Details

sample66.0ms

Algorithm

intervals

Results

36.0ms	84×	body	1280	valid
8.0ms	29×	body	2560	valid
8.0ms	34×	body	640	valid
4.0ms	32×	body	320	valid
2.0ms	69×	body	80	valid
1.0ms	8×	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: 51.6b

localize6.0ms

Local error

Found 3 expressions with local error:

0.8b	(+ x (sqrt (+ (* x x) 1.0)))
1.8b	(log (+ x (sqrt (+ (* x x) 1.0))))
13.9b	(sqrt (+ (* x x) 1.0))

rewrite16.0ms

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:

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

series278.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(+ x (sqrt (+ (* x x) 1.0)))
171.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
47.0ms	(sqrt (+ (* x x) 1.0))

simplify142.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (136.0ms)

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

prune143.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

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)))

rewrite82.0ms

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:

15.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
48.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series301.0ms

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))))
143.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify119.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 1 (22.0ms)

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

prune409.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 0.0625) (pow x 5))
0.2b	(/ 0.125 (pow x 3))
13.6b	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
18.3b	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite156.0ms

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:

6.0ms	(/ (- 0.0625) (pow x 5))
5.0ms	(/ 0.125 (pow x 3))
68.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
67.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series327.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (- 0.0625) (pow x 5))
36.0ms	(/ 0.125 (pow x 3))
179.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
57.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify98.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (77.0ms)

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

prune571.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
0.0b	(+ x (/ 0.5 x))
0.2b	(/ 0.125 (pow x 3))
12.2b	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
36×	`times-frac`
30×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`add-log-exp`
12×	`unpow-prod-down` `cube-prod` `associate-/r*`
10×	`add-exp-log`
9×	`distribute-lft-out`
6×	`log-prod` `add-cbrt-cube`
5×	`pow1` `sum-log`
4×	`cube-mult` `unpow3` `distribute-lft-out--` `sqr-pow`
3×	`associate-+r+` `flip3-+` `div-exp` `flip-+` `associate-/l*`
2×	`+-commutative` `log-div` `diff-log`
1×	`cbrt-undiv` `pow-to-exp` `associate-+r-` `sub-neg` `frac-2neg` `rem-log-exp` `pow-exp` `associate--l+` `clear-num` `log-pow` `div-inv`

Counts

4 → 114

Calls

4 calls:

19.0ms	(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
5.0ms	(+ x (/ 0.5 x))
5.0ms	(/ 0.125 (pow x 3))
23.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series287.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
40.0ms	(+ x (/ 0.5 x))
42.0ms	(/ 0.125 (pow x 3))
155.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	436	787
1	2073	725
2	5002	723

prune220.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes100.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.2b

bsearch73.0ms

Steps

Iters	Range		Point
7	0.04032056371688071	6.164824567421913	0.8968882936176147
9	-3875183.9477288676	-0.008763241487176904	-0.9973237802495053

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	27
1	41	27

end0.0ms

sample1.9s

Algorithm

intervals

Results

952.0ms	2341×	body	1280	valid
350.0ms	1504×	body	640	valid
233.0ms	862×	body	2560	valid
115.0ms	810×	body	320	valid
70.0ms	2112×	body	80	valid
28.0ms	371×	body	160	valid