Details

sample214.0ms

Algorithm

intervals

Results

70.0ms	74×	body	2560	valid
59.0ms	117×	body	1280	valid
49.0ms	57×	body	10240	exit
10.0ms	37×	body	640	valid
6.0ms	313×	pre	80	true
2.0ms	10×	body	320	valid
1.0ms	14×	body	80	valid
0.0ms	4×	body	160	valid

simplify96.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

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

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.2b	(- (exp (* a eps)) 1.0)
2.6b	(- (exp (* b eps)) 1.0)
3.7b	(- (exp (* (+ a b) eps)) 1.0)

rewrite41.0ms

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:

16.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
7.0ms	(- (exp (* a eps)) 1.0)
7.0ms	(- (exp (* b eps)) 1.0)
9.0ms	(- (exp (* (+ a b) eps)) 1.0)

series173.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
35.0ms	(- (exp (* a eps)) 1.0)
37.0ms	(- (exp (* b eps)) 1.0)
47.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	346	733
1	1449	673
2	5001	673

prune345.0ms

Filtered

88 candidates to 66 candidates (75.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 49.0b

Counts

89 → 4

localize28.0ms

Local error

Found 4 expressions with local error:

3.7b	(- (exp (* (+ a b) eps)) 1.0)
3.7b	(* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
14.1b	(* (pow a 3) (pow eps 3))
15.2b	(* (pow a 2) (pow eps 2))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
46×	`associate-l`
33×	`unswap-sqr`
30×	`add-exp-log`
28×	`unpow-prod-down`
25×	`associate-r`
20×	`add-cube-cbrt` `sqr-pow`
19×	`prod-exp`
18×	`distribute-lft-out`
17×	`pow-prod-down`
16×	`pow-unpow`
14×	`pow1` `cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`add-cbrt-cube` `unpow2`
6×	`add-log-exp`
4×	`frac-times` `flip3--` `pow-pow` `flip--`
3×	`sub-neg` `flip3-+` `*-commutative` `cbrt-unprod` `flip-+`
2×	`distribute-rgt-in` `cube-mult` `distribute-lft-in` `unpow3` `associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log`

Counts

4 → 180

Calls

4 calls:

9.0ms	(- (exp (* (+ a b) eps)) 1.0)
126.0ms	(* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
13.0ms	(* (pow a 3) (pow eps 3))
16.0ms	(* (pow a 2) (pow eps 2))

series278.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (exp (* (+ a b) eps)) 1.0)
123.0ms	(* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
70.0ms	(* (pow a 3) (pow eps 3))
33.0ms	(* (pow a 2) (pow eps 2))

simplify132.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 2 (114.0ms)

Iter	Nodes	Cost
0	729	1701
1	3677	1547
2	5001	1504

prune723.0ms

Filtered

192 candidates to 97 candidates (50.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	189	3	192
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	190	6	196

Merged error: 48.5b

Counts

196 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

3.0b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
3.7b	(- (exp (* (+ a b) eps)) 1.0)
3.7b	(* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
15.2b	(* (pow a 2) (pow eps 2))

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

666×	`*-un-lft-identity`
499×	`associate-l`
336×	`times-frac`
314×	`add-sqr-sqrt`
288×	`distribute-lft-out`
213×	`associate-r`
132×	`add-cube-cbrt`
57×	`unswap-sqr`
42×	`*-commutative` `distribute-lft-out--` `difference-of-squares`
30×	`add-exp-log`
24×	`associate-/r*`
20×	`add-cbrt-cube`
14×	`unpow-prod-down` `prod-exp` `associate-/l*`
10×	`pow1` `unpow2` `sqr-pow`
9×	`pow-prod-down`
8×	`frac-times` `pow-unpow` `flip3--` `associate-/r/` `flip--`
6×	`pow-to-exp` `flip3-+` `associate-*r/` `pow-exp` `cbrt-unprod` `flip-+` `add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-*l/`
3×	`sub-neg`
2×	`distribute-rgt-in` `pow-pow` `distribute-lft-in` `associate-/l/`
1×	`frac-2neg` `diff-log` `clear-num` `div-inv`

Counts

4 → 516

Calls

4 calls:

129.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
10.0ms	(- (exp (* (+ a b) eps)) 1.0)
106.0ms	(* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
11.0ms	(* (pow a 2) (pow eps 2))

series1.0s

Counts

4 → 12

Calls

4 calls:

790.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
52.0ms	(- (exp (* (+ a b) eps)) 1.0)
118.0ms	(* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
42.0ms	(* (pow a 2) (pow eps 2))

simplify150.0ms

Algorithm

egg-herbie

Counts

528 → 528

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1750	12883
1	5001	12598

prune1.7s

Filtered

528 candidates to 233 candidates (44.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	527	1	528
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	531	3	534

Merged error: 0.0b

Counts

534 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-add`
54×	`associate-/r` `associate-/l`
49×	`*-un-lft-identity`
39×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`frac-2neg` `clear-num`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 99

Calls

1 calls:

15.0ms

(+ (/ 1 b) (/ 1 a))

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

(+ (/ 1 b) (/ 1 a))

simplify63.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	706	750
1	2834	572
2	5001	464

prune67.0ms

Filtered

102 candidates to 27 candidates (26.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	101	4	105

Merged error: 0b

Counts

105 → 4

regimes79.0ms

Accuracy

0% (2.9b remaining)

Error of 3.2b against oracle of 0.3b and baseline of 3.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.6s	2654×	body	2560	valid
1.7s	3427×	body	1280	valid
1.7s	1929×	body	10240	exit
295.0ms	1037×	body	640	valid
173.0ms	9933×	pre	80	true
60.0ms	335×	body	320	valid
25.0ms	429×	body	80	valid
14.0ms	122×	body	160	valid