Details

sample35.0ms

Algorithm

intervals

Results

10.0ms	69×	body	1280	valid
7.0ms	72×	body	10240	exit
6.0ms	60×	body	640	valid
2.0ms	26×	body	320	valid
2.0ms	88×	body	80	valid
1.0ms	13×	body	160	valid

simplify5.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

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: 41.9b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1.0))
4.4b	(- (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:

7.0ms	(/ (exp x) (- (exp x) 1.0))
4.0ms	(- (exp x) 1.0)

series44.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(/ (exp x) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)

simplify68.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	180	378
1	542	357
2	2210	354
3	5001	354

prune102.0ms

Filtered

57 candidates to 41 candidates (71.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	52	5	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	5	58

Merged error: 0.1b

Counts

58 → 5

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/12 x) (/ 1 x))
0.3b	(* 1/12 x)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 29

Calls

2 calls:

5.0ms	(+ (* 1/12 x) (/ 1 x))
3.0ms	(* 1/12 x)

series53.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(+ (* 1/12 x) (/ 1 x))
13.0ms	(* 1/12 x)

simplify67.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	130	119
1	448	110
2	2305	109
3	5001	109

prune50.0ms

Filtered

35 candidates to 23 candidates (65.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	35	5	40

Merged error: 0.1b

Counts

40 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
0.0b	(* (exp x) (exp x))
4.3b	(- (* (exp x) (exp x)) (* 1.0 1.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
18×	`exp-prod`
16×	`times-frac`
11×	`pow1`
8×	`add-cbrt-cube` `add-log-exp`
6×	`add-exp-log` `distribute-lft-out` `difference-of-squares`
4×	`pow-prod-down` `associate-/r` `pow-sqr` `pow-prod-up` `associate-/l`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow2` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `div-exp` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

6.0ms	(+ (exp x) 1.0)
11.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
6.0ms	(* (exp x) (exp x))
6.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

series97.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (exp x) 1.0)
50.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
13.0ms	(* (exp x) (exp x))
26.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	376	823
1	1712	737
2	5001	719

prune193.0ms

Filtered

112 candidates to 78 candidates (69.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	113	4	117

Merged error: 0.1b

Counts

117 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp 2) x)
0.0b	(+ (exp x) 1.0)
0.0b	(/ (- (pow (exp 2) x) (* 1.0 1.0)) (+ (exp x) 1.0))
4.6b	(- (pow (exp 2) x) (* 1.0 1.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
28×	`times-frac`
24×	`difference-of-squares`
20×	`add-cube-cbrt`
16×	`unpow-prod-down`
9×	`distribute-lft-out`
8×	`add-log-exp`
7×	`exp-lft-sqr` `associate-/l*` `sqr-pow`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`pow-pow` `associate-/r*`
3×	`pow-unpow` `exp-prod`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 105

Calls

4 calls:

4.0ms	(pow (exp 2) x)
4.0ms	(+ (exp x) 1.0)
9.0ms	(/ (- (pow (exp 2) x) (* 1.0 1.0)) (+ (exp x) 1.0))
5.0ms	(- (pow (exp 2) x) (* 1.0 1.0))

series126.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow (exp 2) x)
8.0ms	(+ (exp x) 1.0)
59.0ms	(/ (- (pow (exp 2) x) (* 1.0 1.0)) (+ (exp x) 1.0))
36.0ms	(- (pow (exp 2) x) (* 1.0 1.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	425	966
1	1434	891
2	5002	839

prune211.0ms

Filtered

117 candidates to 79 candidates (67.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	115	6	121

Merged error: 0.1b

Counts

121 → 6

regimes74.0ms

Accuracy

99% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 21.0b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	33
1	31	33

end0.0ms

sample1.1s

Algorithm

intervals

Results

379.0ms	2324×	body	1280	valid
267.0ms	2564×	body	10240	exit
170.0ms	1638×	body	640	valid
59.0ms	2804×	body	80	valid
55.0ms	829×	body	320	valid
17.0ms	406×	body	160	valid