Details

sample63.0ms

Algorithm

intervals

Results

33.0ms	77×	body	1280	valid
12.0ms	54×	body	640	valid
6.0ms	21×	body	2560	valid
2.0ms	78×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	10×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	5
1	10	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.7b

localize6.0ms

Local error

Found 3 expressions with local error:

0.5b	(+ x (sqrt (+ (* x x) 1.0)))
2.2b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.5b	(sqrt (+ (* x x) 1.0))

rewrite25.0ms

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:

11.0ms	(+ x (sqrt (+ (* x x) 1.0)))
8.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms	(sqrt (+ (* x x) 1.0))

series273.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(+ x (sqrt (+ (* x x) 1.0)))
170.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
42.0ms	(sqrt (+ (* x x) 1.0))

simplify34.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (28.0ms)

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

prune183.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize14.0ms

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)))

rewrite233.0ms

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:

141.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
74.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series302.0ms

Counts

2 → 6

Calls

2 calls:

162.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
139.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify118.0ms

Algorithm

egg-herbie

Counts

306 → 306

Iterations

Useful iterations: 2 (94.0ms)

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

prune465.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
2.2b	(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

2.0ms	(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
2.0ms	(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

series429.0ms

Counts

2 → 6

Calls

2 calls:

127.0ms	(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
302.0ms	(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

simplify95.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	255	366
1	909	318
2	3872	309
3	5001	304

prune113.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
0.5b	(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
2.2b	(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))
2.2b	(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

2.0ms	(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
2.0ms	(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
2.0ms	(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))
2.0ms	(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

series848.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
129.0ms	(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
297.0ms	(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))
286.0ms	(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

simplify98.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	255	732
1	909	636
2	3872	618
3	5001	608

prune285.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes34.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.2b

bsearch84.0ms

Steps

Iters	Range		Point
10	3.2824798326487284e-15	0.08347146558812443	0.0009199034035155784
9	-5.7596417613087905	-6.7357437175194845e-09	-1.03811431304858

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	30
1	54	30
2	57	30
3	57	30

end0.0ms

sample1.8s

Algorithm

intervals

Results

917.0ms	2308×	body	1280	valid
365.0ms	1563×	body	640	valid
212.0ms	786×	body	2560	valid
102.0ms	767×	body	320	valid
63.0ms	2171×	body	80	valid
31.0ms	405×	body	160	valid