
Time bar (total: 11.6s)
| 1× | search |
| Probability | Valid | Unknown | Precondition | Infinite | Domain | Can't | Iter |
|---|---|---|---|---|---|---|---|
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 0 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 1 |
| 0% | 0% | 50.6% | 49.4% | 0% | 0% | 0% | 2 |
| 0% | 0% | 25.3% | 49.4% | 0% | 25.3% | 0% | 3 |
| 0% | 0% | 25.3% | 49.4% | 0% | 25.3% | 0% | 4 |
| 0% | 0% | 19% | 49.4% | 0% | 31.6% | 0% | 5 |
| 0% | 0% | 15.8% | 49.4% | 0% | 34.8% | 0% | 6 |
| 0% | 0% | 11.1% | 49.4% | 0% | 39.5% | 0% | 7 |
| 0% | 0% | 8.7% | 49.4% | 0% | 41.9% | 0% | 8 |
| 0% | 0% | 5.9% | 49.4% | 0% | 44.6% | 0% | 9 |
| 0% | 0% | 4.5% | 49.4% | 0% | 46% | 0% | 10 |
| 0% | 0% | 3.1% | 49.4% | 0% | 47.5% | 0% | 11 |
| 0% | 0% | 2.7% | 49.4% | 0% | 47.9% | 0% | 12 |
Compiled 27 to 19 computations (29.6% saved)
| 3.6s | 25 655× | 0 | invalid |
| 610.0ms | 5 493× | 0 | valid |
| 506.0ms | 2 763× | 1 | valid |
const: 693.0ms (20.6% of total)ival-sin: 640.0ms (19% of total)ival-sub: 432.0ms (12.8% of total)ival-add: 336.0ms (10% of total)ival-fabs: 329.0ms (9.8% of total)ival-mult: 263.0ms (7.8% of total)ival-<: 225.0ms (6.7% of total)ival-<=: 212.0ms (6.3% of total)ival-and: 111.0ms (3.3% of total)adjust: 71.0ms (2.1% of total)exact: 46.0ms (1.4% of total)ival-assert: 13.0ms (0.4% of total)| Ground Truth | Overpredictions | Example | Underpredictions | Example | Subexpression |
|---|---|---|---|---|---|
| 223 | 2 | (1.7546240273162958e-126 6.550519857156619e-129) | 3 | (-3.1523641566605306e-233 5.959924382692986e-235) | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 1 | 0 | - | 0 | - | (sin.f64 (+.f64 x eps)) |
| 0 | 0 | - | 0 | - | eps |
| 0 | 0 | - | 0 | - | (+.f64 x eps) |
| 0 | 0 | - | 0 | - | (sin.f64 x) |
| 0 | 0 | - | 0 | - | x |
| Operator | Subexpression | Explanation | Count | |
|---|---|---|---|---|
-.f64 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) | cancellation | 222 | 9 |
sin.f64 | (sin.f64 (+.f64 x eps)) | sensitivity | 1 | 0 |
| Predicted + | Predicted - | |
|---|---|---|
| + | 220 | 3 |
| - | 2 | 31 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 220 | 3 | 0 |
| - | 2 | 6 | 25 |
| number | freq |
|---|---|
| 0 | 34 |
| 1 | 221 |
| 2 | 1 |
| Predicted + | Predicted Maybe | Predicted - | |
|---|---|---|---|
| + | 1 | 0 | 0 |
| - | 0 | 0 | 0 |
| 24.0ms | 320× | 0 | valid |
| 19.0ms | 184× | 1 | valid |
| 2.0ms | 6× | 3 | valid |
| 0.0ms | 2× | 2 | valid |
Compiled 65 to 28 computations (56.9% saved)
ival-sin: 16.0ms (60% of total)adjust: 4.0ms (15% of total)ival-add: 3.0ms (11.3% of total)ival-sub: 3.0ms (11.3% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 18 | 39 |
| 1 | 38 | 35 |
| 2 | 86 | 35 |
| 3 | 169 | 35 |
| 4 | 310 | 35 |
| 5 | 367 | 35 |
| 6 | 445 | 35 |
| 7 | 482 | 35 |
| 8 | 491 | 35 |
| 0 | 6 | 7 |
| 0 | 10 | 7 |
| 1 | 13 | 7 |
| 2 | 18 | 7 |
| 3 | 24 | 7 |
| 4 | 32 | 7 |
| 5 | 47 | 7 |
| 6 | 80 | 7 |
| 7 | 107 | 7 |
| 8 | 151 | 7 |
| 9 | 166 | 7 |
| 10 | 174 | 7 |
| 0 | 174 | 7 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| 1× | saturated |
| Inputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Outputs |
|---|
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
Compiled 7 to 6 computations (14.3% saved)
Compiled 0 to 2 computations (-∞% saved)
| Status | Accuracy | Program |
|---|---|---|
| ▶ | 61.5% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 7 to 6 computations (14.3% saved)
| 1× | egg-herbie |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (sin.f64 x) | |
| cost-diff | 0 | (+.f64 x eps) | |
| cost-diff | 0 | (sin.f64 (+.f64 x eps)) | |
| cost-diff | 0 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 18 |
| 0 | 10 | 18 |
| 1 | 13 | 18 |
| 2 | 18 | 18 |
| 3 | 24 | 18 |
| 4 | 32 | 18 |
| 5 | 47 | 18 |
| 6 | 80 | 18 |
| 7 | 107 | 18 |
| 8 | 151 | 18 |
| 9 | 166 | 18 |
| 10 | 174 | 18 |
| 0 | 174 | 18 |
| 1× | iter limit |
| 1× | saturated |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
x |
eps |
(sin.f64 x) |
| Outputs |
|---|
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(sin.f64 (+.f64 eps x)) |
(+.f64 eps x) |
x |
eps |
(sin.f64 x) |
Found 4 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0 | (+.f64 x eps) | |
| accuracy | 0 | (sin.f64 x) | |
| accuracy | 0.05680115865370908 | (sin.f64 (+.f64 x eps)) | |
| accuracy | 24.589759804507242 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 9.0ms | 92× | 1 | valid |
| 8.0ms | 160× | 0 | valid |
| 1.0ms | 3× | 3 | valid |
| 0.0ms | 1× | 2 | valid |
Compiled 38 to 14 computations (63.2% saved)
ival-sin: 5.0ms (48.7% of total)adjust: 2.0ms (19.5% of total)ival-add: 2.0ms (19.5% of total)ival-sub: 1.0ms (9.7% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf eps) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sin.f64 (+.f64 x eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sin.f64 x) #<representation binary64>) () ())) ()) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 1.0ms | x | @ | 0 | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x)) |
| 1.0ms | eps | @ | inf | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x)) |
| 1.0ms | eps | @ | 0 | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x)) |
| 1.0ms | eps | @ | -inf | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x)) |
| 0.0ms | x | @ | -inf | ((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) (sin x)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 107 | 496 |
| 1 | 314 | 496 |
| 2 | 775 | 489 |
| 3 | 2829 | 489 |
| 4 | 6198 | 489 |
| 0 | 8140 | 458 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(sin x) |
(+ (sin x) (* eps (cos x))) |
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) |
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) |
x |
(+ eps x) |
(+ eps x) |
(+ eps x) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
eps |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
(* eps (+ 1 (/ x eps))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
(sin (- x (* -1 eps))) |
eps |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(* -1 (* eps (- (* -1 (/ x eps)) 1))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(sin eps) |
(+ (sin eps) (* x (cos eps))) |
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps)))))) |
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))))) |
eps |
(+ eps x) |
(+ eps x) |
(+ eps x) |
x |
(* x (+ 1 (* -1/6 (pow x 2)))) |
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))) |
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
(sin (+ eps x)) |
x |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
(* x (+ 1 (/ eps x))) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
(sin (- eps (* -1 x))) |
x |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(* -1 (* x (- (* -1 (/ eps x)) 1))) |
(sin x) |
(sin x) |
(sin x) |
(sin x) |
| Outputs |
|---|
(*.f64 (cos.f64 x) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (*.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 (*.f64 #s(literal -1/6 binary64) (cos.f64 x)) eps)) eps (cos.f64 x)) eps) |
(sin.f64 x) |
(fma.f64 (cos.f64 x) eps (sin.f64 x)) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps (sin.f64 x)) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps (sin.f64 x)) |
x |
(+.f64 eps x) |
(+.f64 eps x) |
(+.f64 eps x) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(sin.f64 (+.f64 eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin.f64 (+.f64 eps x)) |
eps |
(+.f64 eps x) |
(+.f64 eps x) |
(+.f64 eps x) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(sin.f64 (+.f64 eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin.f64 (+.f64 eps x)) |
eps |
(+.f64 eps x) |
(+.f64 eps x) |
(+.f64 eps x) |
(sin.f64 eps) |
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 eps) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
(sin.f64 eps) |
(fma.f64 (cos.f64 eps) x (sin.f64 eps)) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps)) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) x (sin.f64 eps)) |
eps |
(+.f64 eps x) |
(+.f64 eps x) |
(+.f64 eps x) |
x |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) |
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) (*.f64 x x) #s(literal -1/6 binary64)) x) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(sin.f64 (+.f64 eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin.f64 (+.f64 eps x)) |
x |
(+.f64 eps x) |
(+.f64 eps x) |
(+.f64 eps x) |
(sin.f64 x) |
(sin.f64 x) |
(sin.f64 x) |
(sin.f64 x) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(sin.f64 (+.f64 eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin.f64 (+.f64 eps x)) |
(sin.f64 (+.f64 eps x)) |
x |
(+.f64 eps x) |
(+.f64 eps x) |
(+.f64 eps x) |
(sin.f64 x) |
(sin.f64 x) |
(sin.f64 x) |
(sin.f64 x) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 53 | 16 |
| 2 | 380 | 16 |
| 3 | 4766 | 16 |
| 0 | 8210 | 16 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(sin.f64 (+.f64 x eps)) |
(+.f64 x eps) |
(sin.f64 x) |
| Outputs |
|---|
#<batchref> |
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Compiled 6 965 to 856 computations (87.7% saved)
8 alts after pruning (7 fresh and 1 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 284 | 7 | 291 |
| Fresh | 0 | 0 | 0 |
| Picked | 0 | 1 | 1 |
| Done | 0 | 0 | 0 |
| Total | 284 | 8 | 292 |
| Status | Accuracy | Program |
|---|---|---|
| 61.6% | (fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))) | |
| ✓ | 61.5% | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| ▶ | 99.9% | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
| ▶ | 99.1% | #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) |
| 99.8% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) | |
| ▶ | 99.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) |
| ▶ | 99.4% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
| ▶ | 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
Compiled 237 to 174 computations (26.6% saved)
| 1× | egg-herbie |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 (sin.f64 eps) x) | |
| cost-diff | 0 | (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) | |
| cost-diff | 0 | (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) | |
