |
(* 1/2 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -3/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2)) |
(/ (- (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 3/8 (sqrt (/ 1 x)))) (pow x 2)) |
(/ (- (+ (* -1 (/ (+ (* -9/32 (sqrt (pow x 5))) (* 1/8 (* (sqrt (pow x 3)) (- 1 (* 9/4 x))))) (pow x 4))) (* 1/2 (sqrt x))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3)))))) (pow x 2)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
x |
(* x (+ 1 (* 1/2 (/ 1 x)))) |
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) |
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) |
(* -1/2 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x)) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) |
(* -1/2 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x)) |
(* -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 (* (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 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x)) |
(* -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 |
1 |
1 |
(* -1/2 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) |
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x)) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (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)))) (* 2 (* (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)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
(/ 3 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(/ (+ (* 3/2 (/ 1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x) |
(* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (* 1/8 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* 3/2 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) |
(* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/16 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* 9/4 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) (* 1/8 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* 3/2 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) |
(/ 1 (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(/ (+ (* -3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow x 2)) |
(/ (- (+ (* -3/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2)) |
(/ (- (+ (* -1 (/ (- (* -1 (/ (- (* -9/4 (/ x (* (pow (sqrt -1) 2) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 1/2 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* -3/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 3))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(/ 1 (pow x 3)) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) |
| Outputs |
|---|
(- 1 (sqrt x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(* 1/16 (sqrt (/ 1 (pow x 5)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 binary64)) |
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3)) |
(/.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (*.f64 (*.f64 x x) x)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3)) |
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (*.f64 (*.f64 x x) x)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3)) |
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (*.f64 (*.f64 x x) x)) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64)) |
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 2)) |
(/.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (*.f64 x x)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2)) |
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (*.f64 x x)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2)) |
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1 |
#s(literal 1 binary64) |
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(* 1/2 (sqrt (/ 1 x))) |
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(* 1/2 (sqrt x)) |
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(sqrt (/ 1 (pow x 3))) |
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(* 1/2 (sqrt (/ 1 x))) |
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(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
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(sqrt x) |
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(sqrt x) |
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(/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (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) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x)) |
(/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) #s(literal -5/128 binary64) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (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) x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) (neg.f64 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 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/2 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)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/2 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 (neg.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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
(* -1/2 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x) |
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) |
(/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (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) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x) |
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x)) |
(/.f64 (fma.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (neg.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (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) x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) (neg.f64 x)) |
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)) |
(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 x)) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (neg.f64 x) (fma.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)))) |
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64))))) |
(* -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)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
(*.f64 (neg.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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)))))) |
(/ 3 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(/.f64 #s(literal -3 binary64) #s(literal 0 binary64)) |
(/ (+ (* 3/2 (/ 1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x) |
(/.f64 (-.f64 (/.f64 #s(literal 3/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) x) |
(* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (* 1/8 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* 3/2 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) |
(-.f64 (-.f64 (/.f64 #s(literal 3/2 binary64) #s(literal 0 binary64)) (fma.f64 #s(literal 9/2 binary64) (/.f64 (sqrt.f64 x) #s(literal 0 binary64)) (/.f64 #s(literal 1/8 binary64) #s(literal 0 binary64)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) |
(* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/16 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* 9/4 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) (* 1/8 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* 3/2 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) |
(+.f64 (neg.f64 (/.f64 (neg.f64 (-.f64 (/.f64 #s(literal 3/2 binary64) #s(literal 0 binary64)) (/.f64 (fma.f64 #s(literal 9/2 binary64) (/.f64 (sqrt.f64 x) #s(literal 0 binary64)) (-.f64 (/.f64 #s(literal 1/8 binary64) #s(literal 0 binary64)) (/.f64 (fma.f64 #s(literal -27/4 binary64) (/.f64 (sqrt.f64 x) #s(literal 0 binary64)) (/.f64 #s(literal 1/16 binary64) #s(literal 0 binary64))) x))) x))) (*.f64 x x))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) |
(/ 1 (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) |
(/ (+ (* -3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow x 2)) |
(fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 0 binary64)) #s(literal -3/2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64))) |
(/ (- (+ (* -3/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2)) |
(/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 0 binary64)) #s(literal -3/2 binary64) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 0 binary64)) #s(literal -3/2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))) (*.f64 x x)) |
(/ (- (+ (* -1 (/ (- (* -1 (/ (- (* -9/4 (/ x (* (pow (sqrt -1) 2) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 1/2 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* -3/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 3))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2)) |
(fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 0 binary64)) #s(literal -3/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) (/.f64 (fma.f64 (/.f64 #s(literal 3/2 binary64) #s(literal 0 binary64)) (sqrt.f64 x) (fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal -9/4 binary64) x #s(literal 1 binary64)) #s(literal 0 binary64))) (sqrt.f64 x) (/.f64 (*.f64 #s(literal 9/4 binary64) x) #s(literal 0 binary64)))) (*.f64 x x)))) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) |
(/ 1 (pow x 3)) |
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) |
(+.f64 (neg.f64 x) #s(literal -1/2 binary64)) |
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) |
(fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) x (neg.f64 x)) |
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) |
(fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x)) x) x (neg.f64 x)) |
| 5 776× | lower-*.f32 |
| 5 766× | lower-*.f64 |
| 3 256× | lower-/.f32 |
| 3 246× | lower-/.f64 |
| 3 070× | lower-fma.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 38 | 202 |
| 0 | 67 | 175 |
| 1 | 302 | 139 |
| 2 | 2660 | 135 |
| 0 | 8680 | 131 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
#s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) |
(sqrt.f64 x) |
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) |
#s(approx (sqrt (+ x 1)) (sqrt.f64 x)) |
(-.f64 (+.f64 #s(literal 1 binary64) x) x) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(+.f64 #s(literal 1 binary64) x) |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) |
(sqrt.f64 (fma.f64 x x x)) |
| Outputs |
|---|
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) |
(*.f64 (pow.f64 (/.f64 x (-.f64 (*.f64 #s(literal 1/256 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))) |
(*.f64 (pow.f64 (/.f64 x (fma.f64 (*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/4096 binary64) (*.f64 (*.f64 (sqrt.f64 x) x) (*.f64 (*.f64 x x) x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/256 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) (*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (-.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x))))))) |
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (neg.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) (/.f64 #s(literal 1 binary64) (neg.f64 x))) |
(*.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) |
(*.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) |
(pow.f64 (/.f64 (/.f64 x (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 x (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) #s(literal -1 binary64)) |
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(/.f64 (*.f64 (fma.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x) (*.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))) #s(literal 1 binary64)) (*.f64 (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)) (fma.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x) (*.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)) #s(literal 1 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)) #s(literal 1 binary64)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x))))) |
(/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x))) |
(neg.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)))) |
(neg.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x))))) |
(fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (*.f64 (*.f64 x x) x) (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (-.f64 (*.f64 (sqrt.f64 x) x) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))) (neg.f64 (/.f64 x (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x))))) |
(fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 (*.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (*.f64 (*.f64 (sqrt.f64 x) x) (*.f64 (*.f64 x x) x)))) (fma.f64 (*.f64 x x) x (fma.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x x))) (fma.f64 x x x)))) (neg.f64 (/.f64 x (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x))))) |
(fma.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x))) (neg.f64 (/.f64 x (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x))))) |
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x))) (/.f64 x (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)))) |
(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x))) (neg.f64 (/.f64 x (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x))))) |
(exp.f64 (*.f64 (log.f64 (*.f64 (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)) #s(literal 1 binary64))) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (log.f64 (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x))) #s(literal -1 binary64))) |
(*.f64 (pow.f64 (*.f64 (*.f64 (sqrt.f64 x) x) x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) (*.f64 x x)))) |
