Details

sample60.0ms

Algorithm

intervals

Results

22.0ms

266×

body

valid

simplify6.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
11	4203
10	1582
9	731
8	425
7	258
6	185
5	149
4	115
3	75
2	43
1	24
0	14

prune52.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize39.0ms

Local error

Found 2 expressions with local error:

0.8b	(fma z (- t a) (* x y))
23.0b	(/ (fma z (- t a) (* x y)) (fma (- b y) z y))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube` `add-exp-log`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

2 → 41

Calls

2 calls:

2.0ms	(fma z (- t a) (* x y))
11.0ms	(/ (fma z (- t a) (* x y)) (fma (- b y) z y))

series894.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(fma z (- t a) (* x y))
798.0ms	(/ (fma z (- t a) (* x y)) (fma (- b y) z y))

simplify7.8s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
4	4944
3	957
2	276
1	120
0	71

prune946.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 18.5b

localize46.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (/ (fma (- b y) z y) (fma z (- t a) (* x y))))
0.8b	(fma z (- t a) (* x y))
23.0b	(/ (fma (- b y) z y) (fma z (- t a) (* x y)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*` `add-exp-log`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`associate-/r/` `fma-udef` `pow-flip` `inv-pow`

Counts

3 → 120

Calls

3 calls:

27.0ms	(/ 1 (/ (fma (- b y) z y) (fma z (- t a) (* x y))))
2.0ms	(fma z (- t a) (* x y))
20.0ms	(/ (fma (- b y) z y) (fma z (- t a) (* x y)))

series2.7s

Counts

3 → 9

Calls

3 calls:

2.3s	(/ 1 (/ (fma (- b y) z y) (fma z (- t a) (* x y))))
87.0ms	(fma z (- t a) (* x y))
368.0ms	(/ (fma (- b y) z y) (fma z (- t a) (* x y)))

simplify4.9s

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
3	2856
2	915
1	382
0	173

prune2.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.2b

localize52.0ms

Local error

Found 3 expressions with local error:

0.7b	(/ 1 (fma (- b y) z y))
0.8b	(fma z (- t a) (* x y))
22.5b	(* (/ 1 (fma (- b y) z y)) (fma z (- t a) (* x y)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`associate-l`
10×	`add-cbrt-cube`
6×	`pow1`
4×	`div-exp` `prod-exp`
3×	`expm1-log1p-u` `associate-/r` `associate-r` `fma-udef` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `-commutative` `pow-flip` `inv-pow`

Counts

3 → 85

Calls

3 calls:

7.0ms	(/ 1 (fma (- b y) z y))
1.0ms	(fma z (- t a) (* x y))
35.0ms	(* (/ 1 (fma (- b y) z y)) (fma z (- t a) (* x y)))

series2.3s

Counts

3 → 9

Calls

3 calls:

193.0ms	(/ 1 (fma (- b y) z y))
76.0ms	(fma z (- t a) (* x y))
2.1s	(* (/ 1 (fma (- b y) z y)) (fma z (- t a) (* x y)))

simplify4.7s

Counts

94 → 94

Iterations

Iter	Nodes
done	5015
3	2237
2	651
1	250
0	116

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.2b

localize82.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (fma (- b y) z y) (/ 1 (fma z (- t a) (* x y)))))
0.8b	(fma z (- t a) (* x y))
0.8b	(/ 1 (fma z (- t a) (* x y)))
22.2b	(* (fma (- b y) z y) (/ 1 (fma z (- t a) (* x y))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
29×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `times-frac`
22×	`add-cube-cbrt`
20×	`add-cbrt-cube` `div-exp`
16×	`prod-exp`
13×	`associate-r`
10×	`pow1` `rec-exp` `1-exp`
6×	`cbrt-undiv` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r*` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `div-inv` `pow-flip` `unswap-sqr`
2×	`clear-num` `frac-2neg` `pow-prod-down` `associate-*r/` `associate-/r/` `un-div-inv` `inv-pow`
1×	`*-commutative` `fma-udef`

Counts

4 → 127

Calls

4 calls:

41.0ms	(/ 1 (* (fma (- b y) z y) (/ 1 (fma z (- t a) (* x y)))))
1.0ms	(fma z (- t a) (* x y))
8.0ms	(/ 1 (fma z (- t a) (* x y)))
34.0ms	(* (fma (- b y) z y) (/ 1 (fma z (- t a) (* x y))))

series3.0s

Counts

4 → 12

Calls

4 calls:

2.4s	(/ 1 (* (fma (- b y) z y) (/ 1 (fma z (- t a) (* x y)))))
93.0ms	(fma z (- t a) (* x y))
174.0ms	(/ 1 (fma z (- t a) (* x y)))
365.0ms	(* (fma (- b y) z y) (/ 1 (fma z (- t a) (* x y))))

simplify6.2s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
3	2835
2	797
1	328
0	151

prune1.9s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 11.2b

regimes3.1s

Accuracy

31.5% (8.5b remaining)

Error of 19.5b against oracle of 11.0b and baseline of 23.4b

bsearch179.0ms

Steps

Iters	Range		Point
7	2.881819794786346e+117	1.4369199905592724e+119	5.088199112679185e+118
8	-3.79888392172931e+195	-2.0131075904441452e+192	-5.613549175387801e+193

simplify15.0ms

Iterations

Iter	Nodes
done	25
1	25
0	21

end0.0ms

sample1.6s

Algorithm

intervals

Results

829.0ms

8442×

body

valid