Details

sample31.0ms

Algorithm

intervals

Results

17.0ms

265×

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize11.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (* a c) (* b d))
27.8b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite49.0ms

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:

14.0ms	(+ (* a c) (* b d))
34.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series191.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(+ (* a c) (* b d))
141.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify2.2s

Counts

48 → 48

Iterations

Useful iterations: 3 (804.0ms)

Iter	Nodes	Cost
0	85	924
1	237	906
2	883	826
3	3898	820
done	5001	820

prune271.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 27.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* a c) (* d b))
17.6b	(/ (+ (* a c) (* d b)) (sqrt (+ (* c c) (* d d))))
30.5b	(sqrt (+ (* c c) (* d d)))
30.5b	(sqrt (+ (* c c) (* d d)))

rewrite80.0ms

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:

8.0ms	(+ (* a c) (* d b))
52.0ms	(/ (+ (* a c) (* d b)) (sqrt (+ (* c c) (* d d))))
9.0ms	(sqrt (+ (* c c) (* d d)))
9.0ms	(sqrt (+ (* c c) (* d d)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(+ (* a c) (* d b))
210.0ms	(/ (+ (* a c) (* d b)) (sqrt (+ (* c c) (* d d))))
68.0ms	(sqrt (+ (* c c) (* d d)))
58.0ms	(sqrt (+ (* c c) (* d d)))

simplify900.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (145.0ms)

Iter	Nodes	Cost
0	114	1780
1	278	1649
2	1017	1541
done	5000	1541

prune457.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.5b	(+ (* a c) (* b d))
0.6b	(/ 1 (+ (* c c) (* d d)))
27.5b	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 86

Calls

3 calls:

10.0ms	(+ (* a c) (* b d))
18.0ms	(/ 1 (+ (* c c) (* d d)))
90.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

series235.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(+ (* a c) (* b d))
68.0ms	(/ 1 (+ (* c c) (* d d)))
118.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

simplify4.5s

Counts

95 → 95

Iterations

Useful iterations: done (4.5s)

Iter	Nodes	Cost
0	126	1623
1	374	1507
2	3105	1300
done	5000	1294

prune267.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 24.2b

localize28.0ms

Local error

Found 4 expressions with local error:

30.5b	(sqrt (+ (* c c) (* d d)))
30.5b	(sqrt (+ (* c c) (* d d)))
30.5b	(sqrt (+ (* c c) (* d d)))
30.5b	(sqrt (+ (* c c) (* d d)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

9.0ms	(sqrt (+ (* c c) (* d d)))
9.0ms	(sqrt (+ (* c c) (* d d)))
18.0ms	(sqrt (+ (* c c) (* d d)))
13.0ms	(sqrt (+ (* c c) (* d d)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(sqrt (+ (* c c) (* d d)))
58.0ms	(sqrt (+ (* c c) (* d d)))
54.0ms	(sqrt (+ (* c c) (* d d)))
58.0ms	(sqrt (+ (* c c) (* d d)))

simplify839.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (133.0ms)

Iter	Nodes	Cost
0	38	852
1	91	744
2	220	680
3	528	656
4	1456	656
done	5001	656

prune396.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 24.2b

regimes215.0ms

Accuracy

3.9% (2.8b remaining)

Error of 25.8b against oracle of 23.0b and baseline of 25.9b

bsearch51.0ms

Steps

Iters	Range		Point
8	1.267959276101694e+93	1.0044135886792885e+96	1.7284643974157362e+95

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	39
1	21	39
done	21	39

end0.0ms

sample1.4s

Algorithm

intervals

Results

973.0ms

8462×

body

valid