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 (*.f64 (*.f64 (sqrt.f64 x) x) x) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) x))) |
(*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) |
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)) |
(pow.f64 (neg.f64 (*.f64 (neg.f64 x) (*.f64 x x))) #s(literal -1 binary64)) |
(pow.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x)) #s(literal -1/2 binary64)) |
(pow.f64 (*.f64 (sqrt.f64 x) x) #s(literal -2 binary64)) |
(pow.f64 (sqrt.f64 x) #s(literal -6 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) x)) #s(literal 2 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) #s(literal 1 binary64)) |
(pow.f64 (*.f64 (*.f64 x x) x) #s(literal -1 binary64)) |
(pow.f64 (*.f64 x x) #s(literal -3/2 binary64)) |
(pow.f64 x #s(literal -3 binary64)) |
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 x)) |
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x) |
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) (*.f64 x x))) |
(/.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 x x)) |
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (neg.f64 x) (*.f64 x x)))) |
(/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) |
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 (*.f64 x x) x))) |
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)) (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)))) |
(exp.f64 (fma.f64 (*.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64) (*.f64 (*.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64)))) |
(exp.f64 (*.f64 (log.f64 x) #s(literal -3 binary64))) |
(exp.f64 (*.f64 #s(literal -3 binary64) (log.f64 x))) |
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (sqrt.f64 (fma.f64 x x x)))) |
(*.f64 (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) (fma.f64 x x (neg.f64 x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (neg.f64 x))))) |
(*.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) (fma.f64 x x (neg.f64 x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (neg.f64 x))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) (*.f64 (*.f64 x x) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) x (*.f64 x (-.f64 x (*.f64 x x))))))) |
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) (*.f64 (*.f64 x x) x))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) x (*.f64 x (-.f64 x (*.f64 x x))))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) |
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(pow.f64 (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (fma.f64 x x x) (fma.f64 x x x)) #s(literal 1/4 binary64)) |
(pow.f64 (sqrt.f64 (fma.f64 x x x)) #s(literal 1 binary64)) |
(pow.f64 (fma.f64 x x x) #s(literal 1/2 binary64)) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)) x)) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)) x)) (sqrt.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))) |
(/.f64 (sqrt.f64 (-.f64 (*.f64 x x) (*.f64 (*.f64 (*.f64 x x) x) x))) (sqrt.f64 (-.f64 x (*.f64 x x)))) |
(/.f64 (sqrt.f64 (neg.f64 (*.f64 (fma.f64 x x x) (fma.f64 x x (neg.f64 x))))) (sqrt.f64 (neg.f64 (fma.f64 x x (neg.f64 x))))) |
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) (*.f64 (*.f64 x x) x)))) (sqrt.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (*.f64 x (-.f64 x (*.f64 x x))))))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x x) (fma.f64 x x (neg.f64 x)))) (sqrt.f64 (fma.f64 x x (neg.f64 x)))) |
(/.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) (*.f64 (*.f64 x x) x))) (sqrt.f64 (fma.f64 x x (-.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 (*.f64 x x) x))))) |
(/.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) (*.f64 (*.f64 x x) x))) (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (*.f64 x (-.f64 x (*.f64 x x)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 x x (neg.f64 x)) (*.f64 (fma.f64 x x x) (fma.f64 x x (neg.f64 x)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (*.f64 x (-.f64 x (*.f64 x x)))) (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) (*.f64 (*.f64 x x) x))))) |
(sqrt.f64 (fma.f64 x x x)) |
(fabs.f64 (sqrt.f64 (fma.f64 x x x))) |
(hypot.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 x)) |
(hypot.f64 (neg.f64 (sqrt.f64 x)) x) |
(hypot.f64 (neg.f64 x) (neg.f64 (sqrt.f64 x))) |
(hypot.f64 (neg.f64 x) (sqrt.f64 x)) |
(hypot.f64 (sqrt.f64 x) (neg.f64 x)) |
(hypot.f64 (sqrt.f64 x) x) |
(hypot.f64 x (neg.f64 (sqrt.f64 x))) |
(hypot.f64 x (sqrt.f64 x)) |
(exp.f64 (*.f64 (log.f64 (fma.f64 x x x)) #s(literal 1/2 binary64))) |
Compiled 42 707 to 3 426 computations (92% saved)
13 alts after pruning (10 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 1 378 | 9 | 1 387 |
| Fresh | 2 | 1 | 3 |
| Picked | 3 | 2 | 5 |
| Done | 0 | 1 | 1 |
| Total | 1 383 | 13 | 1 396 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 7.2% | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (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)))) (sqrt.f64 x))) |
| 41.0% | (/.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)))) | |
| ▶ | 99.6% | (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
| ✓ | 6.0% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 4.3% | (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) | |
| ✓ | 3.8% | (-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) |
| ✓ | 1.6% | (-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
| 99.0% | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) | |
| ▶ | 18.8% | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
| ▶ | 98.4% | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
| 99.3% | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) | |
| 98.2% | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 (* (* x x) x))) 1/16) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) | |
| ▶ | 0.9% | #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) |
Compiled 313 to 183 computations (41.5% saved)
| 1× | egg-herbie |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (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)))) (sqrt.f64 x)) | |
| cost-diff | 0 | (+.f64 #s(literal 1 binary64) x) | |
| cost-diff | 0 | (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (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)))) (sqrt.f64 x))) | |
| cost-diff | 384 | (-.f64 (+.f64 #s(literal 1 binary64) x) x) | |
| cost-diff | 0 | (/.f64 #s(literal 1 binary64) x) | |
| cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) | |
| cost-diff | 0 | (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) | |
| cost-diff | 0 | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #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 | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) | |
| cost-diff | 0 | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) | |
| cost-diff | 0 | (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)) | |
| cost-diff | 0 | #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) | |
| cost-diff | 0 | (sqrt.f64 x) | |
| cost-diff | 0 | (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) | |
| cost-diff | 0 | #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) | |
| cost-diff | 0 | (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
| 27 336× | lower-fma.f32 |
| 27 332× | lower-fma.f64 |
| 3 230× | lower-+.f32 |
| 3 224× | lower-+.f64 |
| 2 844× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 45 | 221 |
| 0 | 69 | 217 |
| 1 | 116 | 193 |
| 2 | 216 | 191 |
| 3 | 449 | 191 |
| 4 | 1471 | 191 |
| 5 | 5344 | 191 |
| 0 | 8067 | 188 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
#s(approx (- (+ 1 x) x) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 x) |
x |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(+.f64 #s(literal 1 binary64) x) |
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) |
(/.f64 #s(literal -3 binary64) #s(literal 0 binary64)) |
#s(literal -3 binary64) |
#s(literal 0 binary64) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) |
#s(literal 1 binary64) |
(+.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(sqrt.f64 x) |
x |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
#s(literal 1/2 binary64) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (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)))) (sqrt.f64 x))) |
(-.f64 (+.f64 #s(literal 1 binary64) x) x) |
(+.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
(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)))) (sqrt.f64 x)) |
(sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) |
(fma.f64 x x #s(literal -1 binary64)) |
#s(literal -1 binary64) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))) |
(-.f64 x #s(literal 1 binary64)) |
(sqrt.f64 x) |
| Outputs |
|---|
(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x))) |
#s(approx (- (+ 1 x) x) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(+.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (sqrt.f64 x)) |
(sqrt.f64 x) |
x |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(sqrt.f64 (-.f64 x #s(literal -1 binary64))) |
(+.f64 #s(literal 1 binary64) x) |
(-.f64 x #s(literal -1 binary64)) |
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) |
(/.f64 #s(literal -3 binary64) #s(literal 0 binary64)) |
#s(literal -3 binary64) |
#s(literal 0 binary64) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) |
#s(literal 1 binary64) |
(+.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
(sqrt.f64 x) |
x |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
#s(literal 1/2 binary64) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (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)))) (sqrt.f64 x))) |
(/.f64 #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))) (sqrt.f64 x))) |
(-.f64 (+.f64 #s(literal 1 binary64) x) x) |
#s(literal 1 binary64) |
(+.f64 #s(literal 1 binary64) x) |
(-.f64 x #s(literal -1 binary64)) |
#s(literal 1 binary64) |
x |
(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)))) (sqrt.f64 x)) |
(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))) (sqrt.f64 x)) |
(sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) |
(fma.f64 x x #s(literal -1 binary64)) |
#s(literal -1 binary64) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))) |
(-.f64 x #s(literal 1 binary64)) |
(sqrt.f64 x) |
Found 18 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (+.f64 #s(literal 1 binary64) x) | |
| accuracy | 0 | (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) | |
| accuracy | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 0 | (/.f64 #s(literal 1 binary64) x) | |
| accuracy | 0 | (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) | |
| accuracy | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) | |
| accuracy | 0 | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) | |
| accuracy | 0 | (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) | |
| accuracy | 0 | (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 0 | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) | |
| accuracy | 0 | (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)) | |
| accuracy | 0 | #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) | |
| accuracy | 0 | (+.f64 #s(literal 1 binary64) x) | |
| accuracy | 0 | (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 0 | #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) |
| 56.0ms | 256× | 0 | invalid |
Compiled 207 to 38 computations (81.6% saved)
ival-div: 9.0ms (23.6% of total)ival-add: 9.0ms (23.6% of total)ival-sqrt: 9.0ms (23.6% of total)ival-mult: 8.0ms (21% of total)ival-sub: 3.0ms (7.9% 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 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ()) |
#s(alt #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (patch #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ()) |
#s(alt #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) (patch #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)) (patch (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) (patch #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (+.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 (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (patch #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #<representation binary64>) () ()) |
#s(alt (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (patch (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ()) |
#s(alt (-.f64 (+.f64 #s(literal 1 binary64) x) x) (patch (-.f64 (+.f64 #s(literal 1 binary64) x) x) #<representation binary64>) () ()) |
#s(alt (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (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)))) (sqrt.f64 x))) (patch (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (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)))) (sqrt.f64 x))) #<representation binary64>) () ()) |
#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ()) |
