Details

sample209.0ms

Algorithm

intervals

Results

84.0ms	76×	body	2560	valid
62.0ms	112×	body	1280	valid
14.0ms	41×	body	640	valid
9.0ms	14×	body	1280	overflowed
6.0ms	306×	pre	80	true
4.0ms	5×	body	2560	overflowed
2.0ms	10×	body	320	valid
2.0ms	9×	body	320	overflowed
2.0ms	6×	body	640	overflowed
1.0ms	14×	body	80	valid
1.0ms	13×	body	80	overflowed
0.0ms	3×	body	160	valid
0.0ms	3×	body	160	overflowed

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4970	24
1	4970	24

prune15.0ms

Filtered

1 candidates to 1 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: 60.2b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.6b	(- (exp (* a eps)) 1.0)
4.2b	(- (exp (* b eps)) 1.0)
6.9b	(- (exp (* (+ a b) eps)) 1.0)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`flip3--` `flip--`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`frac-times`
3×	`diff-log`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

9.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* b eps)) 1.0)
6.0ms	(- (exp (* (+ a b) eps)) 1.0)

series41.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
7.0ms	(- (exp (* a eps)) 1.0)
7.0ms	(- (exp (* b eps)) 1.0)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify34.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5222	1190

prune145.0ms

Filtered

70 candidates to 88 candidates (-25.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	85	5	90

Merged error: 46.4b

Counts

90 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

5.7b	(* eps (* 1/6 (pow a 3)))
6.9b	(- (exp (* (+ a b) eps)) 1.0)
9.5b	(+ (* a (* a 1/2)) (* eps (* 1/6 (pow a 3))))
13.4b	(* (* eps eps) (+ (* a (* a 1/2)) (* eps (* 1/6 (pow a 3)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

6.0ms	(* eps (* 1/6 (pow a 3)))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
5.0ms	(+ (* a (* a 1/2)) (* eps (* 1/6 (pow a 3))))
9.0ms	(* (* eps eps) (+ (* a (* a 1/2)) (* eps (* 1/6 (pow a 3)))))

series55.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* eps (* 1/6 (pow a 3)))
14.0ms	(- (exp (* (+ a b) eps)) 1.0)
8.0ms	(+ (* a (* a 1/2)) (* eps (* 1/6 (pow a 3))))
23.0ms	(* (* eps eps) (+ (* a (* a 1/2)) (* eps (* 1/6 (pow a 3)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4963	1004
1	4963	1004

prune132.0ms

Filtered

52 candidates to 79 candidates (-51.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	79	5	84

Merged error: 45.7b

Counts

84 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

4.2b	(- (exp (* b eps)) 1.0)
4.6b	(* eps (* eps (* (* a a) (+ 1/2 (* (* eps 1/6) a)))))
5.1b	(* eps (* (* a a) (+ 1/2 (* (* eps 1/6) a))))
6.9b	(- (exp (* (+ a b) eps)) 1.0)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1` `add-exp-log` `add-cbrt-cube`
16×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt` `-un-lft-identity` `associate-r/`
8×	`add-log-exp`
6×	`add-cube-cbrt` `associate-l`
2×	`sub-neg` `flip3--` `flip3-+` `diff-log` `associate-r` `*-commutative` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 89

Calls

4 calls:

3.0ms	(- (exp (* b eps)) 1.0)
11.0ms	(* eps (* eps (* (* a a) (+ 1/2 (* (* eps 1/6) a)))))
8.0ms	(* eps (* (* a a) (+ 1/2 (* (* eps 1/6) a))))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series53.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (exp (* b eps)) 1.0)
15.0ms	(* eps (* eps (* (* a a) (+ 1/2 (* (* eps 1/6) a)))))
17.0ms	(* eps (* (* a a) (+ 1/2 (* (* eps 1/6) a))))
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify27.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5349	1422

prune133.0ms

Filtered

62 candidates to 101 candidates (-62.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	101	5	106

Merged error: 45.5b

Counts

106 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* a eps) (* eps (* (* a (* a eps)) (+ 1/2 (* (* eps 1/6) a))))) (- (exp (* b eps)) 1.0)))
4.2b	(- (exp (* b eps)) 1.0)
4.6b	(* eps (* (* a (* a eps)) (+ 1/2 (* (* eps 1/6) a))))
6.9b	(- (exp (* (+ a b) eps)) 1.0)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

13.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* a eps) (* eps (* (* a (* a eps)) (+ 1/2 (* (* eps 1/6) a))))) (- (exp (* b eps)) 1.0)))
3.0ms	(- (exp (* b eps)) 1.0)
10.0ms	(* eps (* (* a (* a eps)) (+ 1/2 (* (* eps 1/6) a))))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series300.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* a eps) (* eps (* (* a (* a eps)) (+ 1/2 (* (* eps 1/6) a))))) (- (exp (* b eps)) 1.0)))
7.0ms	(- (exp (* b eps)) 1.0)
17.0ms	(* eps (* (* a (* a eps)) (+ 1/2 (* (* eps 1/6) a))))
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify40.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4990	2381
1	4990	2381

prune143.0ms

Filtered

70 candidates to 101 candidates (-44.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	102	4	106

Merged error: 0.1b

Counts

106 → 4

regimes155.0ms

Accuracy

0% (3.4b remaining)

Error of 3.6b against oracle of 0.2b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	7
1	8	7

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.8s	2515×	body	2560	valid
2.0s	3514×	body	1280	valid
359.0ms	1026×	body	640	valid
269.0ms	622×	body	1280	overflowed
193.0ms	9888×	pre	80	true
111.0ms	160×	body	2560	overflowed
108.0ms	365×	body	640	overflowed
78.0ms	335×	body	320	valid
42.0ms	192×	body	320	overflowed
35.0ms	488×	body	80	valid
33.0ms	467×	body	80	overflowed
19.0ms	124×	body	160	valid
11.0ms	80×	body	160	overflowed

Details

sample209.0ms

simplify45.0ms

prune15.0ms

localize16.0ms

rewrite25.0ms

series41.0ms

simplify34.0ms

prune145.0ms

localize25.0ms

rewrite26.0ms

series55.0ms

simplify50.0ms

prune132.0ms

localize23.0ms

rewrite29.0ms

series53.0ms

simplify27.0ms

prune133.0ms

localize22.0ms

rewrite33.0ms

series300.0ms

simplify40.0ms

prune143.0ms

regimes155.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.5s

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