Details

sample73.0ms

Algorithm

intervals

Results

34.0ms	77×	body	1280	valid
13.0ms	46×	body	640	valid
8.0ms	23×	body	2560	valid
5.0ms	30×	body	320	valid
3.0ms	70×	body	80	valid
1.0ms	10×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	9	9
done	9	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.1b

localize13.0ms

Local error

Found 3 expressions with local error:

1.1b	(+ x (sqrt (+ (* x x) 1.0)))
2.2b	(log (+ x (sqrt (+ (* x x) 1.0))))
13.3b	(sqrt (+ (* x x) 1.0))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

41.0ms	(+ x (sqrt (+ (* x x) 1.0)))
29.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
17.0ms	(sqrt (+ (* x x) 1.0))

series353.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(+ x (sqrt (+ (* x x) 1.0)))
221.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
67.0ms	(sqrt (+ (* x x) 1.0))

simplify1.6s

Counts

51 → 51

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	133	761
1	308	691
2	848	618
3	2737	602
done	5001	590

prune179.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
0.3b	(* -1/6 (/ (* x x) 1.0))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
29×	`associate-r`
24×	`times-frac`
19×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-prod`
6×	`pow1` `associate-l` `prod-exp` `cbrt-unprod`
5×	`unswap-sqr`
3×	`cbrt-undiv` `div-exp`
2×	`frac-times` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip-+` `div-inv` `add-log-exp`

Counts

2 → 74

Calls

2 calls:

106.0ms	(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
27.0ms	(* -1/6 (/ (* x x) 1.0))

series302.0ms

Counts

2 → 6

Calls

2 calls:

256.0ms	(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
45.0ms	(* -1/6 (/ (* x x) 1.0))

simplify1.4s

Counts

80 → 80

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	162	1283
1	411	1174
2	1550	1066
done	5000	1034

prune266.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 1 expressions with local error:

0.1b	(/ (pow x 3) (/ 1.0 -1/6))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

273×	`times-frac`
134×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
42×	`unpow-prod-down` `cube-prod`
14×	`add-exp-log` `cube-mult` `unpow3` `div-inv` `sqr-pow`
13×	`associate-/r*`
12×	`associate-/l*`
9×	`div-exp`
6×	`add-cbrt-cube`
3×	`cbrt-undiv`
2×	`pow-to-exp` `pow-exp`
1×	`pow1` `frac-2neg` `clear-num` `associate-/r/` `add-log-exp`

Counts

1 → 200

Calls

1 calls:

24.0ms

(/ (pow x 3) (/ 1.0 -1/6))

series57.0ms

Counts

1 → 3

Calls

1 calls:

57.0ms

(/ (pow x 3) (/ 1.0 -1/6))

simplify1.2s

Counts

203 → 203

Iterations

Useful iterations: 2 (518.0ms)

Iter	Nodes	Cost
0	302	3458
1	577	2805
2	2293	2751
done	5000	2751

prune564.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* -1/6 (/ (* x x) 1.0))
13.8b	(cbrt (+ (* -1/6 (/ (* x x) 1.0)) 1))
13.8b	(cbrt (+ (* -1/6 (/ (* x x) 1.0)) 1))
13.8b	(cbrt (+ (* -1/6 (/ (* x x) 1.0)) 1))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

34.0ms	(* -1/6 (/ (* x x) 1.0))
22.0ms	(cbrt (+ (* -1/6 (/ (* x x) 1.0)) 1))
23.0ms	(cbrt (+ (* -1/6 (/ (* x x) 1.0)) 1))
17.0ms	(cbrt (+ (* -1/6 (/ (* x x) 1.0)) 1))

series880.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* -1/6 (/ (* x x) 1.0))
322.0ms	(cbrt (+ (* -1/6 (/ (* x x) 1.0)) 1))
250.0ms	(cbrt (+ (* -1/6 (/ (* x x) 1.0)) 1))
281.0ms	(cbrt (+ (* -1/6 (/ (* x x) 1.0)) 1))

simplify2.8s

Counts

79 → 79

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	141	1566
1	327	1477
2	950	1365
3	3809	1230
done	5001	1176

prune446.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes105.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.9b

bsearch143.0ms

Steps

Iters	Range		Point
10	8.937283511995443e-05	28405617999702.24	0.8904752561288425
9	-7465.585501010854	-0.008005822963963436	-1.0042810433581868

simplify9.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	36	56
1	42	54
done	42	54

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.8s	2405×	body	1280	valid
639.0ms	1512×	body	640	valid
352.0ms	770×	body	2560	valid
165.0ms	803×	body	320	valid
143.0ms	2109×	body	80	valid
48.0ms	401×	body	160	valid