#s(alt (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)))) (sqrt.f64 x)) (patch (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)))) (sqrt.f64 x)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (/ 1 (+ 1 (sqrt x))) (taylor 0 x) (#s(alt (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) (taylor 0 x) (#s(alt (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) (taylor 0 x) (#s(alt (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) (taylor 0 x) (#s(alt (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (patch #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (patch #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (patch #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (patch #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (sqrt x)) (taylor 0 x) (#s(alt (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (+ (sqrt x) (* 1/2 x))) (taylor 0 x) (#s(alt (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x))))) (taylor 0 x) (#s(alt (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ()) |
#s(alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))) (taylor 0 x) (#s(alt (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) 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 (- 1 (sqrt x)) (taylor 0 x) (#s(alt #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) (patch #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x)) (taylor 0 x) (#s(alt #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) (patch #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x)) (taylor 0 x) (#s(alt #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) (patch #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x)) (taylor 0 x) (#s(alt #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) (patch #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (/ 1 (+ 1 (sqrt x))) (taylor 0 x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) (patch #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) (taylor 0 x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) (patch #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) (taylor 0 x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) (patch #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) (taylor 0 x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) (patch #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
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#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt (* -2 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (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)))) (sqrt.f64 x)) (patch (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)))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (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)))) (sqrt.f64 x)) (patch (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)))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (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)))) (sqrt.f64 x)) (patch (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)))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) (taylor -inf x) (#s(alt (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)))) (sqrt.f64 x)) (patch (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)))) (sqrt.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<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 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<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 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<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 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ()) |
#s(alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ 1 (* -1/4 x)))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt (* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ()) |
3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 6.0ms | x | @ | -inf | ((/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x))) (sqrt x) (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/ -3 0) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/ 1 (+ (sqrt x) 1)) (+ (sqrt x) 1) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (* (sqrt (/ 1 x)) 1/2) (sqrt (/ 1 x)) (/ 1 x) (- (+ 1 x) x) (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (+ 1 x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x)) (sqrt (+ 1 x)) (sqrt (/ 1 (- x 1))) (sqrt (+ (* x x) -1))) |
| 3.0ms | x | @ | 0 | ((/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x))) (sqrt x) (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/ -3 0) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/ 1 (+ (sqrt x) 1)) (+ (sqrt x) 1) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (* (sqrt (/ 1 x)) 1/2) (sqrt (/ 1 x)) (/ 1 x) (- (+ 1 x) x) (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (+ 1 x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x)) (sqrt (+ 1 x)) (sqrt (/ 1 (- x 1))) (sqrt (+ (* x x) -1))) |
| 2.0ms | x | @ | inf | ((/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x))) (sqrt x) (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/ -3 0) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/ 1 (+ (sqrt x) 1)) (+ (sqrt x) 1) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (* (sqrt (/ 1 x)) 1/2) (sqrt (/ 1 x)) (/ 1 x) (- (+ 1 x) x) (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (+ 1 x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x)) (sqrt (+ 1 x)) (sqrt (/ 1 (- x 1))) (sqrt (+ (* x x) -1))) |
| 1× | egg-herbie |
| 11 018× | lower-fma.f64 |
| 11 018× | lower-fma.f32 |
| 4 590× | lower-*.f64 |
| 4 590× | lower-*.f32 |
| 3 690× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 452 | 3436 |
| 1 | 1394 | 2954 |
| 2 | 4799 | 2929 |
| 0 | 8633 | 2754 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(/ 1 (+ 1 (sqrt x))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
1 |
1 |
1 |
1 |
(+ 1 (sqrt x)) |
(+ 1 (+ (sqrt x) (* 1/2 x))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x))))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(- 1 (sqrt x)) |
(- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x)) |
(- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x)) |
(- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x)) |
(/ 1 (+ 1 (sqrt x))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(/ 1 (+ 1 (sqrt x))) |
(/ 1 (+ 1 (sqrt x))) |
(/ 1 (+ 1 (sqrt x))) |
(/ 1 (+ 1 (sqrt x))) |
(+ 1 (sqrt x)) |
(+ 1 (sqrt x)) |
(+ 1 (sqrt x)) |
(+ 1 (sqrt x)) |
(/ 1 (+ 1 (sqrt x))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
1 |
1 |
1 |
1 |
(/ 1 (+ 1 (sqrt x))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
1 |
(+ 1 x) |
(+ 1 x) |
(+ 1 x) |
(+ 1 (sqrt x)) |
(+ 1 (+ (sqrt x) (* 1/2 x))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x))))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))) |
1 |
(+ 1 (* 1/2 x)) |
(+ 1 (* x (+ 1/2 (* -1/8 x)))) |
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
(sqrt -1) |
(+ (sqrt -1) (* -1/2 (/ x (sqrt -1)))) |
(+ (sqrt -1) (* x (- (* -1/2 (/ (* x (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2))))) (sqrt -1))) (* 1/2 (/ 1 (sqrt -1)))))) |
(+ (sqrt -1) (* x (- (* x (+ (* -1/2 (/ (* x (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2))))) (sqrt -1))) (* -1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (sqrt -1))))) (* 1/2 (/ 1 (sqrt -1)))))) |
(sqrt -1) |
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1)))) |
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))) |
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1)))))) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x) |
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x) |
1 |
1 |
1 |
1 |
(* 2 (sqrt x)) |
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x) |
(/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) x) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x) |
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x) |
(sqrt (/ 1 x)) |
(/ (- (sqrt x) 1) x) |
(/ (- (+ (sqrt x) (sqrt (/ 1 x))) 1) x) |
(/ (- (sqrt x) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (/ 1 x)))) x) |
(sqrt x) |
(* x (+ (sqrt (/ 1 x)) (/ 1 x))) |
(* x (+ (sqrt (/ 1 x)) (/ 1 x))) |
(* x (+ (sqrt (/ 1 x)) (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x) |
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
1 |
1 |
1 |
1 |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x) |
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* 2 (sqrt x)) |
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))) |
(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)))))))) |
(sqrt (/ 1 x)) |
(+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) |
(+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))) |
(+ (sqrt (/ 1 x)) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 1 (* 1/4 x))))))) |
x |
(* x (- 1 (* 1/2 (/ 1 (pow x 2))))) |
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))) |
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))) |
(* -1/2 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) |
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x)) |
1 |
1 |
1 |
1 |
(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (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)))) (* 2 (* (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)))) (* 2 (* (sqrt (/ 1 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 (* (sqrt x) (pow (sqrt -1) 2))) |
(/ 3 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(/ (+ (* 3/2 (/ 1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x) |
(* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (* 1/8 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* 3/2 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) |
(* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/16 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* 9/4 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) (* 1/8 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* 3/2 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) |
(* -1/2 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) |
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x)) |
(* -1 (sqrt (/ 1 x))) |
(* -1 (/ (- (sqrt x) (/ 1 (pow (sqrt -1) 2))) x)) |
(* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x)) |
(* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (/ (- (/ x (pow (sqrt -1) 4)) (* -1 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1 (/ x (pow (sqrt -1) 2)))) x))) 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 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) |
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x)) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
(/ 1 x) |
1 |
1 |
1 |
1 |
(* -1/2 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* 1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* -1/8 (sqrt (/ 1 x)))) x)) |
(* -1 (/ (- (+ (* -1 (/ (+ (* -1/32 (sqrt (pow x 7))) (* -1/128 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/8 (sqrt (/ 1 x))) (* -1/16 (sqrt (/ 1 (pow x 3)))))) x)) |
x |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* x (+ 1 (/ 1 x))) |
(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
(* -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))))))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ 1 (* -1/4 x)))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(* -1 x) |
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))) |
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))) |
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))) |
| Outputs |
|---|
(/ 1 (+ 1 (sqrt x))) |
(/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(fma.f64 (/.f64 x (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) |
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(fma.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))))) x (/.f64 #s(literal -1/2 binary64) (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))))) x (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) |
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))))) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))))) (/.f64 #s(literal 1/16 binary64) (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))))) x (/.f64 #s(literal -1/2 binary64) (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))))) x (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
(+ 1 (sqrt x)) |
(-.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(+ 1 (+ (sqrt x) (* 1/2 x))) |
(fma.f64 #s(literal 1/2 binary64) x (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x))))) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(- 1 (sqrt x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x)) |
(fma.f64 (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x)) |
(fma.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (*.f64 #s(literal -3/8 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))) x (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x)) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (*.f64 #s(literal -3/8 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) (fma.f64 #s(literal 3/8 binary64) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (*.f64 #s(literal -1/16 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (*.f64 #s(literal -3/8 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))) x (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/ 1 (+ 1 (sqrt x))) |
(/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(fma.f64 (/.f64 x (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) |
