Details

sample241.0ms

Algorithm

intervals

Results

82.0ms	76×	body	2560	valid
65.0ms	112×	body	1280	valid
50.0ms	50×	body	5120	exit
13.0ms	41×	body	640	valid
7.0ms	306×	pre	80	true
2.0ms	10×	body	320	valid
1.0ms	14×	body	80	valid
0.0ms	3×	body	160	valid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4970	24
1	4970	24

prune17.0ms

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)

rewrite22.0ms

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
7.0ms	(- (exp (* a eps)) 1.0)
7.0ms	(- (exp (* b eps)) 1.0)
13.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify33.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5222	1190

prune146.0ms

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

localize28.0ms

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))))
10.0ms	(* (* eps eps) (+ (* a (* a 1/2)) (* eps (* 1/6 (pow a 3)))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* eps (* 1/6 (pow a 3)))
13.0ms	(- (exp (* (+ a b) eps)) 1.0)
8.0ms	(+ (* a (* a 1/2)) (* eps (* 1/6 (pow a 3))))
21.0ms	(* (* eps eps) (+ (* a (* a 1/2)) (* eps (* 1/6 (pow a 3)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4963	1004
1	4963	1004

prune134.0ms

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)

rewrite32.0ms

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

series50.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify32.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5349	1422

prune138.0ms

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

localize23.0ms

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)

rewrite36.0ms

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)))
4.0ms	(- (exp (* b eps)) 1.0)
12.0ms	(* eps (* (* a (* a eps)) (+ 1/2 (* (* eps 1/6) a))))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series286.0ms

Counts

4 → 12

Calls

4 calls:

251.0ms	(/ (* 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)
14.0ms	(* eps (* (* a (* a eps)) (+ 1/2 (* (* eps 1/6) a))))
13.0ms	(- (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

prune141.0ms

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

regimes157.0ms

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

sample7.7s

Algorithm

intervals

Results

2.7s	2515×	body	2560	valid
2.0s	3514×	body	1280	valid
1.8s	1886×	body	5120	exit
340.0ms	1026×	body	640	valid
216.0ms	9888×	pre	80	true
75.0ms	335×	body	320	valid
34.0ms	488×	body	80	valid
18.0ms	124×	body	160	valid

Details

sample241.0ms

simplify44.0ms

prune17.0ms

localize16.0ms

rewrite22.0ms

series42.0ms

simplify33.0ms

prune146.0ms

localize28.0ms

rewrite26.0ms

series56.0ms

simplify51.0ms

prune134.0ms

localize23.0ms

rewrite32.0ms

series50.0ms

simplify32.0ms

prune138.0ms

localize23.0ms

rewrite36.0ms

series286.0ms

simplify40.0ms

prune141.0ms

regimes157.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample7.7s

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