Details

sample66.0ms

Algorithm

intervals

Results

34.0ms	83×	body	1280	valid
11.0ms	47×	body	640	valid
8.0ms	33×	body	2560	valid
2.0ms	69×	body	80	valid
2.0ms	15×	body	320	valid
1.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	5
1	10	5
done	10	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.5b	(+ x (sqrt (+ (* x x) 1.0)))
2.4b	(log (+ x (sqrt (+ (* x x) 1.0))))
17.5b	(sqrt (+ (* x x) 1.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-prod`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow` `hypot-def`

Counts

3 → 52

Calls

3 calls:

17.0ms	(+ x (sqrt (+ (* x x) 1.0)))
16.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
9.0ms	(sqrt (+ (* x x) 1.0))

series267.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(+ x (sqrt (+ (* x x) 1.0)))
168.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
44.0ms	(sqrt (+ (* x x) 1.0))

simplify35.0ms

Counts

61 → 61

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	331	422
1	1127	385
2	5002	366
done	5002	366

prune182.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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)))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
184×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
126×	`*-un-lft-identity`
120×	`add-cube-cbrt`
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×	`pow1` `pow-to-exp` `pow-exp` `add-log-exp`
5×	`fma-neg` `prod-diff`
4×	`distribute-lft-out`
3×	`associate-r/` `associate-l*`
2×	`expm1-log1p-u` `diff-log` `log-pow` `frac-sub` `cbrt-unprod` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `flip-+` `div-inv`

Counts

2 → 300

Calls

2 calls:

187.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
80.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series293.0ms

Counts

2 → 6

Calls

2 calls:

148.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
144.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify120.0ms

Counts

306 → 306

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	888	2291
1	4768	1819
2	5001	1795
done	5001	1795

prune441.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (hypot x (sqrt 1.0)) x)
2.4b	(log (+ (hypot x (sqrt 1.0)) x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
4×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod` `add-log-exp`
3×	`pow1` `add-exp-log` `fma-def`
2×	`expm1-log1p-u` `log-div` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `rem-log-exp` `sum-log` `log-pow`

Counts

2 → 34

Calls

2 calls:

8.0ms	(+ (hypot x (sqrt 1.0)) x)
5.0ms	(log (+ (hypot x (sqrt 1.0)) x))

series396.0ms

Counts

2 → 6

Calls

2 calls:

123.0ms	(+ (hypot x (sqrt 1.0)) x)
273.0ms	(log (+ (hypot x (sqrt 1.0)) x))

simplify76.0ms

Counts

40 → 40

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	238	286
1	790	257
2	3276	249
3	5001	245
done	5001	245

prune103.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (hypot x (sqrt 1.0)) x)
0.5b	(+ (hypot x (sqrt 1.0)) x)
2.4b	(log (sqrt (+ (hypot x (sqrt 1.0)) x)))
2.4b	(log (sqrt (+ (hypot x (sqrt 1.0)) x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
14×	`log-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`pow1` `sqrt-prod` `add-log-exp`
6×	`add-exp-log` `fma-def` `log-pow`
4×	`expm1-log1p-u` `log-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`+-commutative` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log`

Counts

4 → 78

Calls

4 calls:

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

series837.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(+ (hypot x (sqrt 1.0)) x)
130.0ms	(+ (hypot x (sqrt 1.0)) x)
287.0ms	(log (sqrt (+ (hypot x (sqrt 1.0)) x)))
295.0ms	(log (sqrt (+ (hypot x (sqrt 1.0)) x)))

simplify102.0ms

Counts

90 → 90

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	285	728
1	887	662
2	4009	634
3	5001	624
done	5001	624

prune279.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.3b

bsearch93.0ms

Steps

Iters	Range		Point
10	4.250299402880914e-15	0.02319676823116778	0.0012626333411218892
10	-1.8070707071506563e+17	-0.15939393977811658	-0.9993980925116871

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	39
1	47	39
done	47	39

end0.0ms

sample1.9s

Algorithm

intervals

Results

918.0ms	2311×	body	1280	valid
365.0ms	1559×	body	640	valid
214.0ms	829×	body	2560	valid
106.0ms	799×	body	320	valid
62.0ms	2129×	body	80	valid
28.0ms	373×	body	160	valid