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(fma.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))))) x (/.f64 #s(literal -1/2 binary64) (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))))) x (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) |
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))))) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))))) (/.f64 #s(literal 1/16 binary64) (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))))) x (/.f64 #s(literal -1/2 binary64) (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))))) x (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) |
(/ 1 (+ 1 (sqrt x))) |
(/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(/ 1 (+ 1 (sqrt x))) |
(/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(/ 1 (+ 1 (sqrt x))) |
(/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(/ 1 (+ 1 (sqrt x))) |
(/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(+ 1 (sqrt x)) |
(-.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(+ 1 (sqrt x)) |
(-.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(+ 1 (sqrt x)) |
(-.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(+ 1 (sqrt x)) |
(-.f64 (sqrt.f64 x) #s(literal -1 binary64)) |
(/ 1 (+ 1 (sqrt x))) |
(/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(fma.f64 (/.f64 x (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) |
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(fma.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) (/.f64 #s(literal 1/8 binary64) (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))))) x (/.f64 #s(literal -1/2 binary64) (*.f64 (-.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal -1 binary64))))) x (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) #s(literal -1 binary64)))) |
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
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(+ 1 (+ (sqrt x) (* 1/2 x))) |
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(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) |
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(sqrt.f64 #s(literal -1 binary64)) |
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(sqrt -1) |
(sqrt.f64 #s(literal -1 binary64)) |
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(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1)))))) |
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(* 1/2 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
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(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x) |
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1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
(* 2 (sqrt x)) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 x)) |
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))) |
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(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))) |
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(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))) |
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(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
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(/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
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(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x) |
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(/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) x) |
(/.f64 (-.f64 (fma.f64 #s(literal -1/32 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 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) (fma.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 3/8 binary64) (*.f64 #s(literal 3/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)))))) x) |
(* 1/2 (sqrt (/ 1 x))) |
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(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x) |
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x) |
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(/.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) x) |
(/ (- (sqrt x) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (/ 1 x)))) x) |
(/.f64 (-.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x) |
(sqrt x) |
(sqrt.f64 x) |
(* x (+ (sqrt (/ 1 x)) (/ 1 x))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal 1 binary64)) |
(* x (+ (sqrt (/ 1 x)) (/ 1 x))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal 1 binary64)) |
(* x (+ (sqrt (/ 1 x)) (/ 1 x))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal 1 binary64)) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
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(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x) |
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(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x) |
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(* 1/2 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
(/ 1 x) |
(/.f64 #s(literal 1 binary64) x) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
1 |
#s(literal 1 binary64) |
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(* -1 (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* -1/8 (sqrt (/ 1 x)))) x)) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) (neg.f64 x)) |
(* -1 (/ (- (+ (* -1 (/ (+ (* -1/32 (sqrt (pow x 7))) (* -1/128 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/8 (sqrt (/ 1 x))) (* -1/16 (sqrt (/ 1 (pow x 3)))))) x)) |
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) (neg.f64 x)) |
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)) |
(* -2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 2 binary64) (sqrt.f64 x)) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (neg.f64 x) (fma.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)))) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) |
(*.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64))))) |
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))) |
(*.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 #s(literal -2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64)))))) |
(* -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 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/2 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)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (neg.f64 x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/2 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 (neg.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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(fma.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
(+ (* -1 (/ (+ (* 1/2 (* (sqrt x) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ 1 (* -1/4 x)))))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(fma.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x))) (*.f64 (*.f64 x x) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))) |
(*.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)) x) |
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))) |
(fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x)) x (neg.f64 x)) |
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))) |
(*.f64 (neg.f64 x) (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (*.f64 (*.f64 x x) (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))) |
| 6 326× | lower-*.f32 |
| 6 324× | lower-*.f64 |
| 4 964× | lower-fma.f32 |
| 4 960× | lower-fma.f64 |
| 3 332× | lower-/.f32 |
Useful iterations: 2 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 45 | 190 |
| 0 | 69 | 183 |
| 1 | 286 | 115 |
| 2 | 2469 | 111 |
| 0 | 9059 | 111 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
#s(approx (- (+ 1 x) x) #s(literal 1 binary64)) |
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) |
(sqrt.f64 x) |
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) |
(/.f64 #s(literal -3 binary64) #s(literal 0 binary64)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) |
(+.f64 (sqrt.f64 x) #s(literal 1 binary64)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
(-.f64 (+.f64 #s(literal 1 binary64) x) x) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (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)))) (sqrt.f64 x))) |
(+.f64 #s(literal 1 binary64) x) |
(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)))) (sqrt.f64 x)) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) |
(sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) |
| Outputs |
|---|
(*.f64 (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (-.f64 x (+.f64 x #s(literal 1 binary64)))) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(*.f64 (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64)) (*.f64 (sqrt.f64 x) x))) (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x x)))) |
(*.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (pow.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (+ 1 x) x) #s(literal 1 binary64))) #s(literal -1 binary64))) |
(*.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (+ 1 x) x) #s(literal 1 binary64))) |
(*.f64 (neg.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))))) |
(*.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) |
(*.f64 #s(literal 1 binary64) (*.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (+ 1 x) x) #s(literal 1 binary64)))) |
(pow.f64 (/.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (+ 1 x) x) #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (+ 1 x) x) #s(literal 1 binary64))) #s(literal -1 binary64)) |
(/.f64 (*.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) |
(/.f64 (neg.f64 (neg.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))))) |
(/.f64 (neg.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64))) (neg.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (+ 1 x) x) #s(literal 1 binary64))))) |
(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) |
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (+ 1 x) x) #s(literal 1 binary64))) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (+ 1 x) x) #s(literal 1 binary64)))) |
(neg.f64 (/.f64 (neg.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) |
(neg.f64 (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (neg.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))))) |
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(approx (- (+ 1 x) x) #s(literal 1 binary64)))) #s(literal -1 binary64))) |
#s(approx (- (+ 1 x) x) #s(literal 1 binary64)) |
(*.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(literal 1 binary64))) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) |
(*.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (*.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)) (*.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))) #s(literal 1 binary64))) (fma.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)) (*.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))))) |
(*.f64 (-.f64 x (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(*.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64)) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x x))))) |
(*.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) |
(pow.f64 (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x x))) (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64)) (*.f64 (sqrt.f64 x) x))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 x (+.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal -1 binary64)) |
(pow.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 1 binary64)) |
(/.f64 (neg.f64 (-.f64 x (+.f64 x #s(literal 1 binary64)))) (neg.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(/.f64 (-.f64 x (+.f64 x #s(literal 1 binary64))) (*.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) |
(/.f64 (-.f64 x (+.f64 x #s(literal 1 binary64))) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) |
(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64)) (*.f64 (sqrt.f64 x) x))) (neg.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x x))))) |
(/.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) #s(literal -1 binary64)) |
(/.f64 #s(literal -1 binary64) (neg.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) |
(/.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64)) (*.f64 (sqrt.f64 x) x)) (*.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x x))) #s(literal 1 binary64))) |
(/.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64)) (*.f64 (sqrt.f64 x) x)) (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x x)))) |
(/.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 1 binary64)) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x x))) (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64)) (*.f64 (sqrt.f64 x) x)))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 x (+.f64 x #s(literal 1 binary64))))) |
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 1 binary64))) |
(/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) |
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(fma.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) (sqrt.f64 x)) |
(fma.f64 (sqrt.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))))) (sqrt.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 x)) |
(fma.f64 (sqrt.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))) (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))) (sqrt.f64 x)) |