| cost-diff | 0 | (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) | |
| cost-diff | 0 | (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) | |
| cost-diff | 0 | (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) | |
| cost-diff | 0 | (cos.f64 x) | |
| cost-diff | 0 | (*.f64 (cos.f64 x) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) | |
| cost-diff | 0 | (sin.f64 eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) | |
| cost-diff | 0 | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| cost-diff | 128 | (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) | |
| cost-diff | 192 | (+.f64 #s(literal 0 binary64) eps) | |
| cost-diff | 576 | (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 36 | 203 |
| 0 | 60 | 193 |
| 1 | 99 | 193 |
| 2 | 182 | 193 |
| 3 | 359 | 193 |
| 4 | 629 | 193 |
| 5 | 953 | 193 |
| 6 | 1323 | 193 |
| 7 | 2172 | 193 |
| 8 | 2772 | 193 |
| 9 | 3025 | 190 |
| 10 | 3260 | 190 |
| 11 | 3602 | 190 |
| 12 | 5183 | 190 |
| 13 | 6421 | 190 |
| 0 | 8038 | 188 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) |
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps)) |
#s(literal 1/2 binary64) |
(+.f64 #s(literal 0 binary64) eps) |
#s(literal 0 binary64) |
eps |
#s(literal 2 binary64) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(fma.f64 #s(literal 2 binary64) x eps) |
x |
#s(literal -2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
(sin.f64 eps) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
(*.f64 (cos.f64 x) eps) |
(cos.f64 x) |
x |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) |
(*.f64 (sin.f64 x) #s(literal -1/2 binary64)) |
(sin.f64 x) |
x |
#s(literal -1/2 binary64) |
eps |
(cos.f64 x) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(*.f64 (sin.f64 eps) x) |
(sin.f64 eps) |
eps |
x |
#s(literal -1/2 binary64) |
(-.f64 (cos.f64 eps) #s(literal 1 binary64)) |
(cos.f64 eps) |
#s(literal 1 binary64) |
| Outputs |
|---|
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64))) |
(*.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) #s(literal -2 binary64)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(*.f64 eps #s(literal 1/2 binary64)) |
#s(literal 1/2 binary64) |
eps |
#s(literal 0 binary64) |
eps |
#s(literal 2 binary64) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(neg.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
#s(literal -2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
(sin.f64 eps) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
(*.f64 (cos.f64 x) eps) |
(cos.f64 x) |
x |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(sin.f64 x) |
x |
#s(literal -1/2 binary64) |
eps |
(cos.f64 x) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(*.f64 (sin.f64 eps) x) |
(sin.f64 eps) |
eps |
x |
#s(literal -1/2 binary64) |
(-.f64 (cos.f64 eps) #s(literal 1 binary64)) |
(cos.f64 eps) |
#s(literal 1 binary64) |
Found 17 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.010966230164287516 | (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) | |
| accuracy | 0.1328125 | (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) | |
| accuracy | 0.5985758066975249 | #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) | |
| accuracy | 32.198699648653644 | (-.f64 (cos.f64 eps) #s(literal 1 binary64)) | |
| accuracy | 0 | (cos.f64 x) | |
| accuracy | 0.0078125 | (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) | |
| accuracy | 0.015625 | (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) | |
| accuracy | 0.18366890401871294 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) | |
| accuracy | 0 | (cos.f64 x) | |
| accuracy | 0.0078125 | (*.f64 (cos.f64 x) eps) | |
| accuracy | 0.38891303231774027 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) | |
| accuracy | 0 | (sin.f64 eps) | |
| accuracy | 0.8509012071072087 | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) | |
| accuracy | 0 | (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) | |
| accuracy | 0.00390625 | (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) | |
| accuracy | 0.015625 | (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| accuracy | 0.04875505822121523 | (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
| 177.0ms | 254× | 1 | valid |
| 1.0ms | 2× | 0 | valid |
Compiled 383 to 73 computations (80.9% saved)
ival-cos: 46.0ms (33% of total)ival-mult: 30.0ms (21.5% of total)adjust: 18.0ms (12.9% of total)exact: 16.0ms (11.5% of total)ival-sin: 12.0ms (8.6% of total)ival-add: 10.0ms (7.2% of total)ival-sub: 5.0ms (3.6% of total)ival-div: 2.0ms (1.4% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(alt #<batchref> (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (sin.f64 eps) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (*.f64 (cos.f64 x) eps) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (cos.f64 x) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (*.f64 (sin.f64 eps) x) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (-.f64 (cos.f64 eps) #s(literal 1 binary64)) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (+.f64 #s(literal 0 binary64) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (sin.f64 eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (sin.f64 eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (sin.f64 eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (sin.f64 eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (cos.f64 x) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (cos.f64 x) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (cos.f64 x) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (cos.f64 x) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (sin.f64 eps) x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (sin.f64 eps) x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (sin.f64 eps) x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (sin.f64 eps) x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #<representation binary64>) () ())) ()) |
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#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) #<representation binary64>) () ())) ()) |
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#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (sin.f64 eps) x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (sin.f64 eps) x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (sin.f64 eps) x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (sin.f64 eps) x) #<representation binary64>) () ())) ()) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 8.0ms | eps | @ | inf | ((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- (cos eps) 1)) |
| 5.0ms | eps | @ | 0 | ((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- (cos eps) 1)) |
| 5.0ms | x | @ | 0 | ((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- (cos eps) 1)) |
| 4.0ms | x | @ | inf | ((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- (cos eps) 1)) |
| 4.0ms | x | @ | -inf | ((/ (+ (* 2 x) eps) -2) (+ 0 eps) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (- (cos eps) 1)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 408 | 3712 |
| 1 | 1248 | 3510 |
| 2 | 3420 | 3428 |
| 0 | 8203 | 3203 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* -1 x) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1 x) (* -1/2 eps)) |
eps |
eps |
eps |
eps |
(cos (* -1 x)) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(* eps (cos (* -1 x))) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
eps |
(* eps (+ 1 (* -1/6 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))) |
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))) |
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6))))))) |
(* -1/2 (* eps x)) |
(* eps (+ (* -1/2 eps) (* -1/2 x))) |
(* eps (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2)))) |
(* eps (+ (* -1/2 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/12 x))) 1/2)))) |
(* eps x) |
(* eps (+ x (* -1/6 (* (pow eps 2) x)))) |
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* 1/120 (* (pow eps 2) x)))))) |
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) x)) (* 1/120 x))))))) |
eps |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
(* 1/2 eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(* -1/2 (pow eps 2)) |
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)) |
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2)) |
(* -1/2 eps) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
eps |
eps |
eps |
eps |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1) |
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1) |
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1) |
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1) |
(* x (sin eps)) |
(* x (sin eps)) |
(* x (sin eps)) |
(* x (sin eps)) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(- (cos eps) 1) |
(- (cos eps) 1) |
(- (cos eps) 1) |
(- (cos eps) 1) |
(* -1/2 eps) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
eps |
eps |
eps |
eps |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(sin eps) |
(sin eps) |
(sin eps) |
(sin eps) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1) |
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1) |
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1) |
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1) |
(* x (sin eps)) |
(* x (sin eps)) |
(* x (sin eps)) |
(* x (sin eps)) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(- (cos eps) 1) |
(- (cos eps) 1) |
(- (cos eps) 1) |
(- (cos eps) 1) |
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1 x) (* -1/2 eps)) |
(cos (* -1/2 eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
1 |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(* -1/2 x) |
(* x (- (* 1/12 (pow x 2)) 1/2)) |
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) |
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2)) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(- (cos eps) 1) |
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1) |
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1) |
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1) |
(* x (sin eps)) |
(* x (sin eps)) |
