Details

sample185.0ms

Algorithm

intervals

Results

70.0ms	120×	body	1280	valid
66.0ms	63×	body	2560	valid
13.0ms	38×	body	640	valid
7.0ms	325×	pre	80	true
4.0ms	68×	body	80	overflowed
4.0ms	17×	body	320	valid
1.0ms	14×	body	80	valid
1.0ms	5×	body	160	valid

simplify98.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	245	13
3	697	13
4	3463	13
5	5001	13

prune3.0ms

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: 60.4b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (* a eps))
3.3b	(- (exp (* b eps)) 1.0)
3.9b	(- (exp (* a eps)) 1.0)
6.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-log-exp`
10×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`exp-prod` `exp-to-pow` `rem-exp-log`

Counts

4 → 52

Calls

4 calls:

2.0ms	(exp (* a eps))
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series131.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(exp (* a eps))
31.0ms	(- (exp (* b eps)) 1.0)
34.0ms	(- (exp (* a eps)) 1.0)
50.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify72.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	246	355
1	721	326
2	2405	322
3	5001	320

prune211.0ms

Filtered

64 candidates to 46 candidates (71.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	59	5	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	5	65

Merged error: 47.9b

Counts

65 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

3.9b	(- (exp (* a eps)) 1.0)
6.1b	(- (exp (* (+ a b) eps)) 1.0)
6.9b	(* (* 1/2 (pow eps 2)) b)
14.6b	(* (* 1/6 (pow eps 3)) (pow b 2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-exp-log`
28×	`prod-exp`
14×	`add-cbrt-cube`
11×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*`
8×	`pow-to-exp` `pow-exp` `add-log-exp`
7×	`add-cube-cbrt`
6×	`pow1` `cbrt-unprod`
3×	`unpow-prod-down`
2×	`sub-neg` `flip3--` `diff-log` `associate-l` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`pow-prod-down` `unpow2` `sqr-pow`

Counts

4 → 78

Calls

4 calls:

4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
10.0ms	(* (* 1/2 (pow eps 2)) b)
8.0ms	(* (* 1/6 (pow eps 3)) (pow b 2))

series148.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (exp (* a eps)) 1.0)
52.0ms	(- (exp (* (+ a b) eps)) 1.0)
20.0ms	(* (* 1/2 (pow eps 2)) b)
42.0ms	(* (* 1/6 (pow eps 3)) (pow b 2))

simplify62.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	420	496
1	1952	441
2	5001	437

prune324.0ms

Filtered

90 candidates to 51 candidates (56.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	89	6	95

Merged error: 47.3b

Counts

95 → 6

localize32.0ms

Local error

Found 4 expressions with local error:

3.9b	(- (exp (* a eps)) 1.0)
5.7b	(* (* 1/6 (* (pow eps 3) b)) b)
6.1b	(- (exp (* (+ a b) eps)) 1.0)
6.9b	(* (* 1/2 (pow eps 2)) b)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log`
19×	`prod-exp`
18×	`add-cbrt-cube`
11×	`pow1`
10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`cbrt-unprod`
8×	`add-log-exp`
6×	`add-cube-cbrt` `associate-r`
4×	`pow-prod-down`
2×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `associate-l` `pow-exp` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 69

Calls

4 calls:

4.0ms	(- (exp (* a eps)) 1.0)
8.0ms	(* (* 1/6 (* (pow eps 3) b)) b)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (* 1/2 (pow eps 2)) b)

series148.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (exp (* a eps)) 1.0)
43.0ms	(* (* 1/6 (* (pow eps 3) b)) b)
50.0ms	(- (exp (* (+ a b) eps)) 1.0)
21.0ms	(* (* 1/2 (pow eps 2)) b)

simplify67.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	413	465
1	1884	401
2	5002	398

prune295.0ms

Filtered

81 candidates to 49 candidates (60.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	81	6	87

Merged error: 47.2b

Counts

87 → 6

localize34.0ms

Local error

Found 4 expressions with local error:

5.3b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (/ (+ (neg (* 1.0 1.0)) (pow (exp a) (* 2 eps))) (+ (exp (* a eps)) 1.0)) (* b (+ (+ (* (* 1/2 (pow eps 2)) b) (* (* 1/6 (* (pow eps 3) b)) b)) eps))))
5.7b	(* (* 1/6 (* (pow eps 3) b)) b)
6.1b	(- (exp (* (+ a b) eps)) 1.0)
6.9b	(* (* 1/2 (pow eps 2)) b)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-exp-log`
59×	`add-cbrt-cube`
36×	`prod-exp`
26×	`cbrt-unprod`
14×	`cbrt-undiv` `div-exp`
11×	`pow1`
8×	`add-sqr-sqrt` `-un-lft-identity` `associate-r/`
6×	`add-cube-cbrt` `associate-r` `add-log-exp`
5×	`associate-/r/`
4×	`pow-prod-down`
2×	`frac-times` `pow-to-exp` `flip3--` `flip3-+` `associate-l` `pow-exp` `*-commutative` `flip--` `flip-+` `associate-/l/`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `associate-l/` `clear-num` `associate-/r` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 95

Calls

4 calls:

31.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (/ (+ (neg (* 1.0 1.0)) (pow (exp a) (* 2 eps))) (+ (exp (* a eps)) 1.0)) (* b (+ (+ (* (* 1/2 (pow eps 2)) b) (* (* 1/6 (* (pow eps 3) b)) b)) eps))))
8.0ms	(* (* 1/6 (* (pow eps 3) b)) b)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (* 1/2 (pow eps 2)) b)

series2.9s

Counts

4 → 12

Calls

4 calls:

2.8s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (/ (+ (neg (* 1.0 1.0)) (pow (exp a) (* 2 eps))) (+ (exp (* a eps)) 1.0)) (* b (+ (+ (* (* 1/2 (pow eps 2)) b) (* (* 1/6 (* (pow eps 3) b)) b)) eps))))
42.0ms	(* (* 1/6 (* (pow eps 3) b)) b)
52.0ms	(- (exp (* (+ a b) eps)) 1.0)
21.0ms	(* (* 1/2 (pow eps 2)) b)

simplify48.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1119	2494
1	5002	2013

prune555.0ms

Filtered

107 candidates to 70 candidates (65.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	3	1	4
Picked	1	0	1
Done	1	0	1
Total	110	3	113

Merged error: 0.1b

Counts

113 → 3

regimes74.0ms

Accuracy

0% (3.4b remaining)

Error of 3.5b against oracle of 0.1b and baseline of 3.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	4
1	12	4

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.6s	2488×	body	2560	valid
2.2s	3436×	body	1280	valid
372.0ms	1102×	body	640	valid
214.0ms	9969×	pre	80	true
134.0ms	1966×	body	80	overflowed
89.0ms	374×	body	320	valid
34.0ms	470×	body	80	valid
20.0ms	133×	body	160	valid

Details

sample185.0ms

simplify98.0ms

prune3.0ms

localize16.0ms

rewrite15.0ms

series131.0ms

simplify72.0ms

prune211.0ms

localize27.0ms

rewrite28.0ms

series148.0ms

simplify62.0ms

prune324.0ms

localize32.0ms

rewrite25.0ms

series148.0ms

simplify67.0ms

prune295.0ms

localize34.0ms

rewrite54.0ms

series2.9s

simplify48.0ms

prune555.0ms

regimes74.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.0s

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