(fma.f64 (sqrt.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))) (sqrt.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 x)) |
(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 x)) |
(fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x)) |
(fma.f64 (pow.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) (sqrt.f64 x)) |
(fma.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))) #s(literal 1/2 binary64)) (pow.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
(fma.f64 (pow.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
(fma.f64 (pow.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #s(literal 1/2 binary64)) (pow.f64 (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
(fma.f64 (pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) #s(literal 1/2 binary64)) (pow.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 x)) |
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 x)) |
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
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(*.f64 (pow.f64 (fma.f64 (*.f64 x x) x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))) #s(literal -1/2 binary64))) |
(*.f64 (pow.f64 (fma.f64 x 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 -1/2 binary64))) |
(*.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))) |
(*.f64 (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal -1/2 binary64))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 x) #s(literal 1 binary64))))) |
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 x) #s(literal 1 binary64))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) #s(literal 1 binary64)) |
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 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 1/4 binary64)) |
(pow.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) #s(literal -1 binary64)) |
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64)) |
(pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) |
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64)))) |
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (+.f64 (neg.f64 x) #s(literal 1 binary64))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) |
(fabs.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))))) |
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) #s(literal -1 binary64))) |
(exp.f64 (*.f64 (log.f64 (-.f64 x #s(literal 1 binary64))) #s(literal -1/2 binary64))) |
(exp.f64 (*.f64 (neg.f64 (log.f64 (-.f64 x #s(literal 1 binary64)))) #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/4 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))) |
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (*.f64 x x))))))) |
(*.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (*.f64 x x) x) x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (*.f64 x x))))) #s(literal 1/2 binary64))) |
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) |
(pow.f64 (exp.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64)))) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal 1/4 binary64)) |
(pow.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/2 binary64)) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 x #s(literal 1 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1 binary64)))) (sqrt.f64 (fma.f64 x x (+.f64 x #s(literal 1 binary64))))) |
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 x x) x) x))) (sqrt.f64 (-.f64 #s(literal -1 binary64) (*.f64 x x)))) |
(/.f64 (sqrt.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (+.f64 #s(literal 1 binary64) (*.f64 x x))))) |
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 x x #s(literal 1 binary64))))) |
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) #s(literal -1 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (*.f64 x x))))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 (*.f64 x x) x #s(literal -1 binary64)))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (*.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))) |
(/.f64 (sqrt.f64 (*.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)) (fma.f64 (*.f64 x x) x #s(literal -1 binary64)))) (sqrt.f64 (*.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 x x (+.f64 x #s(literal 1 binary64)))))) |
(/.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) |
(/.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) |
(/.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 #s(literal -1 binary64) (*.f64 x x)))))) |
(/.f64 (sqrt.f64 (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (*.f64 x x)))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 (*.f64 (*.f64 x x) x) x #s(literal -1 binary64))))) |
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 (*.f64 (*.f64 x x) x) x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (*.f64 x x)))) (fma.f64 (*.f64 (*.f64 (*.f64 x x) x) x) (*.f64 x x) #s(literal -1 binary64))))) |
(sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) |
(exp.f64 (*.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64))) #s(literal 1/2 binary64))) |
Compiled 18 152 to 2 036 computations (88.8% saved)
11 alts after pruning (8 fresh and 3 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 861 | 4 | 865 |
| Fresh | 1 | 4 | 5 |
| Picked | 3 | 2 | 5 |
| Done | 2 | 1 | 3 |
| Total | 867 | 11 | 878 |
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 41.0% | (/.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)))) |
| 51.9% | (/.f64 #s(approx (- (+ 1 x) x) #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)))) (sqrt.f64 x))) | |
| ✓ | 99.6% | (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
| ✓ | 6.0% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 4.3% | (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) | |
| ▶ | 99.0% | #s(approx (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
| ▶ | 98.1% | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
| ✓ | 98.4% | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
| ▶ | 99.3% | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) |
| 98.2% | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 (* (* x x) x))) 1/16) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) | |
| ▶ | 3.8% | #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) #s(literal 0 binary64)) |
Compiled 267 to 153 computations (42.7% saved)
| 1× | egg-herbie |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (/.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)))) | |
| cost-diff | 128 | (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) | |
| cost-diff | 320 | (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) #s(literal 1 binary64)) | |
| cost-diff | 448 | (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) | |
| cost-diff | 0 | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) | |
| cost-diff | 0 | (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) | |
| cost-diff | 0 | (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) | |
| cost-diff | 0 | #s(approx (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) | |
| cost-diff | 0 | (sqrt.f64 x) | |
| cost-diff | 0 | (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) | |
| cost-diff | 0 | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) | |
| cost-diff | 0 | #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) #s(literal 0 binary64)) | |
| cost-diff | 0 | (sqrt.f64 x) | |
| cost-diff | 0 | (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) | |
| cost-diff | 0 | (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x) | |
| cost-diff | 0 | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) |
| 13 668× | lower-fma.f32 |
| 13 658× | lower-fma.f64 |
| 3 896× | lower-*.f32 |
| 3 886× | lower-*.f64 |
| 3 118× | lower-+.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 65 | 385 |
| 0 | 101 | 380 |
| 1 | 197 | 364 |
| 2 | 514 | 356 |
| 3 | 1813 | 353 |
| 4 | 3776 | 353 |
| 0 | 8199 | 348 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) |
(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x) |
(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) |
(sqrt.f64 x) |
x |
#s(literal 1/2 binary64) |
(+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) |
(/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) |
#s(literal 1/16 binary64) |
(*.f64 (sqrt.f64 x) x) |
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) |
#s(literal -1/8 binary64) |
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) #s(literal 0 binary64)) |
#s(literal 0 binary64) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
#s(literal 1/2 binary64) |
(sqrt.f64 x) |
x |
#s(approx (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
#s(literal -1/8 binary64) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
#s(literal 1/2 binary64) |
(sqrt.f64 x) |
(/.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)))) |
(*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) #s(literal 1 binary64)) |
(-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) |
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) |
(fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) |
#s(literal 2 binary64) |
x |
#s(literal 1 binary64) |
(fma.f64 x x x) |
(*.f64 (+.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x))) |
(+.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 #s(literal 1 binary64) x)) |
(+.f64 (sqrt.f64 (fma.f64 x x x)) x) |
(sqrt.f64 (fma.f64 x x x)) |
(+.f64 #s(literal 1 binary64) x) |
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(*.f64 (sqrt.f64 x) x) |
(sqrt.f64 x) |
| Outputs |
|---|
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)))) x)) |
(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x) |
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)))) x) |
(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) |
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)))) |
(sqrt.f64 x) |
x |
#s(literal 1/2 binary64) |
(+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) |
(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x))) |
(/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) |
#s(literal 1/16 binary64) |
(*.f64 (sqrt.f64 x) x) |
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) |
#s(literal -1/8 binary64) |
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) #s(literal 0 binary64)) |
#s(literal 0 binary64) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
#s(literal 1/2 binary64) |
(sqrt.f64 x) |
x |
#s(approx (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(/.f64 #s(literal 1 binary64) x) |
#s(literal 1 binary64) |
x |
#s(literal -1/8 binary64) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
#s(literal 1/2 binary64) |
(sqrt.f64 x) |
(/.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)))) |
(/.f64 (fma.f64 (fma.f64 #s(literal 3 binary64) x #s(literal 1 binary64)) (-.f64 x #s(literal -1 binary64)) (neg.f64 x)) (*.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (-.f64 x #s(literal -1 binary64)) (*.f64 (sqrt.f64 x) x)))) |
(*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) #s(literal 1 binary64)) |
(fma.f64 (fma.f64 #s(literal 3 binary64) x #s(literal 1 binary64)) (-.f64 x #s(literal -1 binary64)) (neg.f64 x)) |
(-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) |
(fma.f64 (fma.f64 #s(literal 3 binary64) x #s(literal 1 binary64)) (-.f64 x #s(literal -1 binary64)) (neg.f64 x)) |
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) |
(fma.f64 x (+.f64 (fma.f64 #s(literal 4 binary64) x #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) |
(fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) |
#s(literal 2 binary64) |
x |
#s(literal 1 binary64) |
(fma.f64 x x x) |
(*.f64 (+.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x))) |
(*.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (-.f64 x #s(literal -1 binary64)) (*.f64 (sqrt.f64 x) x))) |
(+.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 #s(literal 1 binary64) x)) |
(+.f64 (sqrt.f64 (fma.f64 x x x)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) |
(+.f64 (sqrt.f64 (fma.f64 x x x)) x) |
(sqrt.f64 (fma.f64 x x x)) |
(+.f64 #s(literal 1 binary64) x) |
(-.f64 x #s(literal -1 binary64)) |
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)) |
(fma.f64 (sqrt.f64 (-.f64 x #s(literal -1 binary64))) (-.f64 x #s(literal -1 binary64)) (*.f64 (sqrt.f64 x) x)) |
(sqrt.f64 (+.f64 #s(literal 1 binary64) x)) |
(sqrt.f64 (-.f64 x #s(literal -1 binary64))) |
(*.f64 (sqrt.f64 x) x) |
(sqrt.f64 x) |
Found 16 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.15625 | (*.f64 (sqrt.f64 x) x) | |
| accuracy | 25.664062500000004 | (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) | |
| accuracy | 29.772995479991767 | (sqrt.f64 (fma.f64 x x x)) | |
| accuracy | 36.910222904268736 | (/.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)))) | |
| accuracy | 0.00390625 | (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) | |
| accuracy | 0.11328125 | (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) | |
| accuracy | 0.23828125 | (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) | |
| accuracy | 0.44430308488148657 | #s(approx (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) | |
| accuracy | 0 | (sqrt.f64 x) | |
| accuracy | 0.265625 | (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) | |
| accuracy | 0.9413407183184179 | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) | |