(* x (sin eps)) |
(* x (sin eps)) |
(* -1 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* -1/2 (* (pow x 2) (sin eps))) |
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x))) |
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x))) |
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x))) |
(* -1/2 (* x (sin eps))) |
(* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x))) |
(* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x))) |
(* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x))) |
(* x (sin eps)) |
(* x (sin eps)) |
(* x (sin eps)) |
(* x (sin eps)) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* -1/2 (* (pow x 2) (sin eps))) |
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps)))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps)))) |
(* -1/2 (* x (sin eps))) |
(* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps))))) |
(* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps))))) |
(* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps))))) |
(* x (sin eps)) |
(* x (sin eps)) |
(* x (sin eps)) |
(* x (sin eps)) |
| Outputs |
|---|
(neg.f64 x) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
eps |
eps |
eps |
eps |
(cos.f64 x) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/8 binary64))) eps (cos.f64 x)) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) eps) (cos.f64 x) (*.f64 (neg.f64 (sin.f64 x)) (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)))) eps (cos.f64 x)) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/24 binary64) eps) (neg.f64 (sin.f64 x)) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)))) eps (cos.f64 x)) eps) |
eps |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64)) eps) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64)) (*.f64 eps eps) #s(literal -1/6 binary64)) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)))) eps (cos.f64 x)) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)))) eps (cos.f64 x)) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(cos.f64 x) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) (cos.f64 x) (*.f64 (sin.f64 x) (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)))) eps (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) |
(*.f64 (fma.f64 (*.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps) |
(*.f64 (fma.f64 (*.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) (fma.f64 (*.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps) |
(*.f64 (fma.f64 (*.f64 (fma.f64 x (fma.f64 #s(literal 1/12 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) #s(literal -1/6 binary64)) eps) eps (fma.f64 (*.f64 x (+.f64 eps x)) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) |
(*.f64 (*.f64 eps x) #s(literal -1/2 binary64)) |
(*.f64 (*.f64 eps (+.f64 eps x)) #s(literal -1/2 binary64)) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (*.f64 eps x) #s(literal -1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x)) eps) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) x (*.f64 #s(literal 1/24 binary64) eps)) eps #s(literal -1/2 binary64)) eps (*.f64 #s(literal -1/2 binary64) x)) eps) |
(*.f64 eps x) |
(*.f64 x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)) |
(*.f64 (fma.f64 (*.f64 x (fma.f64 #s(literal 1/120 binary64) (*.f64 eps eps) #s(literal -1/6 binary64))) (*.f64 eps eps) x) eps) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (*.f64 (*.f64 x (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64))) eps) eps (*.f64 #s(literal -1/6 binary64) x)) (*.f64 eps x)) |
eps |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/1920 binary64) (*.f64 eps eps) #s(literal -1/24 binary64)) eps) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal -1/24 binary64)) eps) |
(*.f64 #s(literal 1/2 binary64) eps) |
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(*.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) |
(*.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/24 binary64) eps) eps #s(literal -1/2 binary64)) eps) eps) |
(*.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps) |
(*.f64 (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (*.f64 eps eps) #s(literal -1/720 binary64)) (*.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps) |
(*.f64 #s(literal -1/2 binary64) eps) |
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps) |
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps) |
(*.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 x eps)) eps) |
eps |
eps |
eps |
eps |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
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(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(cos.f64 x) |
(cos.f64 x) |
(cos.f64 x) |
(cos.f64 x) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(*.f64 (*.f64 (*.f64 (sin.f64 eps) x) x) #s(literal -1/2 binary64)) |
(*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) (*.f64 x x)) |
(*.f64 (+.f64 (/.f64 (/.f64 (sin.f64 eps) x) x) (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x))) (*.f64 x x)) |
(*.f64 (+.f64 (/.f64 (/.f64 (sin.f64 eps) x) x) (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x))) (*.f64 x x)) |
(*.f64 (*.f64 (sin.f64 eps) #s(literal -1/2 binary64)) x) |
(*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) x) |
(*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) x) |
(*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) x) |
(*.f64 (sin.f64 eps) x) |
(*.f64 (sin.f64 eps) x) |
(*.f64 (sin.f64 eps) x) |
(*.f64 (sin.f64 eps) x) |
(neg.f64 x) |
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x)) |
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x)) |
(*.f64 (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x)) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(cos.f64 x) |
(cos.f64 x) |
(cos.f64 x) |
(cos.f64 x) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(*.f64 (*.f64 (*.f64 (sin.f64 eps) x) x) #s(literal -1/2 binary64)) |
(*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) (*.f64 x x)) |
(*.f64 (*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) x))) x)) x) x) |
(*.f64 (*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) x))) x)) x) x) |
(*.f64 (*.f64 (sin.f64 eps) #s(literal -1/2 binary64)) x) |
(*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) x) |
(*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) x) |
(*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) x) |
(*.f64 (sin.f64 eps) x) |
(*.f64 (sin.f64 eps) x) |
(*.f64 (sin.f64 eps) x) |
(*.f64 (sin.f64 eps) x) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 36 | 170 |
| 0 | 60 | 162 |
| 1 | 210 | 162 |
| 2 | 1636 | 162 |
| 0 | 8543 | 162 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(+.f64 #s(literal 0 binary64) eps) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
(sin.f64 eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
(*.f64 (cos.f64 x) eps) |
(cos.f64 x) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) |
(*.f64 (sin.f64 x) #s(literal -1/2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) |
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)) |
(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) |
(*.f64 (sin.f64 eps) x) |
(*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) |
(sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) |
(-.f64 (cos.f64 eps) #s(literal 1 binary64)) |
| Outputs |
|---|
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Compiled 23 664 to 2 152 computations (90.9% saved)
14 alts after pruning (12 fresh and 2 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 805 | 10 | 815 |
| Fresh | 0 | 2 | 2 |
| Picked | 3 | 2 | 5 |
| Done | 1 | 0 | 1 |
| Total | 809 | 14 | 823 |
| Status | Accuracy | Program |
|---|---|---|
| 61.6% | (fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))) | |
| ▶ | 99.9% | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
| 99.9% | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| 99.7% | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| 99.8% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) | |
| ▶ | 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) |
| 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) | |
| ✓ | 99.4% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
| ▶ | 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
| ▶ | 99.1% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
| 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) | |
| ✓ | 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
| ▶ | 99.1% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) |
| 99.1% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps))) |
Compiled 594 to 415 computations (30.1% saved)
| 1× | egg-herbie |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) | |
| cost-diff | 0 | (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) | |
| cost-diff | 0 | (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) | |
| cost-diff | 0 | (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) | |
| cost-diff | 0 | (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) | |
| cost-diff | 0 | (*.f64 #s(literal -1/2 binary64) x) | |
| cost-diff | 0 | (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps) | |
| cost-diff | 0 | #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps)) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) | |
| cost-diff | 0 | #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) | |
| cost-diff | 0 | (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) | |
| cost-diff | 0 | (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) | |
| cost-diff | 0 | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| cost-diff | 128 | (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) | |
| cost-diff | 576 | (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 59 | 462 |
| 0 | 93 | 456 |
| 1 | 160 | 456 |
| 2 | 419 | 456 |
| 3 | 1065 | 456 |
| 4 | 1855 | 456 |
| 5 | 2397 | 456 |
| 6 | 2449 | 456 |
| 7 | 2682 | 456 |
| 8 | 2697 | 456 |
| 9 | 2732 | 456 |
| 10 | 2955 | 456 |
| 11 | 3167 | 456 |
| 12 | 3259 | 456 |
| 13 | 3725 | 456 |
| 14 | 5466 | 456 |
| 15 | 6535 | 456 |
| 16 | 7250 | 453 |
| 17 | 7582 | 453 |
| 18 | 7820 | 453 |
| 0 | 8016 | 446 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) |
