Details

sample30.0ms

Algorithm

intervals

Results

14.0ms

461×

body

valid

simplify53.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	7	15
1	14	14
2	29	11
3	50	8
4	68	8
5	74	8
done	74	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* y y))
0.0b	(+ (* x x) (* y y))
0.1b	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
10×	`sum-log`
7×	`fma-def`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
3×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`associate-+l+`

Counts

3 → 51

Calls

3 calls:

48.0ms	(+ (+ (* x x) (* y y)) (* y y))
9.0ms	(+ (* x x) (* y y))
174.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series157.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(+ (+ (* x x) (* y y)) (* y y))
42.0ms	(+ (* x x) (* y y))
61.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify2.7s

Counts

60 → 60

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	76	863
1	230	683
2	831	572
3	3465	506
done	5000	505

prune195.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
9.3b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
9.3b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`+-commutative` `fma-def` `sum-log` `fma-udef`

Counts

4 → 60

Calls

4 calls:

19.0ms	(+ (* x x) (* y y))
1.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
46.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
57.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (* x x) (* y y))
213.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
91.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
76.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify1.7s

Counts

72 → 72

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	81	1257
1	199	911
2	582	676
3	1708	576
done	5000	562

prune288.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(hypot (hypot (* (sqrt 2) y) x) y)
0.2b	(* (hypot (hypot (* (sqrt 2) y) x) y) (hypot (hypot (* (sqrt 2) y) x) y))
0.4b	(* (sqrt 2) y)
0.4b	(* (sqrt 2) y)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
15×	`pow1` `associate-l`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-r`
8×	`sqrt-prod`
5×	`hypot-udef` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `pow-sqr` `pow-prod-up`

Counts

4 → 87

Calls

4 calls:

1.0ms	(hypot (hypot (* (sqrt 2) y) x) y)
21.0ms	(* (hypot (hypot (* (sqrt 2) y) x) y) (hypot (hypot (* (sqrt 2) y) x) y))
11.0ms	(* (sqrt 2) y)
19.0ms	(* (sqrt 2) y)

series1.3s

Counts

4 → 12

Calls

4 calls:

537.0ms	(hypot (hypot (* (sqrt 2) y) x) y)
640.0ms	(* (hypot (hypot (* (sqrt 2) y) x) y) (hypot (hypot (* (sqrt 2) y) x) y))
54.0ms	(* (sqrt 2) y)
66.0ms	(* (sqrt 2) y)

simplify2.5s

Counts

99 → 99

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	83	1136
1	162	992
2	407	857
3	881	761
4	1951	751
done	5001	725

prune357.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (sqrt 2)) y)
0.2b	(* (hypot (hypot (* (sqrt 2) y) x) y) (hypot (hypot (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) y)) x) y))
0.3b	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) y))
0.4b	(* (sqrt 2) y)

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
27×	`associate-l`
25×	`sqrt-prod`
16×	`add-cube-cbrt` `*-un-lft-identity`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
2×	`hypot-udef`
1×	`sqrt-unprod`

Counts

4 → 99

Calls

4 calls:

20.0ms	(* (sqrt (sqrt 2)) y)
10.0ms	(* (hypot (hypot (* (sqrt 2) y) x) y) (hypot (hypot (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) y)) x) y))
73.0ms	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) y))
21.0ms	(* (sqrt 2) y)

series956.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (sqrt (sqrt 2)) y)
694.0ms	(* (hypot (hypot (* (sqrt 2) y) x) y) (hypot (hypot (* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) y)) x) y))
89.0ms	(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) y))
52.0ms	(* (sqrt 2) y)

simplify3.8s

Counts

111 → 111

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	124	1389
1	253	1077
2	692	904
3	1286	872
4	2196	824
done	5000	815

prune502.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes255.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	10	15
done	10	15

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.3s

14329×

body

valid