Details

sample78.0ms

Algorithm

intervals

Results

38.0ms	79×	body	1280	valid
16.0ms	57×	body	640	valid
9.0ms	27×	body	2560	valid
4.0ms	22×	body	320	valid
2.0ms	58×	body	80	valid
1.0ms	13×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	5
1	9	5

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 53.7b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.8b	(+ x (sqrt (+ (* x x) 1.0)))
2.0b	(log (+ x (sqrt (+ (* x x) 1.0))))
14.3b	(sqrt (+ (* x x) 1.0))

rewrite19.0ms

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:

6.0ms	(+ x (sqrt (+ (* x x) 1.0)))
5.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
7.0ms	(sqrt (+ (* x x) 1.0))

series17.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ x (sqrt (+ (* x x) 1.0)))
9.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

simplify137.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (132.0ms)

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

prune113.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Merged error: 0.0b

Counts

52 → 4

localize11.0ms

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)))

rewrite86.0ms

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:

13.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
51.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series28.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
16.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify115.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	854	2083
1	4642	1650
2	5002	1650

prune390.0ms

Filtered

111 candidates to 292 candidates (-163.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	291	1	292
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	291	5	296

Merged error: 0b

Counts

296 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 0.125 (pow x 3))
0.2b	(/ (neg 0.0625) (pow x 5))
15.6b	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
20.5b	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

rewrite180.0ms

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:

5.0ms	(/ 0.125 (pow x 3))
6.0ms	(/ (neg 0.0625) (pow x 5))
67.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
90.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

series23.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ 0.125 (pow x 3))
4.0ms	(/ (neg 0.0625) (pow x 5))
10.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
5.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

simplify100.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	837	1963
1	3794	1884
2	5002	1876

prune442.0ms

Filtered

152 candidates to 235 candidates (-54.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	235	0	235
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	235	5	240

Merged error: 0b

Counts

240 → 5

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))
12.6b	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite55.0ms

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:

20.0ms	(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
5.0ms	(+ x (/ 0.5 x))
5.0ms	(/ 0.125 (pow x 3))
21.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series24.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
7.0ms	(+ x (/ 0.5 x))
4.0ms	(/ 0.125 (pow x 3))
9.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	436	780
1	2075	717
2	5002	717

prune159.0ms

Filtered

73 candidates to 126 candidates (-72.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	126	5	131

Merged error: 0b

Counts

131 → 5

regimes53.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.9b

bsearch32.0ms

Steps

Iters	Range		Point
9	6.661366802070807e-05	306.28763118649994	0.8995560794456965
9	-3.853535794009	-4.644989184223309e-09	-0.9924110465569844

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	27
1	41	27

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2305×	body	1280	valid
439.0ms	1564×	body	640	valid
258.0ms	775×	body	2560	valid
133.0ms	798×	body	320	valid
90.0ms	2126×	body	80	valid
45.0ms	432×	body	160	valid

Details

sample78.0ms

simplify3.0ms

prune2.0ms

localize6.0ms

rewrite19.0ms

series17.0ms

simplify137.0ms

prune113.0ms

localize11.0ms

rewrite86.0ms

series28.0ms

simplify115.0ms

prune390.0ms

localize13.0ms

rewrite180.0ms

series23.0ms

simplify100.0ms

prune442.0ms

localize10.0ms

rewrite55.0ms

series24.0ms

simplify58.0ms

prune159.0ms

regimes53.0ms

bsearch32.0ms

simplify2.0ms

end0.0ms

sample2.2s

Profiling