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) |
#s(literal 1/3840 binary64) |
(*.f64 eps eps) |
eps |
#s(literal -1/48 binary64) |
#s(literal 1/2 binary64) |
#s(literal 2 binary64) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(fma.f64 #s(literal 2 binary64) x eps) |
x |
#s(literal -2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) |
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) |
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps)) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps) |
(*.f64 #s(literal -1/2 binary64) x) |
#s(literal -1/2 binary64) |
x |
(*.f64 eps (+.f64 eps x)) |
eps |
(+.f64 eps x) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) |
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) |
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) |
#s(literal -1/720 binary64) |
(*.f64 x x) |
x |
#s(literal 1/24 binary64) |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) |
(*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) |
(fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) |
#s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x) |
(fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) |
(*.f64 #s(literal 1/12 binary64) x) |
#s(literal 1/12 binary64) |
x |
#s(literal -1/2 binary64) |
eps |
(cos.f64 x) |
| Outputs |
|---|
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) |
(*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) |
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) |
#s(literal 1/3840 binary64) |
(*.f64 eps eps) |
eps |
#s(literal -1/48 binary64) |
#s(literal 1/2 binary64) |
#s(literal 2 binary64) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(neg.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
#s(literal -2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) |
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) |
#s(literal 1 binary64) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 (+.f64 x eps) eps) (*.f64 #s(literal -1/2 binary64) x) eps))) |
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 (+.f64 x eps) eps) (*.f64 #s(literal -1/2 binary64) x) eps)) |
(fma.f64 (*.f64 (+.f64 x eps) eps) (*.f64 #s(literal -1/2 binary64) x) eps) |
(*.f64 #s(literal -1/2 binary64) x) |
#s(literal -1/2 binary64) |
x |
(*.f64 (+.f64 x eps) eps) |
eps |
(+.f64 x eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) |
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
(fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) |
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) |
#s(literal -1/720 binary64) |
(*.f64 x x) |
x |
#s(literal 1/24 binary64) |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) |
(*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) |
(fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) |
#s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) |
(*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x) |
(fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) |
(*.f64 #s(literal 1/12 binary64) x) |
#s(literal 1/12 binary64) |
x |
#s(literal -1/2 binary64) |
eps |
(cos.f64 x) |
Found 19 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.015625 | (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) | |
| accuracy | 0.18366890401871294 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) | |
| accuracy | 0.3046875 | (*.f64 #s(literal 1/12 binary64) x) | |
| accuracy | 0.566453844697995 | #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) | |
| accuracy | 0.00390625 | (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) | |
| accuracy | 0.0078125 | (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) | |
| accuracy | 0.38891303231774027 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) | |
| accuracy | 0.41589847005492536 | #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) | |
| accuracy | 0.010966230164287516 | (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps) | |
| accuracy | 0.15625 | (*.f64 eps (+.f64 eps x)) | |
| accuracy | 0.18366890401871294 | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) | |
| accuracy | 0.5985758196193748 | #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps)) | |
| accuracy | 0.015625 | (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) | |
| accuracy | 0.18366890401871294 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) | |
| accuracy | 0.8601965047147168 | #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) | |
| accuracy | 0 | #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) | |
| accuracy | 0.00390625 | (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) | |
| accuracy | 0.015625 | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| accuracy | 0.04875505822121523 | (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
| 89.0ms | 92× | 1 | valid |
| 66.0ms | 164× | 0 | valid |
Compiled 749 to 117 computations (84.4% saved)
ival-mult: 42.0ms (40.7% of total)const: 17.0ms (16.5% of total)ival-add: 16.0ms (15.5% of total)ival-sin: 11.0ms (10.7% of total)adjust: 9.0ms (8.7% of total)ival-cos: 4.0ms (3.9% of total)ival-div: 2.0ms (1.9% of total)ival-sub: 1.0ms (1% of total)exact: 1.0ms (1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(alt #<batchref> (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (*.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (*.f64 eps (+.f64 eps x)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (*.f64 #s(literal 1/12 binary64) x) #<representation binary64>) () ()) |
| Outputs |
|---|
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor 0 eps) (#s(alt #<batchref> (patch (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) #<representation binary64>) () ())) ()) |
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#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 eps (+.f64 eps x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 eps (+.f64 eps x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 eps (+.f64 eps x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 eps (+.f64 eps x)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/12 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/12 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/12 binary64) x) #<representation binary64>) () ())) ()) |
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/12 binary64) x) #<representation binary64>) () ())) ()) |
6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 8.0ms | x | @ | -inf | ((/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (sin (* 1/2 (+ 0 eps))) (* eps (+ eps x)) (+ (* -1/720 (* x x)) 1/24) (* 1/12 x)) |
| 7.0ms | x | @ | inf | ((/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (sin (* 1/2 (+ 0 eps))) (* eps (+ eps x)) (+ (* -1/720 (* x x)) 1/24) (* 1/12 x)) |
| 3.0ms | eps | @ | -inf | ((/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (sin (* 1/2 (+ 0 eps))) (* eps (+ eps x)) (+ (* -1/720 (* x x)) 1/24) (* 1/12 x)) |
| 3.0ms | eps | @ | inf | ((/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (sin (* 1/2 (+ 0 eps))) (* eps (+ eps x)) (+ (* -1/720 (* x x)) 1/24) (* 1/12 x)) |
| 2.0ms | eps | @ | 0 | ((/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (* -1/2 x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (+ (* (+ (* -1/720 (* x x)) 1/24) (* x x)) -1/2) (* x x)) 1) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (sin (* 1/2 (+ 0 eps))) (* eps (+ eps x)) (+ (* -1/720 (* x x)) 1/24) (* 1/12 x)) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 360 | 4368 |
| 1 | 1084 | 4128 |
| 2 | 2917 | 4025 |
| 3 | 7082 | 4025 |
| 0 | 8232 | 3767 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* -1 x) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1 x) (* -1/2 eps)) |
(cos (* -1 x)) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(* eps (cos (* -1 x))) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
eps |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ 1 (* -1/2 (pow x 2)))) |
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))) |
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))) |
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* 1/2 eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(* eps x) |
(* eps (+ eps x)) |
(* eps (+ eps x)) |
(* eps (+ eps x)) |
(* -1/2 eps) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps)))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(pow eps 2) |
(* (pow eps 2) (+ 1 (/ x eps))) |
(* (pow eps 2) (+ 1 (/ x eps))) |
(* (pow eps 2) (+ 1 (/ x eps))) |
(* -1/2 eps) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* (pow eps 2) x)) |
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x))) |
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x))) |
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(pow eps 2) |
(* (pow eps 2) (+ 1 (/ x eps))) |
(* (pow eps 2) (+ 1 (/ x eps))) |
(* (pow eps 2) (+ 1 (/ x eps))) |
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1 x) (* -1/2 eps)) |
(cos (* -1/2 eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
1 |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
1 |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(* -1/2 x) |
(* x (- (* 1/12 (pow x 2)) 1/2)) |
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) |
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2)) |
(pow eps 2) |
(+ (* eps x) (pow eps 2)) |
(+ (* eps x) (pow eps 2)) |
(+ (* eps x) (pow eps 2)) |
1/24 |
(+ 1/24 (* -1/720 (pow x 2))) |
(+ 1/24 (* -1/720 (pow x 2))) |
(+ 1/24 (* -1/720 (pow x 2))) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* -1 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* -1/2 (* eps (pow x 2))) |
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x)))) |
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2))))) |
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2))))) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(* -1/720 (pow x 6)) |
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720)) |
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4))))) |
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4))))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* eps x) |
(* x (+ eps (/ (pow eps 2) x))) |
(* x (+ eps (/ (pow eps 2) x))) |
