Details

sample60.0ms

Algorithm

intervals

Results

27.0ms	66×	body	1280	valid
10.0ms	46×	body	640	valid
7.0ms	27×	body	2560	valid
4.0ms	32×	body	320	valid
2.0ms	72×	body	80	valid
1.0ms	13×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	7	9
1	10	8
done	10	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.8b

localize10.0ms

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))

rewrite22.0ms

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:

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

series289.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(+ x (sqrt (+ (* x x) 1.0)))
186.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
44.0ms	(sqrt (+ (* x x) 1.0))

simplify1.5s

Counts

61 → 61

Iterations

Useful iterations: 3 (723.0ms)

Iter	Nodes	Cost
0	139	813
1	329	677
2	941	609
3	3494	595
done	5000	595

prune208.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma -1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

series152.0ms

Counts

1 → 3

Calls

1 calls:

152.0ms

(fma -1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify617.0ms

Counts

13 → 13

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	25	295
1	51	295
2	167	256
3	902	256
done	5001	256

prune54.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

1.1b	(+ x (hypot x (sqrt 1.0)))
3.4b	(log (+ x (hypot x (sqrt 1.0))))

rewrite6.0ms

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:

2.0ms	(+ x (hypot x (sqrt 1.0)))
2.0ms	(log (+ x (hypot x (sqrt 1.0))))

series598.0ms

Counts

2 → 6

Calls

2 calls:

136.0ms	(+ x (hypot x (sqrt 1.0)))
462.0ms	(log (+ x (hypot x (sqrt 1.0))))

simplify1.2s

Counts

40 → 40

Iterations

Useful iterations: 3 (396.0ms)

Iter	Nodes	Cost
0	102	509
1	240	487
2	682	433
3	2977	430
done	5000	430

prune115.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ x (hypot x (sqrt 1.0)))
1.1b	(+ x (hypot x (sqrt 1.0)))
3.4b	(log (sqrt (+ x (hypot x (sqrt 1.0)))))
3.4b	(log (sqrt (+ x (hypot x (sqrt 1.0)))))

rewrite12.0ms

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:

2.0ms	(+ x (hypot x (sqrt 1.0)))
2.0ms	(+ x (hypot x (sqrt 1.0)))
3.0ms	(log (sqrt (+ x (hypot x (sqrt 1.0)))))
3.0ms	(log (sqrt (+ x (hypot x (sqrt 1.0)))))

series881.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(+ x (hypot x (sqrt 1.0)))
134.0ms	(+ x (hypot x (sqrt 1.0)))
299.0ms	(log (sqrt (+ x (hypot x (sqrt 1.0)))))
314.0ms	(log (sqrt (+ x (hypot x (sqrt 1.0)))))

simplify1.4s

Counts

90 → 90

Iterations

Useful iterations: 3 (570.0ms)

Iter	Nodes	Cost
0	124	1234
1	287	1164
2	789	1034
3	3234	1022
done	5000	1022

prune301.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes45.0ms

Accuracy

99.6% (0.1b remaining)

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

bsearch78.0ms

Steps

Iters	Range		Point
9	3.182061564411226e-09	0.0591185632533196	0.001172054851302572
7	-1.204215327568116	-0.04390830018224924	-0.9990009314811332

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	79
1	46	79
done	46	79

end0.0ms

sample1.8s

Algorithm

intervals

Results

946.0ms	2373×	body	1280	valid
363.0ms	1558×	body	640	valid
211.0ms	798×	body	2560	valid
105.0ms	785×	body	320	valid
68.0ms	2073×	body	80	valid
31.0ms	413×	body	160	valid