Details

sample26.0ms

Algorithm

intervals

Results

12.0ms

270×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	15	15
done	15	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(+ (* a c) (* b d))
24.7b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 53

Calls

3 calls:

9.0ms	(+ (* c c) (* d d))
9.0ms	(+ (* a c) (* b d))
38.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series249.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* c c) (* d d))
61.0ms	(+ (* a c) (* b d))
158.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.6s

Counts

62 → 62

Iterations

Useful iterations: 2 (175.0ms)

Iter	Nodes	Cost
0	98	1090
1	270	1067
2	865	951
3	2507	951
done	5001	951

prune234.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* a c) (* b d))
14.7b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
27.6b	(sqrt (+ (* c c) (* d d)))
27.6b	(sqrt (+ (* c c) (* d d)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

12.0ms	(+ (* a c) (* b d))
62.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
14.0ms	(sqrt (+ (* c c) (* d d)))
14.0ms	(sqrt (+ (* c c) (* d d)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(+ (* a c) (* b d))
174.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
47.0ms	(sqrt (+ (* c c) (* d d)))
49.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.7s

Counts

96 → 96

Iterations

Useful iterations: 3 (602.0ms)

Iter	Nodes	Cost
0	116	1780
1	275	1649
2	777	1541
3	2052	1525
done	5000	1525

prune394.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.9b

localize37.0ms

Local error

Found 4 expressions with local error:

7.7b	(* (/ 1 (sqrt (sqrt (+ (* c c) (* d d))))) (/ (+ (* a c) (* b d)) (sqrt (sqrt (+ (* c c) (* d d))))))
27.6b	(sqrt (+ (* c c) (* d d)))
27.6b	(sqrt (+ (* c c) (* d d)))
27.6b	(sqrt (+ (* c c) (* d d)))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

137×	`add-sqr-sqrt`
108×	`sqrt-prod`
99×	`times-frac`
57×	`*-un-lft-identity`
45×	`add-cube-cbrt`
33×	`associate-r` `associate-l`
28×	`unswap-sqr`
26×	`add-exp-log`
16×	`add-cbrt-cube`
14×	`sqrt-div`
9×	`pow1`
8×	`div-exp` `prod-exp`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`rec-exp` `1-exp` `div-inv`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 163

Calls

4 calls:

126.0ms	(* (/ 1 (sqrt (sqrt (+ (* c c) (* d d))))) (/ (+ (* a c) (* b d)) (sqrt (sqrt (+ (* c c) (* d d))))))
8.0ms	(sqrt (+ (* c c) (* d d)))
9.0ms	(sqrt (+ (* c c) (* d d)))
8.0ms	(sqrt (+ (* c c) (* d d)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (/ 1 (sqrt (sqrt (+ (* c c) (* d d))))) (/ (+ (* a c) (* b d)) (sqrt (sqrt (+ (* c c) (* d d))))))
57.0ms	(sqrt (+ (* c c) (* d d)))
55.0ms	(sqrt (+ (* c c) (* d d)))
42.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.0s

Counts

175 → 175

Iterations

Useful iterations: 2 (398.0ms)

Iter	Nodes	Cost
0	198	5510
1	556	5091
2	1972	4307
done	5000	4307

prune703.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 21.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(/ 1 (+ (* c c) (* d d)))
0.7b	(+ (* a c) (* b d))
24.7b	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`flip3-+` `flip-+`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `+-commutative` `frac-times` `rec-exp` `1-exp` `associate-*l/` `sum-log` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 97

Calls

4 calls:

9.0ms	(+ (* c c) (* d d))
15.0ms	(/ 1 (+ (* c c) (* d d)))
9.0ms	(+ (* a c) (* b d))
60.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

series242.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* c c) (* d d))
52.0ms	(/ 1 (+ (* c c) (* d d)))
58.0ms	(+ (* a c) (* b d))
97.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

simplify2.9s

Counts

109 → 109

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	139	1789
1	384	1627
2	1270	1431
3	4313	1417
done	5002	1417

prune610.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 21.9b

regimes331.0ms

Accuracy

20.9% (2.3b remaining)

Error of 25.1b against oracle of 22.9b and baseline of 25.7b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	54
1	25	54
done	25	54

end0.0ms

sample1.0s

Algorithm

intervals

Results

636.0ms

8495×

body

valid