(* x (+ eps (/ (pow eps 2) x))) |
(* -1/720 (pow x 2)) |
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720)) |
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720)) |
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720)) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* -1/2 (* eps (pow x 2))) |
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x)))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps))) |
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps))) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(* -1/2 x) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(* -1/720 (pow x 6)) |
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720)) |
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4))))) |
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4))))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* eps x) |
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x))))) |
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x))))) |
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x))))) |
(* -1/720 (pow x 2)) |
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720)) |
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720)) |
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720)) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
(* 1/12 x) |
| Outputs |
|---|
(neg.f64 x) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(cos.f64 x) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/8 binary64))) eps (cos.f64 x)) |
(fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) (*.f64 (*.f64 (cos.f64 x) eps) #s(literal -1/8 binary64))) eps (cos.f64 x)) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/24 binary64) eps) (neg.f64 (sin.f64 x)) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
eps |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/1920 binary64) (*.f64 eps eps) #s(literal -1/24 binary64)) eps) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal -1/24 binary64)) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps))) eps (cos.f64 x)) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(cos.f64 x) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
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(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(*.f64 eps x) |
(*.f64 (fma.f64 eps (/.f64 eps x) eps) x) |
(*.f64 (fma.f64 eps (/.f64 eps x) eps) x) |
(*.f64 (fma.f64 eps (/.f64 eps x) eps) x) |
(*.f64 #s(literal -1/720 binary64) (*.f64 x x)) |
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/720 binary64)) x) x) |
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/720 binary64)) x) x) |
(*.f64 (*.f64 (-.f64 (/.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/720 binary64)) x) x) |
(*.f64 #s(literal 1/12 binary64) x) |
(*.f64 #s(literal 1/12 binary64) x) |
(*.f64 #s(literal 1/12 binary64) x) |
(*.f64 #s(literal 1/12 binary64) x) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 59 | 370 |
| 0 | 93 | 364 |
| 1 | 342 | 364 |
| 2 | 2873 | 364 |
| 0 | 8729 | 359 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
(*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps) |
#s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) |
#s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps)) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps) |
(*.f64 #s(literal -1/2 binary64) x) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps) |
#s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) |
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) |
(*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps) |
(fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) |
#s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) |
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(*.f64 eps (+.f64 eps x)) |
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) |
(*.f64 #s(literal 1/12 binary64) x) |
| Outputs |
|---|
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Compiled 35 984 to 2 865 computations (92% saved)
15 alts after pruning (10 fresh and 5 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 943 | 3 | 946 |
| Fresh | 0 | 7 | 7 |
| Picked | 2 | 3 | 5 |
| Done | 0 | 2 | 2 |
| Total | 945 | 15 | 960 |
| Status | Accuracy | Program |
|---|---|---|
| 61.6% | (fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))) | |
| ▶ | 99.9% | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
| ▶ | 99.9% | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
| 99.7% | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| 99.8% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) | |
| ✓ | 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) |
| ▶ | 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
| ✓ | 99.4% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
| ✓ | 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
| ✓ | 99.1% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
| ▶ | 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
| ✓ | 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
| 99.1% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) x) #s(literal -1/2 binary64) eps))) | |
| 98.6% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) eps (/.f64 #s(literal -1 binary64) x))) (neg.f64 x))) x) x)))) | |
| ▶ | 99.1% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps))) |
Compiled 631 to 438 computations (30.6% saved)
| 1× | egg-herbie |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| cost-diff | 0 | (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) | |
| cost-diff | 0 | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| cost-diff | 128 | (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) | |
| cost-diff | 576 | (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) | |
| cost-diff | 0 | #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) | |
| cost-diff | 0 | (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) | |
| cost-diff | 0 | (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) | |
| cost-diff | 0 | (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) | |
| cost-diff | 0 | (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps) | |
| cost-diff | 0 | #s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps))) | |
| cost-diff | 0 | (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) | |
| cost-diff | 0 | #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) | |
| cost-diff | 0 | (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) | |
| cost-diff | 0 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) | |
| cost-diff | 0 | (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) | |
| cost-diff | 0 | #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) | |
| cost-diff | 0 | (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) | |
| cost-diff | 0 | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 59 | 441 |
| 0 | 93 | 428 |
| 1 | 162 | 428 |
| 2 | 366 | 428 |
| 3 | 789 | 428 |
| 4 | 1284 | 428 |
| 5 | 1506 | 428 |
| 6 | 1744 | 428 |
| 7 | 3139 | 428 |
| 8 | 4933 | 423 |
| 9 | 6413 | 423 |
| 10 | 7842 | 423 |
| 0 | 8103 | 421 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) |
(fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) |
#s(literal 1/3840 binary64) |
(*.f64 eps eps) |
eps |
#s(literal -1/48 binary64) |
#s(literal 1/2 binary64) |
#s(literal 2 binary64) |
(cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) |
#s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
#s(literal -1/2 binary64) |
(neg.f64 x) |
x |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) |
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(*.f64 x x) |
x |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps))) |
#s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)) |
(fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps) |
(*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) |
eps |
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) |
(*.f64 x x) |
x |
#s(literal 1/24 binary64) |
#s(literal -1/2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
(*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps) |
(fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) |
#s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) |
(*.f64 #s(literal -1/2 binary64) x) |
#s(literal -1/2 binary64) |
x |
eps |
(cos.f64 x) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) |
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps) |
(fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) |
(*.f64 eps eps) |
eps |
#s(literal -1/48 binary64) |
#s(literal 1/2 binary64) |
#s(literal 2 binary64) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(fma.f64 #s(literal 2 binary64) x eps) |
x |
#s(literal -2 binary64) |
| Outputs |
|---|
(*.f64 (*.f64 (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) #s(literal 2 binary64)) |
(*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))) |
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) |
(fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) |
#s(literal 1/3840 binary64) |
(*.f64 eps eps) |
eps |
#s(literal -1/48 binary64) |
#s(literal 1/2 binary64) |
#s(literal 2 binary64) |
(cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) |
#s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
#s(literal -1/2 binary64) |
(neg.f64 x) |
x |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) |
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
(*.f64 x x) |
x |
#s(literal -1/2 binary64) |
#s(literal 1 binary64) |
eps |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps) (*.f64 x x) eps))) |
#s(approx (* (cos x) eps) (fma.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps) (*.f64 x x) eps)) |
(fma.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps) (*.f64 x x) eps) |
(*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps) |
eps |
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) |
(*.f64 x x) |
x |
#s(literal 1/24 binary64) |
#s(literal -1/2 binary64) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
(*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps) |
(fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) |
#s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) |
