Details

sample17.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
2.0ms	92×	body	80	nan

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	122
1	6	122
done	6	122

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
17.7b	(sqrt (+ (* x x) y))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `add-log-exp`
3×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
2×	`flip3-+` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2`

Counts

2 → 26

Calls

2 calls:

11.0ms	(+ (* x x) y)
14.0ms	(sqrt (+ (* x x) y))

series104.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(+ (* x x) y)
82.0ms	(sqrt (+ (* x x) y))

simplify916.0ms

Counts

32 → 32

Iterations

Useful iterations: done (913.0ms)

Iter	Nodes	Cost
0	59	7550
1	154	5783
2	697	5743
done	5000	5663

prune191.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) y)
0.1b	(* (+ (* x x) y) (sqrt (+ (* x x) y)))
17.7b	(sqrt (+ (* x x) y))
31.3b	(cbrt (* (+ (* x x) y) (sqrt (+ (* x x) y))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
14×	`flip3-+` `sqrt-div` `flip-+`
10×	`pow1`
8×	`frac-times` `cbrt-div` `*-un-lft-identity` `add-cube-cbrt`
7×	`sqrt-prod`
6×	`add-cbrt-cube` `associate-r` `add-exp-log` `add-log-exp`
4×	`associate-l/` `associate-r/`
3×	`associate-l`
2×	`sqrt-pow1` `pow1/2` `pow3` `pow-prod-up` `unswap-sqr`
1×	`cbrt-prod` `+-commutative` `rem-sqrt-square` `sum-log` `pow1/3` `pow-prod-down` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 77

Calls

4 calls:

11.0ms	(+ (* x x) y)
45.0ms	(* (+ (* x x) y) (sqrt (+ (* x x) y)))
8.0ms	(sqrt (+ (* x x) y))
18.0ms	(cbrt (* (+ (* x x) y) (sqrt (+ (* x x) y))))

series243.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* x x) y)
82.0ms	(* (+ (* x x) y) (sqrt (+ (* x x) y)))
78.0ms	(sqrt (+ (* x x) y))
51.0ms	(cbrt (* (+ (* x x) y) (sqrt (+ (* x x) y))))

simplify1.3s

Counts

89 → 89

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	130	31183
1	297	24075
2	1468	23835
done	5001	22635

prune430.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* -1/2 (/ y x)) x)
0.0b	(* -1/2 (/ y x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-r`
10×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
7×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `add-log-exp`
3×	`associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv` `flip--`

Counts

2 → 44

Calls

2 calls:

8.0ms	(- (* -1/2 (/ y x)) x)
11.0ms	(* -1/2 (/ y x))

series77.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(- (* -1/2 (/ y x)) x)
23.0ms	(* -1/2 (/ y x))

simplify2.2s

Counts

50 → 50

Iterations

Useful iterations: 2 (208.0ms)

Iter	Nodes	Cost
0	92	9102
1	234	8035
2	732	7835
3	3394	7835
done	5000	7835

prune198.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* 1/2 (/ y x)))
0.0b	(* 1/2 (/ y x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`associate-r`
10×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
7×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `add-log-exp`
3×	`associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `sum-log` `flip3-+` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `flip-+` `div-inv`

Counts

2 → 43

Calls

2 calls:

4.0ms	(+ x (* 1/2 (/ y x)))
14.0ms	(* 1/2 (/ y x))

series68.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(+ x (* 1/2 (/ y x)))
32.0ms	(* 1/2 (/ y x))

simplify2.2s

Counts

49 → 49

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	87	8900
1	238	7833
2	805	7753
3	3513	7752
done	5000	7752

prune158.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes338.0ms

Accuracy

97.4% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 21.5b

bsearch82.0ms

Steps

Iters	Range		Point
11	1.8832230334659124e+24	1.4313346338374724e+48	1.4171690306065683e+48
9	-1.951179920997044e+156	-6.518035068066237e+150	-1.3378267015828925e+154

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	586
1	22	586
done	22	586

end0.0ms

sample667.0ms

Algorithm

intervals

Results

289.0ms	8000×	body	80	valid
73.0ms	2523×	body	80	nan