Details

sample110.0ms

Algorithm

intervals

Results

53.0ms	81×	body	1280	valid
21.0ms	52×	body	640	valid
12.0ms	26×	body	2560	valid
6.0ms	24×	body	320	valid
3.0ms	56×	body	80	valid
2.0ms	17×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.7b

localize8.0ms

Local error

Found 3 expressions with local error:

1.0b	(+ x (sqrt (+ (* x x) 1.0)))
3.6b	(log (+ x (sqrt (+ (* x x) 1.0))))
12.2b	(sqrt (+ (* x x) 1.0))

rewrite81.0ms

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:

44.0ms	(+ x (sqrt (+ (* x x) 1.0)))
21.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
15.0ms	(sqrt (+ (* x x) 1.0))

series342.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(+ x (sqrt (+ (* x x) 1.0)))
198.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
65.0ms	(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

prune194.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
0.4b	(* -1/6 (/ (* x x) 1.0))

rewrite144.0ms

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:

108.0ms	(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
29.0ms	(* -1/6 (/ (* x x) 1.0))

series229.0ms

Counts

2 → 6

Calls

2 calls:

192.0ms	(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
37.0ms	(* -1/6 (/ (* x x) 1.0))

simplify1.3s

Counts

80 → 80

Iterations

Useful iterations: done (1.3s)

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

prune188.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 1 expressions with local error:

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

rewrite29.0ms

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:

17.0ms

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

series47.0ms

Counts

1 → 3

Calls

1 calls:

47.0ms

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

simplify1.1s

Counts

203 → 203

Iterations

Useful iterations: 2 (479.0ms)

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

prune471.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 0.0625 (pow x 5))
0.4b	(/ 0.125 (pow x 3))
10.9b	(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
20.7b	(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

rewrite474.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
94×	`times-frac`
63×	`*-un-lft-identity`
46×	`add-cube-cbrt`
33×	`unpow-prod-down`
22×	`difference-of-squares`
19×	`associate-/r*`
17×	`sqr-pow`
16×	`cube-prod`
15×	`add-exp-log`
8×	`log-prod` `add-cbrt-cube`
7×	`distribute-lft-out--`
6×	`div-exp` `associate-/l*` `add-log-exp`
5×	`pow1` `log-div` `frac-sub`
4×	`cube-mult` `unpow3`
3×	`flip3--` `flip--`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`sub-neg` `diff-log` `rem-log-exp` `log-pow`

Counts

4 → 167

Calls

4 calls:

8.0ms	(/ 0.0625 (pow x 5))
9.0ms	(/ 0.125 (pow x 3))
347.0ms	(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
103.0ms	(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

series498.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ 0.0625 (pow x 5))
64.0ms	(/ 0.125 (pow x 3))
210.0ms	(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
169.0ms	(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

simplify1.1s

Counts

179 → 179

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	338	2966
1	679	2667
2	1858	2553
done	5000	2541

prune584.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes66.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.8b

bsearch128.0ms

Steps

Iters	Range		Point
9	0.0030847216915828425	5729.342694487068	0.8864725828659493
11	-30636816361710.875	-9.292394687435822e-10	-1.014356783985294

simplify7.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	35	56
1	42	54
done	42	54

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.5s	2302×	body	1280	valid
629.0ms	1576×	body	640	valid
571.0ms	788×	body	320	valid
373.0ms	800×	body	2560	valid
147.0ms	2110×	body	80	valid
54.0ms	424×	body	160	valid