Details

sample20.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	11	14
1	16	13
2	26	12
3	32	12
done	32	12

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.2b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite123.0ms

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:

10.0ms	(+ (* x x) (* y y))
80.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
31.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series292.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (* x x) (* y y))
67.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
193.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.5s

Counts

81 → 81

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	134	1510
1	307	1332
2	933	1139
3	3126	1133
done	5001	1132

prune295.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (pow y 2))
0.4b	(/ (sqrt (fma z z (fma x x (pow y 2)))) (sqrt 3.0))
34.1b	(sqrt (fma z z (fma x x (pow y 2))))

rewrite13.0ms

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 (pow y 2))
8.0ms	(/ (sqrt (fma z z (fma x x (pow y 2)))) (sqrt 3.0))
2.0ms	(sqrt (fma z z (fma x x (pow y 2))))

series445.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(fma x x (pow y 2))
277.0ms	(/ (sqrt (fma z z (fma x x (pow y 2)))) (sqrt 3.0))
131.0ms	(sqrt (fma z z (fma x x (pow y 2))))

simplify2.2s

Counts

97 → 97

Iterations

Useful iterations: 3 (143.0ms)

Iter	Nodes	Cost
0	116	1869
1	174	1693
2	335	1631
3	648	1629
4	1357	1629
5	3093	1629
done	5001	1629

prune248.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (pow y 2))
0.4b	(* (sqrt (fma z z (fma x x (pow y 2)))) (sqrt (/ 1 3.0)))
34.1b	(sqrt (fma z z (fma x x (pow y 2))))

rewrite26.0ms

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 (pow y 2))
22.0ms	(* (sqrt (fma z z (fma x x (pow y 2)))) (sqrt (/ 1 3.0)))
2.0ms	(sqrt (fma z z (fma x x (pow y 2))))

series391.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(fma x x (pow y 2))
213.0ms	(* (sqrt (fma z z (fma x x (pow y 2)))) (sqrt (/ 1 3.0)))
133.0ms	(sqrt (fma z z (fma x x (pow y 2))))

simplify2.3s

Counts

81 → 81

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	111	1300
1	189	1182
2	388	1115
3	888	1115
4	2716	1115
done	5000	1115

prune242.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.9b

localize3.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ y (sqrt 3.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 41

Calls

1 calls:

6.0ms

(/ y (sqrt 3.0))

series68.0ms

Counts

1 → 3

Calls

1 calls:

68.0ms

(/ y (sqrt 3.0))

simplify4.7s

Counts

44 → 44

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	68	381
1	105	344
2	190	334
3	301	332
4	504	332
5	763	332
6	1424	332
7	4858	332
done	5002	332

prune77.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.9b

regimes144.0ms

Accuracy

38.9% (19.3b remaining)

Error of 25.7b against oracle of 6.4b and baseline of 37.9b

bsearch74.0ms

Steps

Iters	Range		Point
9	9.511609313434486e+66	2.1557533500351985e+74	2.128703798252542e+74
8	-1.298766087308607e+128	-4.1374788989227053e+124	-1.2792317785522343e+128

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	30
1	26	30
2	28	30
done	28	30

end0.0ms

sample480.0ms

Algorithm

intervals

Results

252.0ms

8000×

body

valid