Details

sample50.0ms

Algorithm

intervals

Results

29.0ms

256×

body

valid

simplify30.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.3b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
32.6b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite188.0ms

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:

16.0ms	(+ (* x x) (* y y))
103.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
67.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series341.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(+ (* x x) (* y y))
66.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
220.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify2.1s

Counts

81 → 81

Iterations

Useful iterations: done (2.1s)

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

prune409.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.7b

localize21.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (sqrt (fma z z (fma x x (pow y 2)))) (sqrt (/ 1 3.0)))
32.7b	(sqrt (fma z z (fma x x (pow y 2))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 62

Calls

2 calls:

25.0ms	(* (sqrt (fma z z (fma x x (pow y 2)))) (sqrt (/ 1 3.0)))
3.0ms	(sqrt (fma z z (fma x x (pow y 2))))

series402.0ms

Counts

2 → 6

Calls

2 calls:

257.0ms	(* (sqrt (fma z z (fma x x (pow y 2)))) (sqrt (/ 1 3.0)))
145.0ms	(sqrt (fma z z (fma x x (pow y 2))))

simplify6.1s

Counts

68 → 68

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	99	1192
1	174	1077
2	338	1030
3	716	1030
4	2048	1030
5	4796	1030
done	5000	1030

prune291.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.6b

localize23.0ms

Local error

Found 2 expressions with local error:

0.4b	(/ (sqrt (fma z z (fma x x (pow y 2)))) (sqrt 3.0))
32.7b	(sqrt (fma z z (fma x x (pow y 2))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`times-frac`
32×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
3×	`pow1`
2×	`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` `div-inv`

Counts

2 → 78

Calls

2 calls:

9.0ms	(/ (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))))

series521.0ms

Counts

2 → 6

Calls

2 calls:

373.0ms	(/ (sqrt (fma z z (fma x x (pow y 2)))) (sqrt 3.0))
148.0ms	(sqrt (fma z z (fma x x (pow y 2))))

simplify3.5s

Counts

84 → 84

Iterations

Useful iterations: 3 (170.0ms)

Iter	Nodes	Cost
0	104	1761
1	159	1588
2	284	1546
3	496	1544
4	926	1544
5	1412	1544
6	2935	1544
done	5000	1544

prune267.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.5b

localize6.0ms

Local error

Found 1 expressions with local error:

0.4b	(/ y (sqrt 3.0))

rewrite14.0ms

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:

11.0ms

(/ y (sqrt 3.0))

series80.0ms

Counts

1 → 3

Calls

1 calls:

80.0ms

(/ y (sqrt 3.0))

simplify5.7s

Counts

44 → 44

Iterations

Useful iterations: 3 (124.0ms)

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

prune70.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.5b

regimes179.0ms

Accuracy

39.5% (18.9b remaining)

Error of 25.2b against oracle of 6.3b and baseline of 37.5b

bsearch69.0ms

Steps

Iters	Range		Point
2	1.9335275214306354e+121	2.2438624246711994e+121	2.188536514136267e+121
10	-1.153867539103521e+97	-6.21347482068611e+82	-3.017165361738838e+89

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	34
1	29	34
2	33	34
3	34	34
done	34	34

end0.0ms

sample945.0ms

Algorithm

intervals

Results

605.0ms

8000×

body

valid