Details

sample73.0ms

Algorithm

intervals

Results

40.0ms	90×	body	1280	valid
13.0ms	54×	body	640	valid
6.0ms	22×	body	2560	valid
3.0ms	24×	body	320	valid
2.0ms	54×	body	80	valid
1.0ms	12×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	5
1	9	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ x (sqrt (+ (* x x) 1.0)))
3.0b	(log (+ x (sqrt (+ (* x x) 1.0))))
11.9b	(sqrt (+ (* x x) 1.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod`
3×	`flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow`

Counts

3 → 42

Calls

3 calls:

8.0ms	(+ x (sqrt (+ (* x x) 1.0)))
9.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

series268.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(+ x (sqrt (+ (* x x) 1.0)))
165.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
46.0ms	(sqrt (+ (* x x) 1.0))

simplify144.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (139.0ms)

Iter	Nodes	Cost
0	309	393
1	1027	364
2	4764	348
3	5002	347

prune144.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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)))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
182×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
118×	`add-cube-cbrt` `*-un-lft-identity`
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×	`pow-to-exp` `pow-exp` `add-log-exp`
4×	`pow1`
3×	`associate-r/` `associate-l*`
2×	`diff-log` `frac-sub` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `flip-+` `div-inv`

Counts

2 → 286

Calls

2 calls:

115.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
71.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series294.0ms

Counts

2 → 6

Calls

2 calls:

158.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
136.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify113.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	854	2089
1	4642	1654
2	5001	1654

prune416.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 0.125 (pow x 3))
0.3b	(/ (- 0.0625) (pow x 5))
16.0b	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
23.9b	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite379.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
110×	`*-un-lft-identity`
102×	`add-sqr-sqrt`
76×	`add-cube-cbrt`
47×	`unpow-prod-down`
26×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
19×	`associate-/r*`
17×	`sqr-pow`
15×	`add-exp-log`
14×	`cube-prod` `distribute-lft-out--`
13×	`associate-/l*`
12×	`log-prod`
10×	`difference-of-squares`
9×	`add-log-exp`
8×	`neg-mul-1` `frac-sub` `add-cbrt-cube`
6×	`div-exp`
5×	`pow1` `log-div`
4×	`cube-mult` `flip3--` `unpow3` `flip--`
3×	`diff-log` `associate--r+`
2×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `sub-neg` `frac-2neg` `div-sub` `pow-exp` `clear-num` `div-inv` `associate--r-`
1×	`distribute-frac-neg` `rem-log-exp` `log-pow`

Counts

4 → 223

Calls

4 calls:

4.0ms	(/ 0.125 (pow x 3))
6.0ms	(/ (- 0.0625) (pow x 5))
170.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
187.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ 0.125 (pow x 3))
46.0ms	(/ (- 0.0625) (pow x 5))
186.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
52.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify102.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	840	2002
1	3820	1923
2	5001	1915

prune554.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

12.9b	(log (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))))
12.9b	(log (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))))
23.9b	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))
23.9b	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite721.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
60×	`add-sqr-sqrt`
40×	`times-frac`
30×	`log-prod`
28×	`distribute-lft-out--`
24×	`sqrt-prod`
20×	`difference-of-squares`
16×	`frac-sub`
14×	`add-log-exp`
10×	`log-div` `sqrt-div`
8×	`pow1` `add-cube-cbrt` `flip3--` `flip--`
6×	`add-exp-log` `diff-log` `log-pow` `associate--r+`
4×	`sub-neg` `unpow-prod-down` `distribute-rgt-neg-in` `cube-prod` `add-cbrt-cube` `associate--r-` `sqr-pow`
2×	`neg-sub0` `sqrt-pow1` `pow1/2` `div-sub` `rem-log-exp`

Counts

4 → 120

Calls

4 calls:

171.0ms	(log (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))))
172.0ms	(log (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))))
184.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))
188.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series292.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(log (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))))
92.0ms	(log (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))))
55.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))
52.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify57.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	406	2180
1	1319	2034
2	5001	1978

prune443.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes30.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.9b

bsearch87.0ms

Steps

Iters	Range		Point
10	2.30341956868392e-10	214.50772926448735	0.8933973184951858
9	-1898619.482837422	-0.12347723982223391	-1.0248436231258424

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	39
1	43	39

end0.0ms

sample1.9s

Algorithm

intervals

Results

956.0ms	2335×	body	1280	valid
362.0ms	1537×	body	640	valid
215.0ms	773×	body	2560	valid
115.0ms	838×	body	320	valid
72.0ms	2100×	body	80	valid
33.0ms	417×	body	160	valid