(*.f64 #s(literal -1/2 binary64) x) |
#s(literal -1/2 binary64) |
x |
eps |
(cos.f64 x) |
(*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64))) |
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) |
(*.f64 eps eps) |
eps |
#s(literal -1/48 binary64) |
#s(literal 1/2 binary64) |
#s(literal 2 binary64) |
(cos.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(fma.f64 x #s(literal 2 binary64) eps) |
x |
#s(literal -2 binary64) |
Found 20 expressions of interest:
| New | Metric | Score | Program |
|---|---|---|---|
| accuracy | 0.00390625 | (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) | |
| accuracy | 0.015625 | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) | |
| accuracy | 0.04577050002276424 | #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) | |
| accuracy | 0.04875505822121523 | (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) | |
| accuracy | 0.0078125 | (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) | |
| accuracy | 0.015625 | (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps) | |
| accuracy | 0.18366890401871294 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) | |
| accuracy | 0.8345237836252916 | #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) | |
| accuracy | 0.00390625 | (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps) | |
| accuracy | 0.01171875 | (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) | |
| accuracy | 0.38891303231774027 | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps))) | |
| accuracy | 0.4204273135457654 | #s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)) | |
| accuracy | 0.00390625 | (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) | |
| accuracy | 0.0078125 | (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) | |
| accuracy | 0.38891303231774027 | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) | |
| accuracy | 0.6089654611268476 | #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) | |
| accuracy | 0 | #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) | |
| accuracy | 0.00390625 | (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) | |
| accuracy | 0.015625 | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) | |
| accuracy | 0.04875505822121523 | (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) |
| 76.0ms | 92× | 1 | valid |
| 62.0ms | 164× | 0 | valid |
Compiled 736 to 116 computations (84.2% saved)
ival-mult: 40.0ms (43.1% of total)ival-add: 15.0ms (16.2% of total)const: 11.0ms (11.8% of total)adjust: 8.0ms (8.6% of total)ival-sin: 6.0ms (6.5% of total)ival-cos: 6.0ms (6.5% of total)ival-div: 2.0ms (2.2% of total)ival-sub: 1.0ms (1.1% of total)exact: 1.0ms (1.1% of total)ival-neg: 1.0ms (1.1% of total)ival-assert: 0.0ms (0% of total)ival-true: 0.0ms (0% of total)| Inputs |
|---|
#s(alt #<batchref> (patch (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) #<representation binary64>) () ()) |
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#s(alt #<batchref> (patch (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ()) |
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#s(alt #<batchref> (patch (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #<representation binary64>) () ()) |
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#s(alt #<batchref> (patch (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) #<representation binary64>) () ()) |
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#s(alt #<batchref> (patch (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) #<representation binary64>) () ()) |
#s(alt #<batchref> (patch (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) #<representation binary64>) () ()) |
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| Outputs |
|---|
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6 calls:
| Time | Variable | Point | Expression | |
|---|---|---|---|---|
| 4.0ms | eps | @ | -inf | ((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* eps (+ (* (* x x) 1/24) -1/2)) (* x x)) eps) (* eps (+ (* (* x x) 1/24) -1/2)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2)) (sin (* 1/2 (+ 0 eps)))) |
| 4.0ms | eps | @ | inf | ((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* eps (+ (* (* x x) 1/24) -1/2)) (* x x)) eps) (* eps (+ (* (* x x) 1/24) -1/2)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2)) (sin (* 1/2 (+ 0 eps)))) |
| 4.0ms | eps | @ | 0 | ((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* eps (+ (* (* x x) 1/24) -1/2)) (* x x)) eps) (* eps (+ (* (* x x) 1/24) -1/2)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2)) (sin (* 1/2 (+ 0 eps)))) |
| 3.0ms | x | @ | inf | ((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* eps (+ (* (* x x) 1/24) -1/2)) (* x x)) eps) (* eps (+ (* (* x x) 1/24) -1/2)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2)) (sin (* 1/2 (+ 0 eps)))) |
| 2.0ms | x | @ | -inf | ((* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (sin (* 1/2 (+ 0 eps))) (* (+ (* (+ (* 1/3840 (* eps eps)) -1/48) (* eps eps)) 1/2) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* eps (+ (* (* x x) 1/24) -1/2)) (* x x)) eps) (* eps (+ (* (* x x) 1/24) -1/2)) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (+ (* (* (sin x) -1/2) eps) (cos x)) (* (sin x) -1/2) (/ (+ (* 2 x) eps) -2) (cos (/ (+ (* 2 x) eps) -2)) (* (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (* 1/2 (+ 0 eps))) 2) (cos (/ (+ (* 2 x) eps) -2)) (sin (* 1/2 (+ 0 eps)))) |
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 339 | 4268 |
| 1 | 1008 | 3971 |
| 2 | 2715 | 3878 |
| 3 | 6362 | 3878 |
| 0 | 8411 | 3638 |
| 1× | iter limit |
| 1× | node limit |
| Inputs |
|---|
(* eps (cos (* -1 x))) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
eps |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
(* 1/2 eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(* 1/2 eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))) |
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))) |
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))) |
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))) |
(* eps (- (* 1/24 (pow x 2)) 1/2)) |
(* eps (- (* 1/24 (pow x 2)) 1/2)) |
(* eps (- (* 1/24 (pow x 2)) 1/2)) |
(* eps (- (* 1/24 (pow x 2)) 1/2)) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))) |
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))) |
(* eps (cos x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(cos x) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* -1 x) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1 x) (* -1/2 eps)) |
(cos (* -1 x)) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(* eps (cos (* -1 x))) |
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))) |
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))) |
eps |
(* eps (+ 1 (* -1/24 (pow eps 2)))) |
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24)))) |
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24)))) |
(cos (* -1 x)) |
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))) |
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x)))))) |
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x)))))) |
(* 1/2 eps) |
(* eps (+ 1/2 (* -1/48 (pow eps 2)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))) |
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(* 1/3840 (pow eps 5)) |
(* (pow eps 5) (- 1/3840 (* 1/48 (/ 1 (pow eps 2))))) |
(* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2))))) |
(* (pow eps 5) (- (+ 1/3840 (/ 1/2 (pow eps 4))) (* 1/48 (/ 1 (pow eps 2))))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))) |
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))) |
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))) |
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))) |
(* eps (- (* 1/24 (pow x 2)) 1/2)) |
(* eps (- (* 1/24 (pow x 2)) 1/2)) |
(* eps (- (* 1/24 (pow x 2)) 1/2)) |
(* eps (- (* 1/24 (pow x 2)) 1/2)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 eps) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(* eps (- (* -1 (/ x eps)) 1/2)) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(* 1/3840 (pow eps 5)) |
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) 1/3840))) |
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4)))))) |
(* -1 (* (pow eps 5) (- (* 1/48 (/ 1 (pow eps 2))) (+ 1/3840 (/ 1/2 (pow eps 4)))))) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1))) |
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1))) |
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1))) |
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1))) |
(* eps (- (* 1/24 (pow x 2)) 1/2)) |
(* eps (- (* 1/24 (pow x 2)) 1/2)) |
(* eps (- (* 1/24 (pow x 2)) 1/2)) |
(* eps (- (* 1/24 (pow x 2)) 1/2)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(- (sin (- x (* -1 eps))) (sin x)) |
(* -1/2 (* (pow eps 2) (sin x))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps))) |
(* -1/2 (* eps (sin x))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))))) |
(* -1/2 eps) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(* -1 (* eps (+ 1/2 (/ x eps)))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(* 2 (sin (* 1/2 eps))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(cos (* -1/2 (- (* 2 x) (* -1 eps)))) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(sin (* 1/2 eps)) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) |
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) |
1 |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* -1/2 (pow x 2))) |
(+ 1 (* -1/2 (pow x 2))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps)))))) |
eps |
(+ eps (* -1/2 (* eps (pow x 2)))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))))) |
(* -1/2 eps) |
(+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))) |
(+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))) |
(+ (* -1/2 eps) (* 1/24 (* eps (pow x 2)))) |
(sin eps) |
(+ (sin eps) (* x (- (cos eps) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1))) |
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1))) |
eps |
(+ eps (* -1/2 (* (pow eps 2) x))) |
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))) |
