Details

sample975.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 24.328959%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results

12.0ms	69×	body	1280	valid
6.0ms	52×	body	640	valid
2.0ms	101×	body	80	valid
2.0ms	26×	body	320	valid
0.0ms	8×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	8	4
2	8	4

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: 38.7b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1.0))
3.0b	(- (exp x) 1.0)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 51

Calls

2 calls:

6.0ms	(/ (exp x) (- (exp x) 1.0))
4.0ms	(- (exp x) 1.0)

series8.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(/ (exp x) (- (exp x) 1.0))
2.0ms	(- (exp x) 1.0)

simplify68.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	180	378
1	542	357
2	2174	354
3	5003	354

prune84.0ms

Filtered

41 candidates to 57 candidates (-39.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	54	3	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	3	58

Merged error: 0.0b

Counts

58 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp x) (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
0.0b	(+ (* x 1/6) 1/2)
0.1b	(* (pow x 2) (+ (* x 1/6) 1/2))
0.3b	(* x 1/6)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
12×	`add-exp-log`
11×	`associate-l`
10×	`add-cbrt-cube`
9×	`times-frac`
6×	`pow1` `associate-r` `add-log-exp`
5×	`unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`associate-r/` `associate-/r/` `-commutative` `cbrt-unprod` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `frac-2neg` `distribute-lft-in` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 89

Calls

4 calls:

9.0ms	(/ (exp x) (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
4.0ms	(+ (* x 1/6) 1/2)
7.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
4.0ms	(* x 1/6)

series17.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (exp x) (+ (* (pow x 2) (+ (* x 1/6) 1/2)) x))
3.0ms	(+ (* x 1/6) 1/2)
6.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
2.0ms	(* x 1/6)

simplify62.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	422	672
1	1952	620
2	5001	618

prune135.0ms

Filtered

71 candidates to 101 candidates (-42.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	101	3	104

Merged error: 0.0b

Counts

104 → 3

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (sqrt (exp x)) (/ (sqrt (exp x)) (- (exp x) 1.0)))
0.0b	(/ (sqrt (exp x)) (- (exp x) 1.0))
3.0b	(- (exp x) 1.0)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-sqr-sqrt`
69×	`*-un-lft-identity`
64×	`times-frac`
41×	`add-cube-cbrt` `sqrt-prod`
36×	`associate-r`
14×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-l` `associate-/l*` `unswap-sqr`
5×	`pow1` `associate-/r*` `add-log-exp`
4×	`associate-/r/`
3×	`flip3--` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 131

Calls

3 calls:

17.0ms	(* (sqrt (exp x)) (/ (sqrt (exp x)) (- (exp x) 1.0)))
8.0ms	(/ (sqrt (exp x)) (- (exp x) 1.0))
4.0ms	(- (exp x) 1.0)

series21.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(* (sqrt (exp x)) (/ (sqrt (exp x)) (- (exp x) 1.0)))
12.0ms	(/ (sqrt (exp x)) (- (exp x) 1.0))
2.0ms	(- (exp x) 1.0)

simplify51.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	358	1290
1	1549	1167
2	5001	1121

prune117.0ms

Filtered

84 candidates to 140 candidates (-66.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	140	3	143

Merged error: 0b

Counts

143 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 7/5760 (pow x 3)) (/ 1 x))
0.1b	(* 7/5760 (pow x 3))
0.3b	(* 1/24 x)
14.8b	(* (sqrt (exp x)) (- (+ (* 7/5760 (pow x 3)) (/ 1 x)) (* 1/24 x)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
18×	`associate-r`
13×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
12×	`associate-l`
10×	`add-cbrt-cube`
8×	`pow1`
7×	`unswap-sqr`
6×	`add-log-exp`
5×	`prod-exp`
4×	`unpow-prod-down` `cube-prod` `sqrt-prod`
3×	`distribute-rgt-in` `distribute-lft-in` `*-commutative` `cbrt-unprod`
2×	`sub-neg` `associate-*r/` `pow-prod-down` `associate--l+` `sqr-pow`
1×	`+-commutative` `cube-mult` `pow-to-exp` `flip3--` `flip3-+` `unpow3` `pow-exp` `sum-log` `flip--` `flip-+`

Counts

4 → 90

Calls

4 calls:

6.0ms	(+ (* 7/5760 (pow x 3)) (/ 1 x))
6.0ms	(* 7/5760 (pow x 3))
3.0ms	(* 1/24 x)
13.0ms	(* (sqrt (exp x)) (- (+ (* 7/5760 (pow x 3)) (/ 1 x)) (* 1/24 x)))

series24.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* 7/5760 (pow x 3)) (/ 1 x))
4.0ms	(* 7/5760 (pow x 3))
2.0ms	(* 1/24 x)
7.0ms	(* (sqrt (exp x)) (- (+ (* 7/5760 (pow x 3)) (/ 1 x)) (* 1/24 x)))

simplify54.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	367	641
1	1664	585
2	5001	584

prune121.0ms

Filtered

63 candidates to 102 candidates (-61.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	102	3	105

Merged error: 0b

Counts

105 → 3

regimes60.0ms

Accuracy

0% (0.6b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

end0.0ms

sample1.8s

Algorithm

intervals

sampling

Space saved by range analysis: 24.328959%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results

395.0ms	2237×	body	1280	valid
190.0ms	1710×	body	640	valid
66.0ms	2818×	body	80	valid
65.0ms	842×	body	320	valid
20.0ms	393×	body	160	valid
0.0ms	3×	body	1280	invalid

Details

sample975.0ms

simplify4.0ms

prune2.0ms

localize4.0ms

rewrite12.0ms

series8.0ms

simplify68.0ms

prune84.0ms

localize10.0ms

rewrite26.0ms

series17.0ms

simplify62.0ms

prune135.0ms

localize6.0ms

rewrite34.0ms

series21.0ms

simplify51.0ms

prune117.0ms

localize12.0ms

rewrite30.0ms

series24.0ms

simplify54.0ms

prune121.0ms

regimes60.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.8s

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