| accuracy | 61.54802851618594 | #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) #s(literal 0 binary64)) | |
| accuracy | 0.19790143039475586 | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) | |
| accuracy | 0.23828125 | (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x) | |
| accuracy | 0.265625 | (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) | |
| accuracy | 1.1679319804185058 | (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) |
| 169.0ms | 237× | 1 | valid |
| 13.0ms | 12× | 2 | valid |
| 2.0ms | 7× | 0 | valid |
Compiled 375 to 60 computations (84% saved)
ival-add: 31.0ms (20.7% of total)ival-div: 31.0ms (20.7% of total)adjust: 29.0ms (19.4% of total)ival-mult: 29.0ms (19.4% of total)ival-sqrt: 19.0ms (12.7% of total)ival-sub: 9.0ms (6% of total)exact: 1.0ms (0.7% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(alt #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) (patch #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) #<representation binary64>) () ()) |
#s(alt (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x) (patch (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x) #<representation binary64>) () ()) |
#s(alt (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (patch (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ()) |
#s(alt #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) #s(literal 0 binary64)) (patch #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) #s(literal 0 binary64)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (patch #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #<representation binary64>) () ()) |
#s(alt #s(approx (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) (patch #s(approx (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) #<representation binary64>) () ()) |
#s(alt (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) (patch (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) #<representation binary64>) () ()) |
#s(alt (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (patch (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ()) |
#s(alt (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) (patch (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) #<representation binary64>) () ()) |
#s(alt (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) #s(literal 1 binary64)) (patch (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (patch (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt (/.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)))) (patch (/.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)))) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (patch (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) #<representation binary64>) () ()) |
#s(alt (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #<representation binary64>) () ()) |
#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ()) |
#s(alt (*.f64 (sqrt.f64 x) x) (patch (*.f64 (sqrt.f64 x) x) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt (- 1 (sqrt x)) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) (patch #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* 1/2 x)) (sqrt x)) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) (patch #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) (patch #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) #<representation binary64>) () ())) ()) |
#s(alt (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) (patch #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) #<representation binary64>) () ())) ()) |
#s(alt (* 1/16 (sqrt (/ 1 (pow x 5)))) (taylor 0 x) (#s(alt (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x) (patch (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x) #<representation binary64>) () ())) ()) |
#s(alt (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3)) (taylor 0 x) (#s(alt (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x) (patch (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x) #<representation binary64>) () ())) ()) |
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3 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 12.0ms | x | @ | -inf | ((- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt x) 1/2) (+ (/ 1/16 (* (sqrt x) x)) (/ -1/8 (sqrt x)))) x) (+ (* (sqrt x) 1/2) (+ (/ 1/16 (* (sqrt x) x)) (/ -1/8 (sqrt x)))) (sqrt x) (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/ 1/2 (sqrt x)) (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (sqrt (/ 1 x)) (- (* (+ (* 2 x) 1) (+ (* 2 x) 1)) (+ (* x x) x)) (* (- (* (+ (* 2 x) 1) (+ (* 2 x) 1)) (+ (* x x) x)) 1) (* (+ (* 2 x) 1) (+ (* 2 x) 1)) (/ (* (- (* (+ (* 2 x) 1) (+ (* 2 x) 1)) (+ (* x x) x)) 1) (* (+ (+ (sqrt (+ (* x x) x)) x) (+ 1 x)) (+ (* (sqrt (+ 1 x)) (+ 1 x)) (* (sqrt x) x)))) (/ 1/16 (* (sqrt x) x)) (/ -1/8 (sqrt x)) (sqrt (+ (* x x) x)) (* (sqrt x) x)) |
| 4.0ms | x | @ | 0 | ((- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt x) 1/2) (+ (/ 1/16 (* (sqrt x) x)) (/ -1/8 (sqrt x)))) x) (+ (* (sqrt x) 1/2) (+ (/ 1/16 (* (sqrt x) x)) (/ -1/8 (sqrt x)))) (sqrt x) (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/ 1/2 (sqrt x)) (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (sqrt (/ 1 x)) (- (* (+ (* 2 x) 1) (+ (* 2 x) 1)) (+ (* x x) x)) (* (- (* (+ (* 2 x) 1) (+ (* 2 x) 1)) (+ (* x x) x)) 1) (* (+ (* 2 x) 1) (+ (* 2 x) 1)) (/ (* (- (* (+ (* 2 x) 1) (+ (* 2 x) 1)) (+ (* x x) x)) 1) (* (+ (+ (sqrt (+ (* x x) x)) x) (+ 1 x)) (+ (* (sqrt (+ 1 x)) (+ 1 x)) (* (sqrt x) x)))) (/ 1/16 (* (sqrt x) x)) (/ -1/8 (sqrt x)) (sqrt (+ (* x x) x)) (* (sqrt x) x)) |
| 3.0ms | x | @ | inf | ((- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt x) 1/2) (+ (/ 1/16 (* (sqrt x) x)) (/ -1/8 (sqrt x)))) x) (+ (* (sqrt x) 1/2) (+ (/ 1/16 (* (sqrt x) x)) (/ -1/8 (sqrt x)))) (sqrt x) (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/ 1/2 (sqrt x)) (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (sqrt (/ 1 x)) (- (* (+ (* 2 x) 1) (+ (* 2 x) 1)) (+ (* x x) x)) (* (- (* (+ (* 2 x) 1) (+ (* 2 x) 1)) (+ (* x x) x)) 1) (* (+ (* 2 x) 1) (+ (* 2 x) 1)) (/ (* (- (* (+ (* 2 x) 1) (+ (* 2 x) 1)) (+ (* x x) x)) 1) (* (+ (+ (sqrt (+ (* x x) x)) x) (+ 1 x)) (+ (* (sqrt (+ 1 x)) (+ 1 x)) (* (sqrt x) x)))) (/ 1/16 (* (sqrt x) x)) (/ -1/8 (sqrt x)) (sqrt (+ (* x x) x)) (* (sqrt x) x)) |
| 1× | egg-herbie |
| 9 506× | lower-fma.f64 |
| 9 506× | lower-fma.f32 |
| 5 210× | lower-*.f64 |
| 5 210× | lower-*.f32 |
| 2 954× | lower-+.f64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 507 | 4060 |
| 1 | 1559 | 3494 |
| 2 | 5208 | 3382 |
| 0 | 8346 | 3171 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(- 1 (sqrt x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
(* 1/16 (sqrt (/ 1 (pow x 5)))) |
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3)) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 2)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2)) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(- 1 (sqrt x)) |
(- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x)) |
(- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x)) |
(- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x)) |
(/ 1 (+ 1 (sqrt x))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(/ 1 (+ 1 (sqrt x))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(* -1/8 (sqrt (/ 1 (pow x 3)))) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(* -1/8 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
1 |
(+ 1 (* 3 x)) |
(+ 1 (* x (+ 3 (* 3 x)))) |
(+ 1 (* x (+ 3 (* 3 x)))) |
1 |
(+ 1 (* 3 x)) |
(+ 1 (* x (+ 3 (* 3 x)))) |
(+ 1 (* x (+ 3 (* 3 x)))) |
1 |
(+ 1 (* 4 x)) |
(+ 1 (* x (+ 4 (* 4 x)))) |
(+ 1 (* x (+ 4 (* 4 x)))) |
(/ 1 (+ 1 (sqrt x))) |
(+ (* x (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (+ (* 3/2 (/ 1 (+ 1 (sqrt x)))) (* x (- (* 21/8 (/ 1 (+ 1 (sqrt x)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (+ (* 2 (/ (+ 3/2 (sqrt x)) (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 2 (* (+ 1 (sqrt x)) (+ 3/2 (sqrt x)))) (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (+ 1 (sqrt x)))))))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (/ 1 (+ 1 (sqrt x)))) |
(+ (* x (- (+ (* 3/2 (/ 1 (+ 1 (sqrt x)))) (* x (- (+ (* 21/8 (/ 1 (+ 1 (sqrt x)))) (* x (- (* 1/16 (/ 1 (+ 1 (sqrt x)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ (+ 3/2 (sqrt x)) (pow (+ 1 (sqrt x)) 2)))) (+ (* 3/4 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (/ (* (+ 2 (* (+ 1 (sqrt x)) (+ 3/2 (sqrt x)))) (- (* 21/8 (/ 1 (+ 1 (sqrt x)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (+ (* 2 (/ (+ 3/2 (sqrt x)) (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 2 (* (+ 1 (sqrt x)) (+ 3/2 (sqrt x)))) (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (+ 1 (sqrt x))))))) (+ 1 (sqrt x))) (/ (* (+ (* 3/8 (+ 1 (sqrt x))) (+ (* 1/2 (sqrt (/ 1 x))) (* 2 (+ 3/2 (sqrt x))))) (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (+ 1 (sqrt x))))))))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (+ (* 2 (/ (+ 3/2 (sqrt x)) (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 2 (* (+ 1 (sqrt x)) (+ 3/2 (sqrt x)))) (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (+ 1 (sqrt x)))))))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (/ 1 (+ 1 (sqrt x)))) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
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(* -1/8 (sqrt (/ 1 x))) |
(* -1/8 (sqrt (/ 1 x))) |
(* -1/8 (sqrt (/ 1 x))) |
(* -1/8 (sqrt (/ 1 x))) |
(sqrt x) |
(+ (sqrt x) (* 1/2 (sqrt (pow x 3)))) |
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) |
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x)))))))) |
(sqrt (pow x 3)) |
(sqrt (pow x 3)) |
(sqrt (pow x 3)) |
(sqrt (pow x 3)) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x) |
(* 1/2 (sqrt (/ 1 x))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) |
(* 1/2 (sqrt x)) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(sqrt x) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x) |
(/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) x) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x) |
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) |
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x) |
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x) |
(* 1/2 (sqrt (/ 1 x))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) |
(* 1/2 (sqrt x)) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) |
(sqrt (/ 1 x)) |
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(sqrt (/ 1 x)) |
(sqrt (/ 1 x)) |
(* 3 (pow x 2)) |
(* (pow x 2) (+ 3 (* 3 (/ 1 x)))) |
(* (pow x 2) (+ 3 (+ (* 3 (/ 1 x)) (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 3 (+ (* 3 (/ 1 x)) (/ 1 (pow x 2))))) |
(* 3 (pow x 2)) |
(* (pow x 2) (+ 3 (* 3 (/ 1 x)))) |
(* (pow x 2) (+ 3 (+ (* 3 (/ 1 x)) (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 3 (+ (* 3 (/ 1 x)) (/ 1 (pow x 2))))) |
(* 4 (pow x 2)) |
(* (pow x 2) (+ 4 (* 4 (/ 1 x)))) |
(* (pow x 2) (+ 4 (+ (* 4 (/ 1 x)) (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 4 (+ (* 4 (/ 1 x)) (/ 1 (pow x 2))))) |
(* 1/2 (sqrt (/ 1 x))) |
(/ (- (+ (* 1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))) (* 1/4 (sqrt (/ 1 x)))) x) |
(/ (- (+ (* 1/6 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (+ (* 1/12 (/ (+ (* -1/4 (sqrt (/ 1 x))) (* 9/2 (sqrt x))) x)) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (/ (- (* 1/2 (sqrt x)) (* 1/4 (sqrt x))) (pow x 2)))))) x) |
(/ (- (+ (* -1 (/ (+ (* 1/12 (* x (+ (* 1/8 (sqrt (/ 1 x))) (+ (* 9/4 (sqrt x)) (* 9/2 (sqrt x)))))) (+ (* 1/6 (* (sqrt x) (* (+ (* -1/4 (sqrt (/ 1 x))) (* 9/2 (sqrt x))) (- (* 1/2 (sqrt x)) (* 1/4 (sqrt x)))))) (* 1/2 (- (* 1/6 (sqrt x)) (+ (* 1/12 (* x (+ (* -1/4 (sqrt (/ 1 x))) (* 9/2 (sqrt x))))) (* 1/2 (- (* 1/2 (sqrt x)) (* 1/4 (sqrt x))))))))) (pow x 3))) (+ (* 1/6 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) (+ (* 1/12 (/ (+ (* -1/4 (sqrt (/ 1 x))) (* 9/2 (sqrt x))) x)) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (/ (- (* 1/2 (sqrt x)) (* 1/4 (sqrt x))) (pow x 2)))))) x) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(* -1/8 (sqrt (/ 1 x))) |
(* -1/8 (sqrt (/ 1 x))) |
(* -1/8 (sqrt (/ 1 x))) |
(* -1/8 (sqrt (/ 1 x))) |
x |
(* x (+ 1 (* 1/2 (/ 1 x)))) |
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) |
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2)))) |
(sqrt (pow x 3)) |
(sqrt (pow x 3)) |
(sqrt (pow x 3)) |
(sqrt (pow x 3)) |
(* -1/2 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x)) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x)) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3))))) |
(+ (* -1 (/ (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(+ (* -1 (/ (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/16 (sqrt (/ 1 (pow x 3))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* -1 (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/16 (sqrt (/ 1 (pow x 3))))) x)) (* 1/2 (* (sqrt (/ 1 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 (* (sqrt x) (pow (sqrt -1) 2))) |
(/ 3 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(/ (+ (* 3/2 (/ 1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x) |
(* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (* 1/8 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* 3/2 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) |
(* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* 1/16 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* 9/4 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) (* 1/8 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* 3/2 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) |
(* -1/2 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) |
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x)) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* 1/2 (sqrt (/ 1 x))) |
(* -1/2 (sqrt (/ 1 x))) |
(* -1 (/ (+ (* 1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)) |
(* -1 (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* -1/8 (sqrt (/ 1 x)))) x)) |
(* -1 (/ (- (+ (* -1 (/ (+ (* -1/32 (sqrt (pow x 7))) (* -1/128 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/8 (sqrt (/ 1 x))) (* -1/16 (sqrt (/ 1 (pow x 3)))))) x)) |
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) |
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(* 3 (pow x 2)) |
(* (pow x 2) (+ 3 (* 3 (/ 1 x)))) |
(* (pow x 2) (+ 3 (+ (* 3 (/ 1 x)) (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 3 (+ (* 3 (/ 1 x)) (/ 1 (pow x 2))))) |
(* 3 (pow x 2)) |
(* (pow x 2) (+ 3 (* 3 (/ 1 x)))) |
(* (pow x 2) (+ 3 (+ (* 3 (/ 1 x)) (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 3 (+ (* 3 (/ 1 x)) (/ 1 (pow x 2))))) |
(* 4 (pow x 2)) |
(* (pow x 2) (+ 4 (* 4 (/ 1 x)))) |
(* (pow x 2) (+ 4 (+ (* 4 (/ 1 x)) (/ 1 (pow x 2))))) |
(* (pow x 2) (+ 4 (+ (* 4 (/ 1 x)) (/ 1 (pow x 2))))) |
(/ 3 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(/ (+ (* 3/2 (/ 1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x) |
(* -1 (/ (- (* -1 (/ (+ (* 3 (/ (+ (* -3/2 (sqrt x)) (* -1/8 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* x (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (/ 1/4 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) |
(* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (+ (* -3/2 (/ (+ (* -3/2 (sqrt x)) (* -1/8 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* x (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 1/2 (/ (+ (* 3 (/ (+ (* -3/2 (sqrt x)) (* -1/8 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 1/4 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ (+ (* -1/16 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* 3/4 (sqrt x)) (* 3/2 (sqrt x)))) (* x (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (+ (* 1/4 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3 (/ (+ (* -3/2 (sqrt x)) (* -1/8 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* 3/2 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(* -1/8 (sqrt (/ 1 x))) |
(* -1/8 (sqrt (/ 1 x))) |
(* -1/8 (sqrt (/ 1 x))) |
(* -1/8 (sqrt (/ 1 x))) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) |
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) |
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) |
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) |
| Outputs |
|---|
(- 1 (sqrt x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(- (+ 1 (* 1/2 x)) (sqrt x)) |
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) |
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(* 1/16 (sqrt (/ 1 (pow x 5)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/16 binary64)) |
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 3)) |
(/.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (*.f64 (*.f64 x x) x)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3)) |
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (*.f64 (*.f64 x x) x)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 3)) |
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (*.f64 (*.f64 x x) x)) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64)) |
(/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/16 (sqrt x))) (pow x 2)) |
(/.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (*.f64 x x)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2)) |
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (*.f64 x x)) |
(/ (+ (* 1/16 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))))) (pow x 2)) |
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (*.f64 x x)) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(sqrt x) |
(sqrt.f64 x) |
(- 1 (sqrt x)) |
(-.f64 #s(literal 1 binary64) (sqrt.f64 x)) |
(- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x)) |
(fma.f64 (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x)) |
(fma.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (*.f64 #s(literal -3/8 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))) x (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x)) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (*.f64 #s(literal -3/8 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) (fma.f64 #s(literal 3/8 binary64) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (*.f64 #s(literal -1/16 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (*.f64 #s(literal -3/8 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))) x (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) |
(/ 1 (+ 1 (sqrt x))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(fma.f64 (/.f64 x (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(fma.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) (/.f64 #s(literal 1/8 binary64) (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))) x (/.f64 #s(literal -1/2 binary64) (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))) x (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) (/.f64 #s(literal 1/8 binary64) (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))) (/.f64 #s(literal 1/16 binary64) (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) (/.f64 #s(literal 1/8 binary64) (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))))) x (/.f64 #s(literal -1/2 binary64) (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))) x (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
(* 1/2 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) |
(/ 1 (+ 1 (sqrt x))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) |
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) |
(fma.f64 (/.f64 x (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(fma.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) (/.f64 #s(literal 1/8 binary64) (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))) x (/.f64 #s(literal -1/2 binary64) (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))) x (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) |
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) (/.f64 #s(literal 1/8 binary64) (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (*.f64 (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))) (/.f64 #s(literal 1/16 binary64) (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))) (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) (/.f64 #s(literal 1/8 binary64) (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))))) x (/.f64 #s(literal -1/2 binary64) (+.f64 (+.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))) x (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
(* -1/8 (sqrt (/ 1 (pow x 3)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal -1/8 binary64)) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(/.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 x x)) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(/.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 x x)) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) |
(/.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (*.f64 x x)) |
(* -1/8 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(/.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(/.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x) |
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x) |
(/.f64 (fma.f64 (sqrt.f64 (*.f64 (*.f64 x x) x)) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(sqrt (/ 1 x)) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 3 x)) |
(fma.f64 #s(literal 3 binary64) x #s(literal 1 binary64)) |
(+ 1 (* x (+ 3 (* 3 x)))) |
(fma.f64 (fma.f64 #s(literal 3 binary64) x #s(literal 3 binary64)) x #s(literal 1 binary64)) |
(+ 1 (* x (+ 3 (* 3 x)))) |
(fma.f64 (fma.f64 #s(literal 3 binary64) x #s(literal 3 binary64)) x #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 3 x)) |
(fma.f64 #s(literal 3 binary64) x #s(literal 1 binary64)) |
(+ 1 (* x (+ 3 (* 3 x)))) |
(fma.f64 (fma.f64 #s(literal 3 binary64) x #s(literal 3 binary64)) x #s(literal 1 binary64)) |
(+ 1 (* x (+ 3 (* 3 x)))) |
(fma.f64 (fma.f64 #s(literal 3 binary64) x #s(literal 3 binary64)) x #s(literal 1 binary64)) |
1 |
#s(literal 1 binary64) |
(+ 1 (* 4 x)) |
(fma.f64 #s(literal 4 binary64) x #s(literal 1 binary64)) |
(+ 1 (* x (+ 4 (* 4 x)))) |
(fma.f64 (fma.f64 #s(literal 4 binary64) x #s(literal 4 binary64)) x #s(literal 1 binary64)) |
(+ 1 (* x (+ 4 (* 4 x)))) |
(fma.f64 (fma.f64 #s(literal 4 binary64) x #s(literal 4 binary64)) x #s(literal 1 binary64)) |
(/ 1 (+ 1 (sqrt x))) |
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) |
(+ (* x (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (/ 1 (+ 1 (sqrt x)))) |
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(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/8 binary64))) |
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/8 binary64))) |
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2))) |
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/8 binary64))) x) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/8 binary64))) x) |
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) |
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/8 binary64))) x) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) |
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) |
(* 3 (pow x 2)) |
(*.f64 (*.f64 #s(literal 3 binary64) x) x) |
(* (pow x 2) (+ 3 (* 3 (/ 1 x)))) |
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 3 binary64) x) #s(literal 3 binary64)) x) x) |
(* (pow x 2) (+ 3 (+ (* 3 (/ 1 x)) (/ 1 (pow x 2))))) |
(fma.f64 (+.f64 (/.f64 #s(literal 3 binary64) x) #s(literal 3 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(* (pow x 2) (+ 3 (+ (* 3 (/ 1 x)) (/ 1 (pow x 2))))) |
(fma.f64 (+.f64 (/.f64 #s(literal 3 binary64) x) #s(literal 3 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(* 3 (pow x 2)) |
(*.f64 (*.f64 #s(literal 3 binary64) x) x) |
(* (pow x 2) (+ 3 (* 3 (/ 1 x)))) |
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 3 binary64) x) #s(literal 3 binary64)) x) x) |
(* (pow x 2) (+ 3 (+ (* 3 (/ 1 x)) (/ 1 (pow x 2))))) |
(fma.f64 (+.f64 (/.f64 #s(literal 3 binary64) x) #s(literal 3 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(* (pow x 2) (+ 3 (+ (* 3 (/ 1 x)) (/ 1 (pow x 2))))) |
(fma.f64 (+.f64 (/.f64 #s(literal 3 binary64) x) #s(literal 3 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(* 4 (pow x 2)) |
(*.f64 (*.f64 #s(literal 4 binary64) x) x) |
(* (pow x 2) (+ 4 (* 4 (/ 1 x)))) |
(*.f64 (*.f64 (+.f64 (/.f64 #s(literal 4 binary64) x) #s(literal 4 binary64)) x) x) |
(* (pow x 2) (+ 4 (+ (* 4 (/ 1 x)) (/ 1 (pow x 2))))) |
(fma.f64 (+.f64 (/.f64 #s(literal 4 binary64) x) #s(literal 4 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(* (pow x 2) (+ 4 (+ (* 4 (/ 1 x)) (/ 1 (pow x 2))))) |
(fma.f64 (+.f64 (/.f64 #s(literal 4 binary64) x) #s(literal 4 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(/ 3 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) |
(/.f64 #s(literal -3 binary64) #s(literal 0 binary64)) |
(/ (+ (* 3/2 (/ 1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x) |
(/.f64 (-.f64 (/.f64 #s(literal 3/2 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) x) |
(* -1 (/ (- (* -1 (/ (+ (* 3 (/ (+ (* -3/2 (sqrt x)) (* -1/8 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* x (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (/ 1/4 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) |
(neg.f64 (-.f64 (/.f64 (neg.f64 (fma.f64 #s(literal -3 binary64) (/.f64 (*.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) #s(literal 0 binary64)) (+.f64 (/.f64 #s(literal 1/4 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 3/2 binary64) #s(literal 0 binary64))))) (*.f64 x x)) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)))) |
(* -1 (/ (- (* -1 (/ (+ (* -1 (/ (- (+ (* -3/2 (/ (+ (* -3/2 (sqrt x)) (* -1/8 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* x (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* 1/2 (/ (+ (* 3 (/ (+ (* -3/2 (sqrt x)) (* -1/8 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))) (* 1/4 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ (+ (* -1/16 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* 3/4 (sqrt x)) (* 3/2 (sqrt x)))) (* x (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) (+ (* 1/4 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3 (/ (+ (* -3/2 (sqrt x)) (* -1/8 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* 3/2 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) |
