Details

sample68.0ms

Algorithm

intervals

Results

30.0ms	72×	body	1280	valid
14.0ms	61×	body	640	valid
6.0ms	22×	body	2560	valid
4.0ms	28×	body	320	valid
3.0ms	11×	body	160	valid
2.0ms	62×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	5
1	10	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.6b	(+ x (sqrt (+ (* x x) 1.0)))
2.3b	(log (+ x (sqrt (+ (* x x) 1.0))))
12.2b	(sqrt (+ (* x x) 1.0))

rewrite49.0ms

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:

21.0ms	(+ x (sqrt (+ (* x x) 1.0)))
16.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
10.0ms	(sqrt (+ (* x x) 1.0))

series278.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(+ x (sqrt (+ (* x x) 1.0)))
172.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
45.0ms	(sqrt (+ (* x x) 1.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (30.0ms)

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

prune192.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 1 expressions with local error:

0.1b	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
181×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
117×	`add-cube-cbrt` `*-un-lft-identity`
80×	`sqrt-prod`
40×	`sqr-pow`
30×	`cube-mult` `unpow3`
25×	`unswap-sqr`
24×	`add-exp-log`
10×	`prod-exp`
9×	`div-exp`
6×	`pow-to-exp` `pow-exp` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`cbrt-unprod`
1×	`cbrt-undiv` `expm1-log1p-u` `associate-r/` `pow-prod-down` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 272

Calls

1 calls:

97.0ms

(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series143.0ms

Counts

1 → 3

Calls

1 calls:

143.0ms

(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify94.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	729	1769
1	3838	1380
2	5003	1380

prune383.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot x (sqrt 1.0))
0.6b	(+ x (hypot x (sqrt 1.0)))
2.3b	(log (+ x (hypot x (sqrt 1.0))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 44

Calls

3 calls:

0.0ms	(hypot x (sqrt 1.0))
6.0ms	(+ x (hypot x (sqrt 1.0)))
5.0ms	(log (+ x (hypot x (sqrt 1.0))))

series508.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(hypot x (sqrt 1.0))
127.0ms	(+ x (hypot x (sqrt 1.0)))
284.0ms	(log (+ x (hypot x (sqrt 1.0))))

simplify85.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	268	349
1	886	321
2	3696	305
3	5001	303

prune136.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ x (hypot x (sqrt 1.0)))
0.6b	(+ x (hypot x (sqrt 1.0)))
2.3b	(log (+ x (hypot x (sqrt 1.0))))
2.3b	(log (+ x (hypot x (sqrt 1.0))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

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

series817.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(+ x (hypot x (sqrt 1.0)))
124.0ms	(+ x (hypot x (sqrt 1.0)))
288.0ms	(log (+ x (hypot x (sqrt 1.0))))
275.0ms	(log (+ x (hypot x (sqrt 1.0))))

simplify79.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	238	568
1	786	510
2	3259	494
3	5001	490

prune256.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes27.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.0b

bsearch75.0ms

Steps

Iters	Range		Point
8	1.317141247235427e-05	0.43775957865898985	0.000650047113090037
9	-3096.4512561506854	-0.0006592480666379122	-1.019834309395676

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	28
1	48	28
2	51	28
3	51	28

end0.0ms

sample1.9s

Algorithm

intervals

Results

928.0ms	2312×	body	1280	valid
370.0ms	1553×	body	640	valid
214.0ms	782×	body	2560	valid
114.0ms	832×	body	320	valid
64.0ms	2115×	body	80	valid
31.0ms	406×	body	160	valid