Details

sample63.0ms

Algorithm

intervals

Results

32.0ms	77×	body	1280	valid
12.0ms	55×	body	640	valid
5.0ms	19×	body	2560	valid
2.0ms	19×	body	320	valid
2.0ms	68×	body	80	valid
1.0ms	18×	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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.3b

localize6.0ms

Local error

Found 3 expressions with local error:

1.0b	(+ (sqrt (fma x x 1.0)) x)
3.2b	(log (+ (sqrt (fma x x 1.0)) x))
14.7b	(sqrt (fma x x 1.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

5.0ms	(+ (sqrt (fma x x 1.0)) x)
4.0ms	(log (+ (sqrt (fma x x 1.0)) x))
1.0ms	(sqrt (fma x x 1.0))

series307.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(+ (sqrt (fma x x 1.0)) x)
183.0ms	(log (+ (sqrt (fma x x 1.0)) x))
56.0ms	(sqrt (fma x x 1.0))

simplify1.3s

Counts

61 → 61

Iterations

Useful iterations: 3 (312.0ms)

Iter	Nodes	Cost
0	125	701
1	284	639
2	867	573
3	3907	523
done	5000	523

prune194.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

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

series148.0ms

Counts

1 → 3

Calls

1 calls:

148.0ms

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

simplify328.0ms

Counts

13 → 13

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	25	295
1	51	295
2	168	259
3	949	256
done	5001	256

prune49.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sqrt 1.0) x)
0.2b	(* (sqrt (hypot (sqrt 1.0) x)) (sqrt (hypot (sqrt 1.0) x)))
3.2b	(log (+ (* (sqrt (hypot (sqrt 1.0) x)) (sqrt (hypot (sqrt 1.0) x))) x))
8.3b	(+ (* (sqrt (hypot (sqrt 1.0) x)) (sqrt (hypot (sqrt 1.0) x))) x)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`pow1`
18×	`sqrt-prod`
13×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
7×	`add-exp-log`
6×	`associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`log-prod` `pow-prod-down` `pow-sqr`
2×	`log-div` `flip3-+` `flip-+`
1×	`+-commutative` `pow2` `hypot-udef` `fma-def` `pow-plus` `sqrt-unprod` `rem-log-exp` `prod-exp` `sum-log` `rem-square-sqrt` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 91

Calls

4 calls:

0.0ms	(hypot (sqrt 1.0) x)
7.0ms	(* (sqrt (hypot (sqrt 1.0) x)) (sqrt (hypot (sqrt 1.0) x)))
5.0ms	(log (+ (* (sqrt (hypot (sqrt 1.0) x)) (sqrt (hypot (sqrt 1.0) x))) x))
5.0ms	(+ (* (sqrt (hypot (sqrt 1.0) x)) (sqrt (hypot (sqrt 1.0) x))) x)

series620.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(hypot (sqrt 1.0) x)
103.0ms	(* (sqrt (hypot (sqrt 1.0) x)) (sqrt (hypot (sqrt 1.0) x)))
286.0ms	(log (+ (* (sqrt (hypot (sqrt 1.0) x)) (sqrt (hypot (sqrt 1.0) x))) x))
132.0ms	(+ (* (sqrt (hypot (sqrt 1.0) x)) (sqrt (hypot (sqrt 1.0) x))) x)

simplify576.0ms

Counts

103 → 103

Iterations

Useful iterations: done (573.0ms)

Iter	Nodes	Cost
0	160	1742
1	351	1013
2	1217	929
done	5001	925

prune232.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ x (hypot (sqrt 1.0) x))
1.0b	(+ x (hypot (sqrt 1.0) x))
3.2b	(log (sqrt (+ x (hypot (sqrt 1.0) x))))
3.2b	(log (sqrt (+ x (hypot (sqrt 1.0) x))))

rewrite13.0ms

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

series886.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(+ x (hypot (sqrt 1.0) x))
130.0ms	(+ x (hypot (sqrt 1.0) x))
311.0ms	(log (sqrt (+ x (hypot (sqrt 1.0) x))))
310.0ms	(log (sqrt (+ x (hypot (sqrt 1.0) x))))

simplify1.4s

Counts

90 → 90

Iterations

Useful iterations: 3 (328.0ms)

Iter	Nodes	Cost
0	124	1234
1	287	1168
2	856	1034
3	3953	1024
done	5000	1024

prune268.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes39.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.1b

bsearch88.0ms

Steps

Iters	Range		Point
9	6.379368274952145e-05	25.411711264148785	0.0012348249841071897
10	-155084744.97222546	-0.0009113054925467739	-1.0079740505275243

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	66
1	42	66
done	42	66

end0.0ms

sample1.8s

Algorithm

intervals

Results

965.0ms	2369×	body	1280	valid
356.0ms	1561×	body	640	valid
201.0ms	758×	body	2560	valid
108.0ms	808×	body	320	valid
64.0ms	2113×	body	80	valid
29.0ms	391×	body	160	valid