Details

sample93.0ms

Algorithm

intervals

Results

30.0ms	62×	body	1280	valid
26.0ms	333×	body	80	valid
10.0ms	34×	body	640	valid
4.0ms	59×	body	80	overflowed
3.0ms	15×	body	320	valid
2.0ms	18×	body	160	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (35.0ms)

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

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 28.6b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b	(* (- 1.0 eps) x)
3.0b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 138

Calls

4 calls:

10.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
11.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
6.0ms	(* (- 1.0 eps) x)
141.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series301.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
44.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
33.0ms	(* (- 1.0 eps) x)
180.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	684	1993
1	2176	1881
2	5002	1880

prune391.0ms

Filtered

150 candidates to 107 candidates (71.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	2	151

Merged error: 0.5b

Counts

151 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (pow x 2))
0.1b	(* 0.33333333333333337 (pow x 3))
5.6b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite21.0ms

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:

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

series105.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* 0.5 (pow x 2))
41.0ms	(* 0.33333333333333337 (pow x 3))
39.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify45.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	281	376
1	1249	330
2	5002	323

prune265.0ms

Filtered

81 candidates to 48 candidates (59.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	80	3	83

Merged error: 0.5b

Counts

83 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

5.6b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
9.7b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
9.7b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
9.7b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite29.0ms

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))))

series472.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
146.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
140.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
142.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

simplify134.0ms

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

prune228.0ms

Filtered

65 candidates to 59 candidates (90.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	64	4	68

Merged error: 0.5b

Counts

68 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

9.7b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
9.7b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
9.7b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
9.7b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3--` `pow1/3` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

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

series588.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
149.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
141.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
149.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

simplify119.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	229	1104
1	830	1044
2	3711	936
3	5003	936

prune274.0ms

Filtered

64 candidates to 64 candidates (100.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	64	4	68

Merged error: 0.5b

Counts

68 → 4

regimes70.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.6b

bsearch147.0ms

Steps

Iters	Range		Point
9	6.599768314344505e-07	24.426543482179152	0.8939352765532171

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	26
1	41	26

end0.0ms

sample2.6s

Algorithm

intervals

Results

883.0ms	1726×	body	1280	valid
716.0ms	10013×	body	80	valid
403.0ms	1282×	body	640	valid
131.0ms	1917×	body	80	overflowed
126.0ms	590×	body	320	valid
48.0ms	350×	body	160	valid

Details

sample93.0ms

simplify37.0ms

prune7.0ms

localize16.0ms

rewrite176.0ms

series301.0ms

simplify64.0ms

prune391.0ms

localize9.0ms

rewrite21.0ms

series105.0ms

simplify45.0ms

prune265.0ms

localize15.0ms

rewrite29.0ms

series472.0ms

simplify134.0ms

prune228.0ms

localize20.0ms

rewrite29.0ms

series588.0ms

simplify119.0ms

prune274.0ms

regimes70.0ms

bsearch147.0ms

simplify1.0ms

end0.0ms

sample2.6s

Profiling