Details

sample227.0ms

Algorithm

intervals

Results

105.0ms

256×

body

valid

simplify8.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	1878
3	505
2	152
1	62
0	29

prune45.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.2b

localize90.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma x (fma (+ 43.3400022514 x) x 263.505074721) 313.399215894)
0.1b	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
5.3b	(/ (- x 2.0) (fma (fma x (fma (+ 43.3400022514 x) x 263.505074721) 313.399215894) x 47.066876606))
28.4b	(* (/ (- x 2.0) (fma (fma x (fma (+ 43.3400022514 x) x 263.505074721) 313.399215894) x 47.066876606)) (fma x (fma x (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) y) z))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
31×	`times-frac`
24×	`add-cube-cbrt`
19×	`associate-l`
11×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-/l*`
4×	`expm1-log1p-u` `fma-udef` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `flip--`

Counts

4 → 102

Calls

4 calls:

1.0ms	(fma x (fma (+ 43.3400022514 x) x 263.505074721) 313.399215894)
1.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
37.0ms	(/ (- x 2.0) (fma (fma x (fma (+ 43.3400022514 x) x 263.505074721) 313.399215894) x 47.066876606))
74.0ms	(* (/ (- x 2.0) (fma (fma x (fma (+ 43.3400022514 x) x 263.505074721) 313.399215894) x 47.066876606)) (fma x (fma x (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) y) z))

series1.1s

Counts

4 → 12

Calls

4 calls:

76.0ms	(fma x (fma (+ 43.3400022514 x) x 263.505074721) 313.399215894)
56.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
345.0ms	(/ (- x 2.0) (fma (fma x (fma (+ 43.3400022514 x) x 263.505074721) 313.399215894) x 47.066876606))
664.0ms	(* (/ (- x 2.0) (fma (fma x (fma (+ 43.3400022514 x) x 263.505074721) 313.399215894) x 47.066876606)) (fma x (fma x (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) y) z))

simplify7.4s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
2	1429
1	476
0	202

prune3.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (/ y (* x x)) 110.1139242984811)
5.8b	(/ y (* x x))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `prod-diff`
19×	`add-cube-cbrt`
16×	`times-frac`
7×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`div-inv`
4×	`add-log-exp`
3×	`associate-/l*`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `difference-of-squares`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `prod-exp` `clear-num` `associate-/r*` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

2 → 68

Calls

2 calls:

62.0ms	(- (/ y (* x x)) 110.1139242984811)
46.0ms	(/ y (* x x))

series128.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(- (/ y (* x x)) 110.1139242984811)
59.0ms	(/ y (* x x))

simplify17.1s

Counts

74 → 74

Iterations

Iter	Nodes
done	5229
3	3215
2	698
1	265
0	109

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize387.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
0.1b	(fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894)
0.1b	(fma (fma 4.16438922228 x 78.6994924154) x 137.519416416)
28.3b	(/ (fma x (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y) z) (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `fma-udef` `associate-/l`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 59

Calls

4 calls:

1.0ms	(fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
1.0ms	(fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894)
1.0ms	(fma (fma 4.16438922228 x 78.6994924154) x 137.519416416)
16.0ms	(/ (fma x (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y) z) (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606))

series2.0s

Counts

4 → 12

Calls

4 calls:

379.0ms	(fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y)
114.0ms	(fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894)
66.0ms	(fma (fma 4.16438922228 x 78.6994924154) x 137.519416416)
1.4s	(/ (fma x (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y) z) (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606))

simplify11.3s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
3	2111
2	626
1	251
0	132

prune2.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize386.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894)
0.1b	(fma (fma 4.16438922228 x 78.6994924154) x 137.519416416)
0.3b	(/ 1 (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606))
28.4b	(* (fma x (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y) z) (/ 1 (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `fma-udef` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 91

Calls

4 calls:

1.0ms	(fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894)
1.0ms	(fma (fma 4.16438922228 x 78.6994924154) x 137.519416416)
11.0ms	(/ 1 (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606))
35.0ms	(* (fma x (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y) z) (/ 1 (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606)))

series1.6s

Counts

4 → 12

Calls

4 calls:

75.0ms	(fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894)
52.0ms	(fma (fma 4.16438922228 x 78.6994924154) x 137.519416416)
355.0ms	(/ 1 (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606))
1.1s	(* (fma x (fma (fma (fma 4.16438922228 x 78.6994924154) x 137.519416416) x y) z) (/ 1 (fma x (fma x (fma x (+ 43.3400022514 x) 263.505074721) 313.399215894) 47.066876606)))

simplify7.2s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
3	3463
2	973
1	370
0	172

prune3.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes2.3s

Accuracy

98.2% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 33.5b

bsearch2.7s

Steps

Iters	Range		Point
8	5.322690163927608e+71	2.884038058407771e+74	5.400940663197947e+71
9	-1.4830573028726113e+41	-9.459107631657709e+33	-1.844664431155969e+40

simplify13.0ms

Iterations

Iter	Nodes
done	38
1	38
0	33

end0.0ms

sample6.8s

Algorithm

intervals

Results

6.4s

8007×

body

valid