Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	11	14
1	16	13
2	26	12
3	30	12
done	30	12

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.6b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`times-frac`
18×	`add-cube-cbrt` `*-un-lft-identity`
13×	`sqrt-prod`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num` `sum-log`

Counts

3 → 72

Calls

3 calls:

3.0ms	(+ (* x x) (* y y))
33.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
15.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series258.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* x x) (* y y))
53.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
177.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.7s

Counts

81 → 81

Iterations

Useful iterations: 3 (694.0ms)

Iter	Nodes	Cost
0	134	1510
1	309	1332
2	1031	1139
3	4018	1133
done	5001	1133

prune287.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* y y))
0.4b	(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
35.5b	(sqrt (fma z z (fma x x (* y y))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`sqrt-prod`
16×	`-un-lft-identity` `associate-r*`
14×	`add-cube-cbrt`
13×	`times-frac`
8×	`pow1` `unswap-sqr`
6×	`associate-l`
5×	`add-exp-log` `add-cbrt-cube`
3×	`expm1-log1p-u` `sqrt-pow1` `pow1/2` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-unprod` `sqrt-div` `associate-r/` `prod-exp` `-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

3 → 72

Calls

3 calls:

0.0ms	(fma x x (* y y))
13.0ms	(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
1.0ms	(sqrt (fma z z (fma x x (* y y))))

series381.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(fma x x (* y y))
215.0ms	(* (sqrt (fma z z (fma x x (* y y)))) (sqrt (/ 1 3.0)))
126.0ms	(sqrt (fma z z (fma x x (* y y))))

simplify1.6s

Counts

81 → 81

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	112	1300
1	190	1182
2	391	1115
3	936	1115
4	2610	1115
done	5000	1115

prune247.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* y y))
0.4b	(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
35.5b	(sqrt (fma z z (fma x x (* y y))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`times-frac`
33×	`add-sqr-sqrt`
32×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-/r` `associate-/l`
5×	`add-exp-log` `add-cbrt-cube`
4×	`pow1`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

3 → 88

Calls

3 calls:

0.0ms	(fma x x (* y y))
4.0ms	(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
1.0ms	(sqrt (fma z z (fma x x (* y y))))

series446.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(fma x x (* y y))
282.0ms	(/ (sqrt (fma z z (fma x x (* y y)))) (sqrt 3.0))
122.0ms	(sqrt (fma z z (fma x x (* y y))))

simplify2.6s

Counts

97 → 97

Iterations

Useful iterations: 3 (149.0ms)

Iter	Nodes	Cost
0	117	1869
1	174	1693
2	333	1631
3	719	1629
4	1776	1629
5	4916	1629
done	5000	1629

prune263.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.9b

localize7.0ms

Local error

Found 1 expressions with local error:

0.2b	(* x (sqrt 0.3333333333333333))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`associate-r`
4×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
3×	`pow1` `add-exp-log` `associate-l` `add-cbrt-cube`
2×	`unswap-sqr`
1×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`

Counts

1 → 24

Calls

1 calls:

5.0ms

(* x (sqrt 0.3333333333333333))

series46.0ms

Counts

1 → 3

Calls

1 calls:

46.0ms

(* x (sqrt 0.3333333333333333))

simplify1.9s

Counts

27 → 27

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	39	168
1	71	151
2	124	143
3	158	143
4	216	143
5	354	143
6	750	143
7	2215	143
done	5000	143

prune55.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 4.9b

regimes321.0ms

Accuracy

37% (20.0b remaining)

Error of 26.5b against oracle of 6.5b and baseline of 38.3b

bsearch170.0ms

Steps

Iters	Range		Point
8	1.5491720421655856e+95	6.147715137559524e+97	4.244899767656578e+97
8	1.7074207915129012e-270	4.835147110927186e-268	1.722563062099152e-270
9	-1.7476729797984468e-228	-7.365325760942331e-238	-9.045780566004202e-238
6	-3.1442305190809916e+143	-5.062787100137526e+142	-7.514594408204408e+142

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	64
1	43	64
2	50	64
done	50	64

end0.0ms

sample468.0ms

Algorithm

intervals

Results

292.0ms

8000×

body

valid