Details

analyze257.0ms

Algorithm: search

sample76.0ms

Algorithm

intervals

Results

29.0ms	49×	body	1280	valid
15.0ms	41×	body	640	valid
11.0ms	128×	body	80	valid
6.0ms	26×	body	320	valid
2.0ms	12×	body	160	valid
1.0ms	7×	body	80	invalid
1.0ms	1×	body	1280	invalid
1.0ms	7×	body	80	overflowed
0.0ms	1×	body	640	invalid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (38.0ms)

Iter	Nodes	Cost
0	46	16
1	122	16
2	347	16
3	1295	16
4	5001	15

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 30.2b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b	(* (+ 1.0 eps) x)
0.0b	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
3.2b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

122×	`*-un-lft-identity`
106×	`times-frac`
94×	`add-sqr-sqrt`
36×	`add-cube-cbrt`
26×	`distribute-lft-out--`
17×	`difference-of-squares`
11×	`distribute-lft-out`
10×	`add-cbrt-cube` `associate-/l*`
8×	`add-exp-log`
6×	`pow1` `associate-/r*` `add-log-exp`
4×	`associate-l` `div-inv` `associate-/l/`
3×	`div-sub` `associate-r`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `associate-*l/` `clear-num` `flip--` `flip-+`
1×	`sub-neg` `distribute-rgt-out--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `sub-div` `associate--r-` `unswap-sqr`

Counts

4 → 137

Calls

4 calls:

13.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
6.0ms	(* (+ 1.0 eps) x)
11.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
156.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series88.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
5.0ms	(* (+ 1.0 eps) x)
12.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
59.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify71.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	689	1986
1	2265	1877
2	5002	1876

prune408.0ms

Filtered

109 candidates to 149 candidates (-36.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	148	2	150

Merged error: 0.4b

Counts

150 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
0.2b	(* 0.5 (pow x 2))
6.6b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`associate-r`
13×	`add-exp-log`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp` `unswap-sqr`
7×	`add-cbrt-cube`
6×	`associate-l` `prod-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`cube-mult` `sub-neg` `flip3--` `unpow3` `associate--l+` `sum-log` `flip--`

Counts

3 → 72

Calls

3 calls:

6.0ms	(* 0.33333333333333337 (pow x 3))
8.0ms	(* 0.5 (pow x 2))
7.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series12.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(* 0.33333333333333337 (pow x 3))
3.0ms	(* 0.5 (pow x 2))
5.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify47.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	281	376
1	1246	330
2	5001	323

prune135.0ms

Filtered

48 candidates to 81 candidates (-68.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	78	5	83

Merged error: 0.4b

Counts

83 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

6.6b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
10.2b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
10.2b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
10.2b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`pow1/3`
2×	`diff-log`
1×	`sub-neg` `associate--l+` `sum-log`

Counts

4 → 53

Calls

4 calls:

7.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
7.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
7.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
7.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

series37.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
10.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
10.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
12.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

simplify139.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	253	983
1	904	924
2	4252	836
3	5001	836

prune371.0ms

Filtered

59 candidates to 65 candidates (-10.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	65	5	70

Merged error: 0.4b

Counts

70 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

5.4b	(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
5.4b	(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
6.6b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
6.6b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `diff-log` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate--l+` `sum-log`

Counts

4 → 58

Calls

4 calls:

7.0ms	(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
7.0ms	(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
7.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
10.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series22.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
7.0ms	(sqrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
5.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
5.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify118.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	199	708
1	707	666
2	3357	652
3	5001	650

prune218.0ms

Filtered

54 candidates to 70 candidates (-29.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	70	5	75

Merged error: 0.4b

Counts

75 → 5

regimes131.0ms

Accuracy

96.5% (0.6b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.8b

bsearch192.0ms

Steps

Iters	Range		Point
10	0.001875032967631575	60023238.580744036	1.743909018348581

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	43
1	45	43

end0.0ms

analyze250.0ms

Algorithm: search

sample2.2s

Algorithm

intervals

Results

978.0ms	1661×	body	1280	valid
451.0ms	1212×	body	640	valid
361.0ms	4150×	body	80	valid
169.0ms	652×	body	320	valid
56.0ms	325×	body	160	valid
17.0ms	187×	body	80	invalid
15.0ms	187×	body	80	overflowed
14.0ms	23×	body	1280	invalid
6.0ms	15×	body	640	invalid
4.0ms	12×	body	320	invalid
0.0ms	2×	body	160	invalid

Details

analyze257.0ms

sample76.0ms

simplify40.0ms

prune12.0ms

localize19.0ms

rewrite194.0ms

series88.0ms

simplify71.0ms

prune408.0ms

localize10.0ms

rewrite24.0ms

series12.0ms

simplify47.0ms

prune135.0ms

localize15.0ms

rewrite30.0ms

series37.0ms

simplify139.0ms

prune371.0ms

localize14.0ms

rewrite33.0ms

series22.0ms

simplify118.0ms

prune218.0ms

regimes131.0ms

bsearch192.0ms

simplify2.0ms

end0.0ms

analyze250.0ms

sample2.2s

Profiling