Details

sample50.0ms

Algorithm

intervals

Results

27.0ms

256×

body

valid

simplify29.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	31
3	31
2	26
1	16
0	11

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.5b

localize29.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (fma x x (fma y y (* z z))) 3.0)
35.7b	(sqrt (/ (fma x x (fma y y (* z z))) 3.0))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`times-frac`
17×	`add-cube-cbrt` `*-un-lft-identity`
13×	`sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`expm1-log1p-u` `rem-sqrt-square` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num`

Counts

2 → 56

Calls

2 calls:

10.0ms	(/ (fma x x (fma y y (* z z))) 3.0)
8.0ms	(sqrt (/ (fma x x (fma y y (* z z))) 3.0))

series501.0ms

Counts

2 → 6

Calls

2 calls:

125.0ms	(/ (fma x x (fma y y (* z z))) 3.0)
376.0ms	(sqrt (/ (fma x x (fma y y (* z z))) 3.0))

simplify3.8s

Counts

62 → 62

Iterations

Iter	Nodes
done	5035
4	2666
3	787
2	323
1	167
0	101

prune656.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.4b

localize62.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (fma x x (fma y y (* z z)))) (cbrt 3.0))
35.6b	(sqrt (fma x x (fma y y (* z z))))
35.6b	(sqrt (fma x x (fma y y (* z z))))
35.7b	(sqrt (* (/ (sqrt (fma x x (fma y y (* z z)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (fma x x (fma y y (* z z)))) (cbrt 3.0))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt` `times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
28×	`sqrt-prod`
21×	`cbrt-prod`
9×	`pow1`
6×	`add-exp-log` `associate-/r` `associate-/l`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2` `sqrt-div`
2×	`rem-sqrt-square`
1×	`cbrt-undiv` `frac-times` `frac-2neg` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `clear-num` `div-inv`

Counts

4 → 108

Calls

4 calls:

17.0ms	(/ (sqrt (fma x x (fma y y (* z z)))) (cbrt 3.0))
3.0ms	(sqrt (fma x x (fma y y (* z z))))
3.0ms	(sqrt (fma x x (fma y y (* z z))))
61.0ms	(sqrt (* (/ (sqrt (fma x x (fma y y (* z z)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (fma x x (fma y y (* z z)))) (cbrt 3.0))))

series2.5s

Counts

4 → 12

Calls

4 calls:

798.0ms	(/ (sqrt (fma x x (fma y y (* z z)))) (cbrt 3.0))
263.0ms	(sqrt (fma x x (fma y y (* z z))))
371.0ms	(sqrt (fma x x (fma y y (* z z))))
1.0s	(sqrt (* (/ (sqrt (fma x x (fma y y (* z z)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (fma x x (fma y y (* z z)))) (cbrt 3.0))))

simplify3.2s

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
4	1447
3	578
2	293
1	197
0	132

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.4b

localize44.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sqrt (fma x x (fma y y (* z z)))) (sqrt (/ 1 3.0)))
35.6b	(sqrt (fma x x (fma y y (* z z))))

rewrite50.0ms

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:

41.0ms	(* (sqrt (fma x x (fma y y (* z z)))) (sqrt (/ 1 3.0)))
4.0ms	(sqrt (fma x x (fma y y (* z z))))

series648.0ms

Counts

2 → 6

Calls

2 calls:

385.0ms	(* (sqrt (fma x x (fma y y (* z z)))) (sqrt (/ 1 3.0)))
263.0ms	(sqrt (fma x x (fma y y (* z z))))

simplify6.3s

Counts

68 → 68

Iterations

Iter	Nodes
done	5004
4	1936
3	660
2	351
1	176
0	99

prune627.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 18.4b

localize14.0ms

Local error

Found 1 expressions with local error:

0.1b	(* (- x) (sqrt 0.3333333333333333))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 32

Calls

1 calls:

29.0ms

(* (- x) (sqrt 0.3333333333333333))

series108.0ms

Counts

1 → 3

Calls

1 calls:

108.0ms

(* (- x) (sqrt 0.3333333333333333))

simplify14.2s

Counts

35 → 35

Iterations

Iter	Nodes
done	5001
4	3056
3	1222
2	390
1	118
0	51

prune220.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 18.3b

regimes947.0ms

Accuracy

63.5% (7.1b remaining)

Error of 25.5b against oracle of 18.5b and baseline of 37.8b

bsearch165.0ms

Steps

Iters	Range		Point
7	4.618629416418565e+91	9.697809572055496e+93	9.445373192608024e+93
8	-2.3248803182338104e+96	-1.0335410165725188e+93	-2.114597052343944e+96

simplify28.0ms

Iterations

Iter	Nodes
done	44
3	44
2	41
1	33
0	27

end0.0ms

sample2.8s

Algorithm

intervals

Results

2.4s

8000×

body

valid