Details

sample101.0ms

Algorithm

intervals

Results

26.0ms	336×	body	80	valid
26.0ms	46×	body	1280	valid
11.0ms	31×	body	640	valid
10.0ms	29×	body	320	valid
4.0ms	58×	body	80	overflowed
2.0ms	12×	body	160	valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (34.0ms)

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

prune8.0ms

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: 26.0b

Counts

2 → 1

localize17.0ms

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

rewrite168.0ms

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:

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)
135.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series84.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
12.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
5.0ms	(* (+ 1.0 eps) x)
56.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	689	1986
1	2265	1877
2	5001	1876

prune390.0ms

Filtered

109 candidates to 149 candidates (-36.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	145	4	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	146	4	150

Merged error: 1.0b

Counts

150 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (pow x 2))
0.1b	(* 0.33333333333333337 (pow x 3))
7.4b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite20.0ms

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)))

series11.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify44.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	281	367
1	1210	327
2	5001	314

prune130.0ms

Filtered

48 candidates to 81 candidates (-68.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	78	7	85

Merged error: 1.0b

Counts

85 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow x 2))
0.0b	(- 1.0 (* 0.5 (pow x 2)))
0.1b	(* 0.33333333333333337 (pow x 3))
7.4b	(+ (* 0.33333333333333337 (pow x 3)) (- 1.0 (* 0.5 (pow x 2))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

5.0ms	(* 0.5 (pow x 2))
2.0ms	(- 1.0 (* 0.5 (pow x 2)))
6.0ms	(* 0.33333333333333337 (pow x 3))
6.0ms	(+ (* 0.33333333333333337 (pow x 3)) (- 1.0 (* 0.5 (pow x 2))))

series16.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify48.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	327	436
1	1334	400
2	5001	390

prune144.0ms

Filtered

59 candidates to 97 candidates (-64.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	98	6	104

Merged error: 1.0b

Counts

104 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

7.4b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
10.3b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
10.3b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
10.3b	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite27.0ms

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

series36.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
9.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
9.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
11.0ms	(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

simplify132.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (24.0ms)

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

prune311.0ms

Filtered

59 candidates to 65 candidates (-10.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	65	6	71

Merged error: 1.0b

Counts

71 → 6

regimes149.0ms

Accuracy

96.4% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 17.7b

bsearch88.0ms

Steps

Iters	Range		Point
8	1.338191449448963	346.4143613432569	1.3538457261082366

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	28
1	43	28

end0.0ms

sample2.9s

Algorithm

intervals

Results

893.0ms	1632×	body	1280	valid
800.0ms	10143×	body	80	valid
426.0ms	1231×	body	640	valid
148.0ms	635×	body	320	valid
146.0ms	1893×	body	80	overflowed
52.0ms	345×	body	160	valid

Details

sample101.0ms

simplify36.0ms

prune8.0ms

localize17.0ms

rewrite168.0ms

series84.0ms

simplify65.0ms

prune390.0ms

localize9.0ms

rewrite20.0ms

series11.0ms

simplify44.0ms

prune130.0ms

localize9.0ms

rewrite21.0ms

series16.0ms

simplify48.0ms

prune144.0ms

localize14.0ms

rewrite27.0ms

series36.0ms

simplify132.0ms

prune311.0ms

regimes149.0ms

bsearch88.0ms

simplify1.0ms

end0.0ms

sample2.9s

Profiling