Details

sample25.0ms

Algorithm

intervals

Results

11.0ms

273×

body

valid

simplify2.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	24	16
2	43	15
3	65	15
4	96	15
5	130	15
6	163	15
7	239	15
8	396	15
9	710	15
10	1479	15
11	4000	15
done	5001	15

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.0b	(fma z (- b y) y)
1.0b	(fma x y (* z (- t a)))
25.6b	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

11.0ms	(* z (- t a))
0.0ms	(fma z (- b y) y)
0.0ms	(fma x y (* z (- t a)))
2.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

series430.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* z (- t a))
24.0ms	(fma z (- b y) y)
49.0ms	(fma x y (* z (- t a)))
319.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

simplify1.4s

Counts

107 → 107

Iterations

Useful iterations: 3 (453.0ms)

Iter	Nodes	Cost
0	171	1678
1	308	1491
2	720	1283
3	2617	1241
done	5000	1241

prune306.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z (- b y) y)
0.9b	(+ (* t z) (* (- a) z))
1.0b	(fma x y (+ (* t z) (* (- a) z)))
25.6b	(/ (fma x y (+ (* t z) (* (- a) z))) (fma z (- b y) y))

rewrite7.0ms

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` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
2×	`distribute-lft-neg-out` `fma-udef`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-out` `fma-def` `frac-2neg` `flip3-+` `div-exp` `unsub-neg` `clear-num` `sum-log` `flip-+` `div-inv`

Counts

4 → 66

Calls

4 calls:

0.0ms	(fma z (- b y) y)
3.0ms	(+ (* t z) (* (- a) z))
0.0ms	(fma x y (+ (* t z) (* (- a) z)))
2.0ms	(/ (fma x y (+ (* t z) (* (- a) z))) (fma z (- b y) y))

series398.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(fma z (- b y) y)
37.0ms	(+ (* t z) (* (- a) z))
44.0ms	(fma x y (+ (* t z) (* (- a) z)))
292.0ms	(/ (fma x y (+ (* t z) (* (- a) z))) (fma z (- b y) y))

simplify1.3s

Counts

78 → 78

Iterations

Useful iterations: 3 (419.0ms)

Iter	Nodes	Cost
0	103	1325
1	233	1089
2	718	978
3	2671	974
done	5000	974

prune243.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 25.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z (- b y) y)
0.3b	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
1.0b	(fma x y (* z (- t a)))
25.7b	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 127

Calls

4 calls:

0.0ms	(fma z (- b y) y)
5.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
0.0ms	(fma x y (* z (- t a)))
2.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

series615.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(fma z (- b y) y)
447.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
48.0ms	(fma x y (* z (- t a)))
97.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

simplify2.2s

Counts

139 → 139

Iterations

Useful iterations: 3 (811.0ms)

Iter	Nodes	Cost
0	178	3291
1	366	3116
2	885	2775
3	2619	2757
done	5000	2757

prune361.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (fma z (- b y) y))
1.0b	(fma x y (* z (- t a)))
1.0b	(/ 1 (fma x y (* z (- t a))))
25.1b	(/ (/ 1 (fma z (- b y) y)) (/ 1 (fma x y (* z (- t a)))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

439×	`times-frac`
216×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
52×	`add-exp-log`
36×	`div-exp`
31×	`div-inv`
20×	`add-cbrt-cube`
19×	`associate-/r` `associate-/l`
10×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`pow-flip` `inv-pow`
1×	`associate-/r/` `fma-udef` `associate-/l/`

Counts

4 → 305

Calls

4 calls:

2.0ms	(/ 1 (fma z (- b y) y))
0.0ms	(fma x y (* z (- t a)))
2.0ms	(/ 1 (fma x y (* z (- t a))))
12.0ms	(/ (/ 1 (fma z (- b y) y)) (/ 1 (fma x y (* z (- t a)))))

series610.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ 1 (fma z (- b y) y))
48.0ms	(fma x y (* z (- t a)))
55.0ms	(/ 1 (fma x y (* z (- t a))))
455.0ms	(/ (/ 1 (fma z (- b y) y)) (/ 1 (fma x y (* z (- t a)))))

simplify2.8s

Counts

317 → 317

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	414	10015
1	1186	9020
2	2787	7810
done	5000	7756

prune396.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 13.0b

regimes486.0ms

Accuracy

32.7% (8.4b remaining)

Error of 19.0b against oracle of 10.6b and baseline of 23.1b

bsearch89.0ms

Steps

Iters	Range		Point
9	8.079801426289644e+166	5.153978580515043e+173	1.0038165603025472e+167
8	-4.549635293905846e+79	-2.7229283140719805e+76	-4.117875698102326e+79

simplify5.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	23	40
1	31	34
2	34	34
3	35	34
done	35	34

end0.0ms

sample639.0ms

Algorithm

intervals

Results

349.0ms

8457×

body

valid