Details

sample36.0ms

Algorithm

intervals

Results

16.0ms

512×

body

valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	19	13
2	50	13
3	159	13
4	298	13
5	384	13
6	392	13
7	463	13
8	620	13
9	632	13
done	632	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* x x) (* (* y 4.0) (- (* z z) t)))
0.0b	(- (* z z) t)
2.6b	(* (* y 4.0) (- (* z z) t))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`add-sqr-sqrt` `sub-neg`
4×	`distribute-rgt-in` `add-cube-cbrt` `-un-lft-identity` `distribute-lft-in` `associate-r*` `associate--r+`
3×	`flip3--` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`diff-log` `associate-*r/` `difference-of-squares`
1×	`associate-l` `*-commutative`

Counts

3 → 54

Calls

3 calls:

9.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
8.0ms	(- (* z z) t)
38.0ms	(* (* y 4.0) (- (* z z) t))

series171.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
22.0ms	(- (* z z) t)
66.0ms	(* (* y 4.0) (- (* z z) t))

simplify3.0s

Counts

63 → 63

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	103	843
1	286	802
2	1013	696
3	4580	690
done	5001	690

prune138.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.0b

localize13.0ms

Local error

Found 4 expressions with local error:

2.6b	(* (* y 4.0) (- (* z z) t))
6.1b	(cbrt (* (* y 4.0) (- (* z z) t)))
6.1b	(cbrt (* (* y 4.0) (- (* z z) t)))
6.1b	(cbrt (* (* y 4.0) (- (* z z) t)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`associate-*r/`
6×	`add-sqr-sqrt` `cbrt-div`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`flip3--` `associate-r` `flip--` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`associate-l` `*-commutative` `difference-of-squares`

Counts

4 → 58

Calls

4 calls:

36.0ms	(* (* y 4.0) (- (* z z) t))
20.0ms	(cbrt (* (* y 4.0) (- (* z z) t)))
20.0ms	(cbrt (* (* y 4.0) (- (* z z) t)))
22.0ms	(cbrt (* (* y 4.0) (- (* z z) t)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (* y 4.0) (- (* z z) t))
145.0ms	(cbrt (* (* y 4.0) (- (* z z) t)))
148.0ms	(cbrt (* (* y 4.0) (- (* z z) t)))
145.0ms	(cbrt (* (* y 4.0) (- (* z z) t)))

simplify2.0s

Counts

70 → 70

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	112	1019
1	287	998
2	915	841
3	3282	817
done	5002	796

prune425.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* y 4.0) (sqrt (- (* z z) t)))
0.2b	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
2.6b	(sqrt (- (* z z) t))
2.6b	(sqrt (- (* z z) t))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1`
18×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
16×	`add-sqr-sqrt` `sqrt-prod`
14×	`associate-r`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r/`
9×	`flip3--` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
4×	`frac-times` `add-log-exp` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `associate-l/` `-commutative`

Counts

4 → 89

Calls

4 calls:

37.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
111.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
10.0ms	(sqrt (- (* z z) t))
10.0ms	(sqrt (- (* z z) t))

series225.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
61.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
49.0ms	(sqrt (- (* z z) t))
46.0ms	(sqrt (- (* z z) t))

simplify1.5s

Counts

101 → 101

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	136	1685
1	368	1362
2	1295	1120
done	5000	1116

prune228.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t))))
2.6b	(sqrt (- (* z z) t))
2.6b	(sqrt (- (* z z) t))
2.6b	(sqrt (- (* z z) t))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

86×	`sqrt-prod`
59×	`add-sqr-sqrt`
35×	`sqrt-pow1`
30×	`pow1` `sqrt-div`
19×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
16×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`flip3--` `pow-prod-up` `flip--` `unswap-sqr`
7×	`difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `add-log-exp`
3×	`rem-sqrt-square`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

64.0ms	(* (sqrt (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t))))
12.0ms	(sqrt (- (* z z) t))
10.0ms	(sqrt (- (* z z) t))
10.0ms	(sqrt (- (* z z) t))

series185.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sqrt (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t))))
43.0ms	(sqrt (- (* z z) t))
47.0ms	(sqrt (- (* z z) t))
49.0ms	(sqrt (- (* z z) t))

simplify2.5s

Counts

146 → 146

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	135	2484
1	243	1578
2	573	1426
3	1243	1391
4	3334	1353
done	5001	1346

prune366.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.0b

regimes367.0ms

Accuracy

84.2% (0.5b remaining)

Error of 3.1b against oracle of 2.5b and baseline of 5.9b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	36
1	25	36
done	25	36

end0.0ms

sample917.0ms

Algorithm

intervals

Results

425.0ms

15845×

body

valid