Details

sample64.0ms

Algorithm

intervals

Results

29.0ms	66×	body	1280	valid
11.0ms	46×	body	640	valid
8.0ms	27×	body	2560	valid
5.0ms	32×	body	320	valid
3.0ms	72×	body	80	valid
1.0ms	13×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 52.8b

localize7.0ms

Local error

Found 3 expressions with local error:

1.1b	(+ x (sqrt (+ (* x x) 1.0)))
3.4b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.7b	(sqrt (+ (* x x) 1.0))

rewrite24.0ms

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:

9.0ms	(+ x (sqrt (+ (* x x) 1.0)))
9.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms	(sqrt (+ (* x x) 1.0))

series281.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(+ x (sqrt (+ (* x x) 1.0)))
170.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
48.0ms	(sqrt (+ (* x x) 1.0))

simplify1.4s

Counts

51 → 51

Iterations

Useful iterations: 3 (622.0ms)

Iter	Nodes	Cost
0	133	761
1	308	691
2	853	618
3	3211	602
done	5001	602

prune149.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.1b	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
182×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
118×	`add-cube-cbrt` `*-un-lft-identity`
80×	`sqrt-prod`
40×	`sqr-pow`
30×	`cube-mult` `unpow3`
25×	`add-exp-log` `unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
4×	`pow1`
3×	`associate-r/` `associate-l*`
2×	`diff-log` `frac-sub` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `flip-+` `div-inv`

Counts

2 → 286

Calls

2 calls:

126.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
79.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series298.0ms

Counts

2 → 6

Calls

2 calls:

159.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
138.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify1.1s

Counts

292 → 292

Iterations

Useful iterations: 2 (514.0ms)

Iter	Nodes	Cost
0	336	4436
1	860	3364
2	2949	2955
done	5001	2955

prune407.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 0.0625 (pow x 5))
0.1b	(/ 0.125 (pow x 3))
11.7b	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
16.5b	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
71×	`times-frac`
68×	`*-un-lft-identity`
46×	`add-cube-cbrt`
26×	`unpow-prod-down`
19×	`associate-/r*`
15×	`add-exp-log`
14×	`cube-prod`
11×	`log-prod`
10×	`difference-of-squares` `sqr-pow`
9×	`add-log-exp`
8×	`add-cbrt-cube`
6×	`div-exp` `frac-sub` `associate-/l*` `distribute-lft-out--`
5×	`pow1` `log-div`
4×	`cube-mult` `unpow3` `distribute-lft-out`
2×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `flip3-+` `diff-log` `frac-add` `pow-exp` `clear-num` `flip--` `flip-+` `div-inv`
1×	`sub-neg` `rem-log-exp` `sum-log` `log-pow` `associate--r+`

Counts

4 → 160

Calls

4 calls:

4.0ms	(/ 0.0625 (pow x 5))
5.0ms	(/ 0.125 (pow x 3))
92.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
108.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series330.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ 0.0625 (pow x 5))
41.0ms	(/ 0.125 (pow x 3))
181.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
57.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify817.0ms

Counts

172 → 172

Iterations

Useful iterations: 2 (369.0ms)

Iter	Nodes	Cost
0	318	2936
1	689	2663
2	2120	2507
done	5001	2507

prune398.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

9.0b	(log (sqrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))))
9.0b	(log (sqrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))))
16.5b	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))
16.5b	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite405.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
28×	`log-prod` `times-frac`
22×	`sqrt-prod`
20×	`difference-of-squares`
14×	`add-log-exp`
12×	`frac-sub` `distribute-lft-out--`
10×	`log-div` `sqrt-div`
8×	`pow1` `add-cube-cbrt` `distribute-lft-out`
6×	`add-exp-log` `log-pow`
4×	`unpow-prod-down` `flip3--` `flip3-+` `diff-log` `cube-prod` `frac-add` `add-cbrt-cube` `flip--` `flip-+` `sqr-pow`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `associate--r+`

Counts

4 → 110

Calls

4 calls:

93.0ms	(log (sqrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))))
94.0ms	(log (sqrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))))
108.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))
105.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series296.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(log (sqrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))))
94.0ms	(log (sqrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))))
50.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))
55.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify562.0ms

Counts

122 → 122

Iterations

Useful iterations: done (552.0ms)

Iter	Nodes	Cost
0	179	3692
1	407	3516
2	1222	3286
done	5000	3242

prune442.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes120.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.1b

bsearch68.0ms

Steps

Iters	Range		Point
8	0.44834868164545755	179.5191949529741	0.8927294336574271
7	-1.204215327568116	-0.04390830018224924	-0.9990009314811332

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	76
1	41	76
done	41	76

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.0s	2373×	body	1280	valid
396.0ms	1558×	body	640	valid
235.0ms	798×	body	2560	valid
116.0ms	785×	body	320	valid
77.0ms	2073×	body	80	valid
36.0ms	413×	body	160	valid