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x))))))) |
1 |
(+ 1 (* -1/2 (* eps x))) |
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x)))) |
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2))))) |
(* -1/2 x) |
(* x (- (* 1/12 (pow x 2)) 1/2)) |
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2)) |
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2)) |
(* -1/2 eps) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1 x) (* -1/2 eps)) |
(+ (* -1 x) (* -1/2 eps)) |
(cos (* -1/2 eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) |
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))) |
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))))) |
(cos (* -1/2 eps)) |
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps)))) |
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps)))))) |
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps)))))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* 1/24 (* eps (pow x 4))) |
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps))) |
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4))))) |
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4))))) |
(* 1/24 (* eps (pow x 2))) |
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps))) |
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps))) |
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps))) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(- (sin (+ eps x)) (sin x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1 x) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(* x (- (* -1/2 (/ eps x)) 1)) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(cos (* -1/2 (+ eps (* 2 x)))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(cos x) |
(cos x) |
(cos x) |
(cos x) |
(* -1/2 (pow x 2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* eps (cos x)) |
(* 1/24 (* eps (pow x 4))) |
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps))) |
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4))))) |
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4))))) |
(* 1/24 (* eps (pow x 2))) |
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps))) |
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps))) |
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps))) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(- (sin (- eps (* -1 x))) (sin x)) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(* eps (+ (cos x) (* -1/2 (* eps (sin x))))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(+ (cos x) (* -1/2 (* eps (sin x)))) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1/2 (sin x)) |
(* -1 x) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(* -1 (* x (+ 1 (* 1/2 (/ eps x))))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(cos (* -1/2 (- eps (* -2 x)))) |
(cos (* -1/2 (- eps (* -2 x)))) |
| Outputs |
|---|
(*.f64 (cos.f64 x) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/24 binary64) eps) (neg.f64 (sin.f64 x)) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
eps |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/1920 binary64) (*.f64 eps eps) #s(literal -1/24 binary64)) eps) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal -1/24 binary64)) eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(*.f64 eps #s(literal 1/2 binary64)) |
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps))) eps (cos.f64 x)) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps))) eps (cos.f64 x)) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps) |
(*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps) |
(*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps) |
(*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 eps (*.f64 #s(literal 1/24 binary64) eps) #s(literal -1/2 binary64)) (*.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps))) eps (cos.f64 x)) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(cos.f64 x) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(neg.f64 x) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(cos.f64 x) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) |
(fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) (*.f64 #s(literal -1/8 binary64) (*.f64 (cos.f64 x) eps))) eps (cos.f64 x)) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal -1/24 binary64) eps) (neg.f64 (sin.f64 x)) (*.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps) |
eps |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal 1/1920 binary64) (*.f64 eps eps) #s(literal -1/24 binary64)) eps) |
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) (*.f64 eps eps) #s(literal -1/24 binary64)) eps) |
(cos.f64 x) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) |
(fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) (*.f64 #s(literal -1/8 binary64) (*.f64 (cos.f64 x) eps))) eps (cos.f64 x)) |
(*.f64 eps #s(literal 1/2 binary64)) |
(*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/645120 binary64) (*.f64 eps eps) #s(literal 1/3840 binary64)) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) |
(*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(sin.f64 (*.f64 eps #s(literal 1/2 binary64))) |
(*.f64 (pow.f64 eps #s(literal 5 binary64)) #s(literal 1/3840 binary64)) |
(*.f64 (-.f64 #s(literal 1/3840 binary64) (/.f64 #s(literal 1/48 binary64) (*.f64 eps eps))) (pow.f64 eps #s(literal 5 binary64))) |
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/48 binary64) (*.f64 eps eps)) #s(literal 1/3840 binary64))) (pow.f64 eps #s(literal 5 binary64))) |
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1/48 binary64) (*.f64 eps eps)) #s(literal 1/3840 binary64))) (pow.f64 eps #s(literal 5 binary64))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps) |
(*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps) |
(*.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps) |
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(*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) |
(fma.f64 (*.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (+.f64 #s(literal 2 binary64) (*.f64 (neg.f64 x) x)) (*.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)))) |
(fma.f64 (*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (fma.f64 (*.f64 #s(literal -1/3 binary64) x) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (neg.f64 (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))))) x) x (*.f64 (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))))) |
(cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) |
(fma.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(fma.f64 (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(fma.f64 (fma.f64 (fma.f64 x (*.f64 #s(literal -1/6 binary64) x) #s(literal 1 binary64)) (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (*.f64 (*.f64 #s(literal -1/2 binary64) x) (cos.f64 (*.f64 #s(literal -1/2 binary64) eps)))) x (cos.f64 (*.f64 #s(literal -1/2 binary64) eps))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(cos.f64 x) |
(cos.f64 x) |
(cos.f64 x) |
(cos.f64 x) |
(*.f64 (*.f64 x x) #s(literal -1/2 binary64)) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) eps) #s(literal 1/24 binary64)) |
(*.f64 (*.f64 eps (+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #s(literal 1/24 binary64))) (pow.f64 x #s(literal 4 binary64))) |
(*.f64 (fma.f64 eps (+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #s(literal 1/24 binary64)) (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64))) |
(*.f64 (fma.f64 eps (+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #s(literal 1/24 binary64)) (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64))) |
(*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/24 binary64)) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(neg.f64 x) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(cos.f64 x) |
(cos.f64 x) |
(cos.f64 x) |
(cos.f64 x) |
(*.f64 (*.f64 x x) #s(literal -1/2 binary64)) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) |
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (cos.f64 x) eps) |
(*.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) eps) #s(literal 1/24 binary64)) |
(*.f64 (*.f64 eps (+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #s(literal 1/24 binary64))) (pow.f64 x #s(literal 4 binary64))) |
(*.f64 (fma.f64 eps (+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #s(literal 1/24 binary64)) (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64))) |
(*.f64 (fma.f64 eps (+.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #s(literal 1/24 binary64)) (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 4 binary64))) |
(*.f64 (*.f64 (*.f64 x x) eps) #s(literal 1/24 binary64)) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) |
(*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(*.f64 #s(literal -1/2 binary64) (sin.f64 x)) |
(neg.f64 x) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(*.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) (*.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
(cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 59 | 340 |
| 0 | 93 | 328 |
| 1 | 324 | 328 |
| 2 | 2588 | 328 |
| 0 | 10210 | 328 |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| Inputs |
|---|
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) |
(*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
(*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps) |
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) |
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps))) |
#s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps)) |
(fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps) |
(*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
(*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps) |
(fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) |
#s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) |
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)) |
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) |
(cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) |
#s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) |
| Outputs |
|---|
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Compiled 34 880 to 2 804 computations (92% saved)