(neg.f64 (-.f64 (/.f64 (neg.f64 (-.f64 (/.f64 #s(literal 3/2 binary64) #s(literal 0 binary64)) (/.f64 (-.f64 (fma.f64 (/.f64 (*.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) #s(literal 0 binary64)) #s(literal -3/2 binary64) (fma.f64 (/.f64 (fma.f64 #s(literal -3 binary64) (/.f64 (*.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) #s(literal 0 binary64)) (/.f64 #s(literal 1/4 binary64) #s(literal 0 binary64))) x) #s(literal 1/2 binary64) (*.f64 (*.f64 (/.f64 (sqrt.f64 x) #s(literal 0 binary64)) #s(literal 9/4 binary64)) #s(literal 3 binary64)))) (fma.f64 #s(literal -3 binary64) (/.f64 (*.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) #s(literal 0 binary64)) (/.f64 #s(literal 1/4 binary64) #s(literal 0 binary64)))) x))) (*.f64 x x)) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)))) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64)) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64)) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64)) |
(* 1/16 (sqrt (/ 1 (pow x 3)))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64)) |
(* -1/8 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) |
(* -1/8 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) |
(* -1/8 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) |
(* -1/8 (sqrt (/ 1 x))) |
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) |
(* -1 x) |
(neg.f64 x) |
(* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) |
(-.f64 (neg.f64 x) #s(literal 1/2 binary64)) |
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) |
(fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) x (neg.f64 x)) |
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) |
(fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x)) x) x (neg.f64 x)) |
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) |
(sqrt.f64 (*.f64 (*.f64 x x) x)) |
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) |
(sqrt.f64 (*.f64 (*.f64 x x) x)) |
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) |
(sqrt.f64 (*.f64 (*.f64 x x) x)) |
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) |
(sqrt.f64 (*.f64 (*.f64 x x) x)) |
| 6 544× | lower-fma.f32 |
| 6 534× | lower-fma.f64 |
| 4 072× | lower-*.f32 |
| 4 062× | lower-*.f64 |
| 2 126× | lower-/.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 65 | 274 |
| 0 | 101 | 253 |
| 1 | 497 | 175 |
| 2 | 5159 | 175 |
| 0 | 8147 | 168 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) |
(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x) |
(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) |
(sqrt.f64 x) |
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) #s(literal 0 binary64)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) |
#s(approx (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) |
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(sqrt.f64 (/.f64 #s(literal 1 binary64) x)) |
(-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) |
(*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) #s(literal 1 binary64)) |
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) |
(/.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)))) |
(/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) |
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) |
(sqrt.f64 (fma.f64 x x x)) |
(*.f64 (sqrt.f64 x) x) |
| Outputs |
|---|
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)))) x)) |
(*.f64 (pow.f64 (/.f64 x (-.f64 (*.f64 #s(literal 1/4 binary64) x) (/.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) x) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) x) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x)))) (*.f64 (*.f64 (*.f64 x x) x) x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)))))) |
(*.f64 (pow.f64 (/.f64 x (fma.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 x) x) (pow.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x))) #s(literal 3 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) x (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x))) (-.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))))) |
(*.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x))))) (/.f64 #s(literal 1 binary64) (neg.f64 x))) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x))))) #s(literal -1 binary64))) |
(*.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x))))) |
(*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)))) (/.f64 #s(literal 1 binary64) x)) |
(*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)))) x)) |
(pow.f64 (/.f64 (/.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x))))) #s(literal 1 binary64)) #s(literal -1 binary64)) |
(pow.f64 (/.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x))))) #s(literal -1 binary64)) |
(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) x) (/.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) x) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) x) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x)))) (*.f64 (*.f64 (*.f64 x x) x) x))) (/.f64 #s(literal 1 binary64) x)) (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x))))) |
(/.f64 (*.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 (sqrt.f64 x) x) (pow.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/4 binary64) x (*.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x))) (-.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))) |
(/.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)))) #s(literal -1 binary64)) (neg.f64 x)) |
(/.f64 (*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)))) #s(literal 1 binary64)) x) |
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)))))) (neg.f64 (neg.f64 x))) |
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(/.f64 (*.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) x) (/.f64 (*.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) x) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x))) (fma.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) x) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 x)))) (*.f64 (*.f64 (*.f64 x x) x) x))) #s(literal 1 binary64)) (*.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)))) x)) |
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(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64)) (*.f64 (sqrt.f64 x) x)) |
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) |
(*.f64 (*.f64 (sqrt.f64 x) x) (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64))) |
(*.f64 (sqrt.f64 x) x) |
(*.f64 x (sqrt.f64 x)) |
(pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 2 binary64)) |
(pow.f64 (*.f64 (*.f64 x x) x) #s(literal 1/2 binary64)) |
(pow.f64 (*.f64 x x) #s(literal 3/4 binary64)) |
(pow.f64 (sqrt.f64 x) #s(literal 3 binary64)) |
(pow.f64 x #s(literal 3/2 binary64)) |
(exp.f64 (*.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 3 binary64))) |
(exp.f64 (*.f64 (log.f64 x) #s(literal 3/2 binary64))) |
(exp.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64))) |
Compiled 32 267 to 2 319 computations (92.8% saved)
11 alts after pruning (5 fresh and 6 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 922 | 3 | 925 |
| Fresh | 1 | 2 | 3 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 3 | 3 |
| Total | 925 | 11 | 936 |
| Status | Accuracy | Program |
|---|---|---|
| 41.0% | (/.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 x x x))) (*.f64 (+.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)))) | |
| 51.9% | (/.f64 #s(approx (- (+ 1 x) x) #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)))) (sqrt.f64 x))) | |
| ✓ | 99.6% | (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
| ✓ | 6.0% | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 4.3% | (-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) | |
| 99.0% | #s(approx (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)) | |
| 98.2% | #s(approx (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) | |
| ✓ | 98.1% | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
| ✓ | 98.4% | #s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
| ✓ | 99.3% | #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) |
| ✓ | 3.8% | #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) #s(literal 0 binary64)) |
Compiled 479 to 158 computations (67% saved)
| Inputs |
|---|
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) #s(literal 0 binary64)) |
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 (* (* x x) x))) 1/16) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
#s(approx (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
#s(approx (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
#s(approx (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
(/.f64 #s(approx (- (+ 1 x) x) #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)))) (sqrt.f64 x))) |
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (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)))) (sqrt.f64 x))) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)) |
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)) |
(/.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 x x x))) (*.f64 (+.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)))) |
(/.f64 (*.f64 (-.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 x x x)) #s(literal 1 binary64)) (*.f64 (+.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (*.f64 (sqrt.f64 x) x)))) |
| Outputs |
|---|
(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
2 calls:
| 7.0ms | x |
| 6.0ms | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.6% | 1 | x |
| 99.6% | 1 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
Compiled 10 to 7 computations (30% saved)
| Inputs |
|---|
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) #s(literal 0 binary64)) |
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 (* (* x x) x))) 1/16) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
#s(approx (/ (- (+ 1 x) x) (+ (* (sqrt (+ (* x x) -1)) (sqrt (/ 1 (- x 1)))) (sqrt x))) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) |
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Outputs |
|---|
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
2 calls:
| 53.0ms | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 4.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.4% | 1 | x |
| 98.4% | 1 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
Compiled 10 to 7 computations (30% saved)
| Inputs |
|---|
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) #s(literal 0 binary64)) |
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))) |
| Outputs |
|---|
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
2 calls:
| 3.0ms | x |
| 2.0ms | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.1% | 1 | x |
| 98.1% | 1 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
Compiled 10 to 7 computations (30% saved)
| Inputs |
|---|
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) #s(literal 0 binary64)) |
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Outputs |
|---|
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
2 calls:
| 2.0ms | x |
| 2.0ms | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 4.3% | 1 | x |
| 4.3% | 1 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
Compiled 10 to 7 computations (30% saved)
Total -1.9b remaining (-3.1%)
Threshold costs -1.9b (-3.1%)
| Inputs |
|---|
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) #s(literal 0 binary64)) |
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) |
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) |
| Outputs |
|---|
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) #s(literal 0 binary64)) |
2 calls:
| 2.0ms | x |
| 1.0ms | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 3.8% | 1 | (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) |
| 3.8% | 1 | x |
Compiled 10 to 7 computations (30% saved)
| 1× | egg-herbie |
| 8× | +-commutative_binary64 |
| 4× | *-commutative_binary64 |
| 4× | sub-neg_binary64 |
| 2× | 1-exp_binary64 |
| 2× | neg-sub0_binary64 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 39 | 93 |
| 1 | 46 | 93 |
| 2 | 50 | 93 |
| 3 | 52 | 93 |
| 4 | 53 | 93 |
| 1× | saturated |
| Inputs |
|---|
(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) #s(literal 0 binary64)) |
| Outputs |
|---|
(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) |
(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) |
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) |
#s(approx (/ (- (+ 1 x) x) (+ (sqrt x) (sqrt (+ 1 x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) |
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x)) |
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (* (sqrt (+ 1 x)) (+ 1 x)))) (- (+ (+ 1 x) x) (sqrt (+ (* x x) x)))) #s(literal 0 binary64)) |
| 17 328× | lower-fma.f64 |
| 17 328× | lower-fma.f32 |
| 9 310× | lower-fma.f64 |
| 9 310× | lower-fma.f32 |
| 6 326× | lower-*.f32 |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 45 | 190 |
| 0 | 69 | 183 |
| 1 | 286 | 115 |
| 2 | 2469 | 111 |
| 0 | 9059 | 111 |
| 0 | 465 | 3478 |
| 1 | 1442 | 2884 |
| 2 | 5004 | 2830 |
| 0 | 8208 | 2626 |
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 43 | 16 |
| 2 | 290 | 16 |
| 3 | 3385 | 16 |
| 0 | 8686 | 16 |
| 0 | 113 | 498 |
| 1 | 299 | 446 |
| 2 | 804 | 442 |
| 3 | 2258 | 434 |
| 4 | 4617 | 434 |
| 0 | 8205 | 398 |
| 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 150 to 80 computations (46.7% saved)
Compiled 114 to 66 computations (42.1% saved)
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