Details

sample29.0ms

Algorithm

intervals

Results

13.0ms

271×

body

valid

simplify16.0ms

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: 24.7b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
1.2b	(+ (* a c) (* b d))
24.2b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite86.0ms

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:

21.0ms	(+ (* c c) (* d d))
14.0ms	(+ (* a c) (* b d))
49.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series209.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* c c) (* d d))
53.0ms	(+ (* a c) (* b d))
119.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.9s

Counts

62 → 62

Iterations

Useful iterations: 2 (209.0ms)

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

prune230.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.0b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* a c) (* b d))
15.7b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
26.0b	(sqrt (+ (* c c) (* d d)))
26.0b	(sqrt (+ (* c c) (* d d)))

rewrite75.0ms

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:

11.0ms	(+ (* a c) (* b d))
42.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
9.0ms	(sqrt (+ (* c c) (* d d)))
9.0ms	(sqrt (+ (* c c) (* d d)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (* a c) (* b d))
180.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
58.0ms	(sqrt (+ (* c c) (* d d)))
49.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.6s

Counts

96 → 96

Iterations

Useful iterations: 3 (493.0ms)

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

prune399.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.8b

localize30.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* a c) (* b d))
15.8b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
26.0b	(sqrt (+ (* c c) (* d d)))
26.0b	(sqrt (+ (* c c) (* d d)))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`associate-l`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

12.0ms	(+ (* a c) (* b d))
100.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
16.0ms	(sqrt (+ (* c c) (* d d)))
15.0ms	(sqrt (+ (* c c) (* d d)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* a c) (* b d))
136.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
46.0ms	(sqrt (+ (* c c) (* d d)))
49.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.9s

Counts

106 → 106

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	145	1886
1	378	1642
2	1153	1474
3	3771	1458
done	5000	1458

prune442.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 21.8b

localize20.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* a c) (* b d))
15.7b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
26.0b	(sqrt (+ (* c c) (* d d)))
26.0b	(sqrt (+ (* c c) (* d d)))

rewrite73.0ms

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:

9.0ms	(+ (* a c) (* b d))
44.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
9.0ms	(sqrt (+ (* c c) (* d d)))
9.0ms	(sqrt (+ (* c c) (* d d)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (* a c) (* b d))
147.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
47.0ms	(sqrt (+ (* c c) (* d d)))
41.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.7s

Counts

96 → 96

Iterations

Useful iterations: 3 (596.0ms)

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

prune335.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 21.8b

regimes327.0ms

Accuracy

25% (2.2b remaining)

Error of 25.2b against oracle of 23.1b and baseline of 26.0b

bsearch4.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	55
1	27	55
done	27	55

end0.0ms

sample1.1s

Algorithm

intervals

Results

640.0ms

8494×

body

valid