17 alts after pruning (10 fresh and 7 done)
| Pruned | Kept | Total | |
|---|---|---|---|
| New | 947 | 7 | 954 |
| Fresh | 2 | 3 | 5 |
| Picked | 2 | 3 | 5 |
| Done | 1 | 4 | 5 |
| Total | 952 | 17 | 969 |
| Status | Accuracy | Program |
|---|---|---|
| 61.6% | (fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))) | |
| 34.5% | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (/.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) | |
| 57.0% | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (/.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) | |
| ✓ | 99.9% | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
| 99.9% | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps))) #s(literal -1 binary64)) (pow.f64 (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)) #s(literal -1 binary64))))) | |
| 99.9% | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) | |
| 99.7% | (*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) | |
| 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps) eps (*.f64 (cos.f64 x) eps))) | |
| ✓ | 99.5% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
| ✓ | 99.4% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
| ✓ | 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
| ✓ | 99.1% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
| 99.0% | #s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps)) | |
| ✓ | 98.7% | #s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
| 99.1% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) x) #s(literal -1/2 binary64) eps))) | |
| 98.6% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) eps (/.f64 #s(literal -1 binary64) x))) (neg.f64 x))) x) x)))) | |
| ✓ | 99.1% | #s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps))) |
Compiled 1 194 to 523 computations (56.2% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) x) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) eps (/.f64 #s(literal -1 binary64) x))) (neg.f64 x))) x) x)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps) eps (*.f64 (cos.f64 x) eps))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (/.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) (neg.f64 (*.f64 eps eps))) (neg.f64 eps))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) #s(literal -1/2 binary64)) eps (cos.f64 x)) eps)) |
(*.f64 (*.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 0 binary64) eps))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (/.f64 (*.f64 (fma.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 3 binary64))) (*.f64 eps eps))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (*.f64 (pow.f64 (/.f64 #s(literal -2 binary64) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (*.f64 (neg.f64 eps) eps))) #s(literal -1 binary64)) (pow.f64 (fma.f64 x #s(literal 2 binary64) (neg.f64 eps)) #s(literal -1 binary64))))) |
(fma.f64 (sin.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 eps) (cos.f64 x) (neg.f64 (sin.f64 x)))) |
| Outputs |
|---|
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
3 calls:
| 17.0ms | eps |
| 8.0ms | x |
| 8.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 1 | x |
| 99.9% | 1 | eps |
| 99.9% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) x) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) eps (/.f64 #s(literal -1 binary64) x))) (neg.f64 x))) x) x)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps) eps (*.f64 (cos.f64 x) eps))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
| Outputs |
|---|
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
3 calls:
| 5.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 5.0ms | eps |
| 5.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.9% | 1 | x |
| 99.9% | 1 | eps |
| 99.9% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) x) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) eps (/.f64 #s(literal -1 binary64) x))) (neg.f64 x))) x) x)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps) eps (*.f64 (cos.f64 x) eps))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 (fma.f64 (*.f64 #s(literal 1/12 binary64) x) x #s(literal -1/2 binary64)) x)) eps (cos.f64 x)) eps)) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))) |
| Outputs |
|---|
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
3 calls:
| 36.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 5.0ms | x |
| 5.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.7% | 1 | x |
| 99.7% | 1 | eps |
| 99.7% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) x) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) eps (/.f64 #s(literal -1 binary64) x))) (neg.f64 x))) x) x)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps) eps (*.f64 (cos.f64 x) eps))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps) eps (*.f64 (cos.f64 x) eps))) |
3 calls:
| 4.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 4.0ms | x |
| 4.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 1 | x |
| 99.5% | 1 | eps |
| 99.5% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) x) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) eps (/.f64 #s(literal -1 binary64) x))) (neg.f64 x))) x) x)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
3 calls:
| 15.0ms | x |
| 4.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 4.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.5% | 1 | x |
| 99.5% | 1 | eps |
| 99.5% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) x) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) eps (/.f64 #s(literal -1 binary64) x))) (neg.f64 x))) x) x)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
3 calls:
| 4.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 3.0ms | x |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.4% | 1 | x |
| 99.4% | 1 | eps |
| 99.4% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) x) #s(literal -1/2 binary64) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) #s(approx (+ (* (* -1/2 x) (* eps (+ eps x))) eps) (*.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 (*.f64 eps (fma.f64 #s(literal 1/2 binary64) eps (/.f64 #s(literal -1 binary64) x))) (neg.f64 x))) x) x)))) |
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps))) |
3 calls:
| 25.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 3.0ms | x |
| 3.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.1% | 1 | x |
| 99.1% | 1 | eps |
| 99.1% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 (*.f64 (+.f64 eps x) eps) x) #s(literal -1/2 binary64) eps))) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) |
3 calls:
| 2.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 2.0ms | x |
| 2.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.1% | 1 | x |
| 99.1% | 1 | eps |
| 99.1% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps)) |
3 calls:
| 2.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 2.0ms | x |
| 2.0ms | eps |
| Accuracy | Segments | Branch |
|---|---|---|
| 99.0% | 1 | x |
| 99.0% | 1 | eps |
| 99.0% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
Total 0.0b remaining (0%)
Threshold costs 0b (0%)
| Inputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
| Outputs |
|---|
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
3 calls:
| 14.0ms | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
| 1.0ms | eps |
| 1.0ms | x |
| Accuracy | Segments | Branch |
|---|---|---|
| 98.7% | 1 | x |
| 98.7% | 1 | eps |
| 98.7% | 1 | (-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x)) |
Compiled 9 to 10 computations (-11.1% saved)
| 1× | egg-herbie |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 76 | 250 |
| 1 | 99 | 250 |
| 2 | 101 | 250 |
| 3 | 102 | 250 |
| 1× | saturated |
| Inputs |
|---|
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps) eps (*.f64 (cos.f64 x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 eps (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 eps (+.f64 eps x)) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
| Outputs |
|---|
(*.f64 (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x)))) (*.f64 #s(literal 2 binary64) #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3840 binary64) (*.f64 eps eps) #s(literal -1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps)))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 (fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
(*.f64 (*.f64 #s(approx (sin (* 1/2 (+ 0 eps))) (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 x))))) |
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (*.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps) eps (*.f64 (cos.f64 x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 #s(approx (* (sin x) -1/2) (*.f64 #s(literal -1/2 binary64) x)) eps (cos.f64 x)) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) eps) (*.f64 x x) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) -1/2) eps) (cos x)) eps) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) (*.f64 (+.f64 x eps) eps) eps))) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) (fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))) eps)) |
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (+ (* (* (sin x) -1/2) eps) (cos x)) #s(literal 1 binary64)) eps)) |
Useful iterations: 0 (0.0ms)
| Iter | Nodes | Cost |
|---|---|---|
| 0 | 107 | 496 |
| 1 | 314 | 496 |
| 2 | 775 | 489 |
| 3 | 2829 | 489 |
| 4 | 6198 | 489 |
| 0 | 8140 | 458 |
| 0 | 408 | 3712 |
| 1 | 1248 | 3510 |
| 2 | 3420 | 3428 |
| 0 | 8203 | 3203 |
| 0 | 6 | 16 |
| 0 | 10 | 16 |
| 1 | 53 | 16 |
| 2 | 380 | 16 |
| 3 | 4766 | 16 |
| 0 | 8210 | 16 |
| 0 | 360 | 4368 |
| 1 | 1084 | 4128 |
| 2 | 2917 | 4025 |
| 3 | 7082 | 4025 |
| 0 | 8232 | 3767 |
| 0 | 339 | 4268 |
| 1 | 1008 | 3971 |
| 2 | 2715 | 3878 |
| 3 | 6362 | 3878 |
| 0 | 8411 | 3638 |
| 0 | 59 | 340 |
| 0 | 93 | 328 |
| 1 | 324 | 328 |
| 2 | 2588 | 328 |
| 0 | 10210 | 328 |
| 1× | fuel |
| 1× | iter limit |
| 1× | node limit |
| 1× | iter limit |
| 1× | iter limit |
| 1× | node limit |
| 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 |
Compiled 557 to 328 computations (41.1% saved)
Compiled 544 to 196 computations (64% saved)
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