Details

sample59.0ms

Algorithm

intervals

Results

27.0ms	71×	body	1280	valid
11.0ms	47×	body	640	valid
7.0ms	27×	body	2560	valid
3.0ms	26×	body	320	valid
2.0ms	74×	body	80	valid
1.0ms	11×	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: 52.8b

localize9.0ms

Local error

Found 3 expressions with local error:

1.2b	(+ x (sqrt (+ (* x x) 1.0)))
1.9b	(log (+ x (sqrt (+ (* x x) 1.0))))
17.6b	(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)))
6.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

series263.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(+ x (sqrt (+ (* x x) 1.0)))
165.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
41.0ms	(sqrt (+ (* x x) 1.0))

simplify143.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (138.0ms)

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

prune137.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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)))

rewrite84.0ms

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:

12.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
52.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series284.0ms

Counts

2 → 6

Calls

2 calls:

150.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
134.0ms	(* 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

prune409.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 0.0625) (pow x 5))
0.3b	(/ 0.125 (pow x 3))
12.4b	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
17.5b	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite162.0ms

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)))))
72.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series319.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (- 0.0625) (pow x 5))
41.0ms	(/ 0.125 (pow x 3))
177.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
56.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify104.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	837	1970
1	3817	1891
2	5002	1883

prune569.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

8.8b	(log (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))))
8.8b	(log (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))))
17.5b	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))
17.5b	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite287.0ms

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:

69.0ms	(log (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))))
70.0ms	(log (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))))
70.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))
71.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series304.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(log (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))))
101.0ms	(log (sqrt (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))))
51.0ms	(- (/ 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))))

simplify54.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	406	2188
1	1319	2042
2	5001	1986

prune458.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes30.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 32.3b

bsearch92.0ms

Steps

Iters	Range		Point
10	9.598072339636849e-08	814.2255113159289	0.8916223552936648
11	-402.67606408878214	-1.1015269942960052e-19	-1.030140799834648

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	39
1	43	39

end0.0ms

sample1.8s

Algorithm

intervals

Results

964.0ms	2374×	body	1280	valid
354.0ms	1550×	body	640	valid
207.0ms	780×	body	2560	valid
103.0ms	763×	body	320	valid
67.0ms	2157×	body	80	valid
28.0ms	376×	body	160	valid