Details

sample31.0ms

Algorithm

intervals

Results

14.0ms

276×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize22.0ms

Local error

Found 2 expressions with local error:

0.6b	(+ (* a c) (* b d))
28.7b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

17.0ms	(+ (* a c) (* b d))
80.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series188.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(+ (* a c) (* b d))
125.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.7s

Counts

48 → 48

Iterations

Useful iterations: 3 (621.0ms)

Iter	Nodes	Cost
0	85	924
1	232	906
2	767	824
3	2337	820
done	5001	820

prune228.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 28.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* a c) (* b d))
18.4b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
30.6b	(sqrt (+ (* c c) (* d d)))
30.6b	(sqrt (+ (* c c) (* d d)))

rewrite109.0ms

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:

17.0ms	(+ (* a c) (* b d))
65.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
16.0ms	(sqrt (+ (* c c) (* d d)))
8.0ms	(sqrt (+ (* c c) (* d d)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (* a c) (* b d))
163.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
49.0ms	(sqrt (+ (* c c) (* d d)))
51.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.7s

Counts

96 → 96

Iterations

Useful iterations: 3 (574.0ms)

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

prune418.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 25.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* a c) (* b d))
18.4b	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
30.6b	(sqrt (+ (* c c) (* d d)))
30.6b	(sqrt (+ (* c c) (* d d)))

rewrite77.0ms

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` `add-cbrt-cube` `associate-/l*` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/r*`
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:

8.0ms	(+ (* a c) (* b d))
34.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
16.0ms	(sqrt (+ (* c c) (* d d)))
16.0ms	(sqrt (+ (* c c) (* d d)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ (* a c) (* b d))
122.0ms	(/ (sqrt (+ (* c c) (* d d))) (+ (* a c) (* b d)))
44.0ms	(sqrt (+ (* c c) (* d d)))
62.0ms	(sqrt (+ (* c c) (* d d)))

simplify4.6s

Counts

96 → 96

Iterations

Useful iterations: 3 (533.0ms)

Iter	Nodes	Cost
0	114	1774
1	265	1656
2	723	1554
3	1731	1540
4	4577	1540
done	5000	1540

prune566.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 25.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* a c) (* b d))
18.5b	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
30.6b	(sqrt (+ (* c c) (* d d)))
30.6b	(sqrt (+ (* c c) (* d d)))

rewrite170.0ms

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:

15.0ms	(+ (* a c) (* b d))
102.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
16.0ms	(sqrt (+ (* c c) (* d d)))
29.0ms	(sqrt (+ (* c c) (* d d)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(+ (* a c) (* b d))
169.0ms	(* (+ (* a c) (* b d)) (/ 1 (sqrt (+ (* c c) (* d d)))))
55.0ms	(sqrt (+ (* c c) (* d d)))
66.0ms	(sqrt (+ (* c c) (* d d)))

simplify3.0s

Counts

106 → 106

Iterations

Useful iterations: 3 (1.7s)

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

prune393.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 25.7b

regimes304.0ms

Accuracy

17.5% (2.7b remaining)

Error of 25.8b against oracle of 23.1b and baseline of 26.3b

bsearch3.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	56
1	29	56
done	29	56

end0.0ms

sample1.0s

Algorithm

intervals

Results

643.0ms

8489×

body

valid