Details

sample188.0ms

Algorithm

intervals

Results

76.0ms	72×	body	2560	valid
68.0ms	117×	body	1280	valid
9.0ms	27×	body	640	valid
7.0ms	326×	pre	80	true
4.0ms	70×	body	80	overflowed
3.0ms	15×	body	320	valid
1.0ms	8×	body	160	valid
1.0ms	17×	body	80	valid

simplify103.0ms

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: 59.5b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.9b	(- (exp (* b eps)) 1.0)
4.3b	(- (exp (* a eps)) 1.0)
5.3b	(- (exp (* (+ a b) eps)) 1.0)

rewrite24.0ms

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:

10.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series172.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
32.0ms	(- (exp (* b eps)) 1.0)
40.0ms	(- (exp (* a eps)) 1.0)
47.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (9.0ms)

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

prune305.0ms

Filtered

88 candidates to 66 candidates (75.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	5	89

Merged error: 48.7b

Counts

89 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

3.0b	(+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps)))
5.3b	(- (exp (* (+ a b) eps)) 1.0)
14.2b	(* (pow a 2) (pow eps 2))
17.4b	(* (pow a 3) (pow eps 3))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
32×	`unswap-sqr`
28×	`add-exp-log` `unpow-prod-down`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`prod-exp`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt` `cube-prod`
12×	`pow-to-exp` `pow-exp`
11×	`add-log-exp`
10×	`unpow2`
8×	`add-cbrt-cube`
4×	`pow1`
3×	`sum-log`
2×	`cube-mult` `unpow3` `pow-prod-down` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `sub-neg` `associate-+r+` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 137

Calls

4 calls:

12.0ms	(+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps)))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow a 2) (pow eps 2))
9.0ms	(* (pow a 3) (pow eps 3))

series254.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps)))
52.0ms	(- (exp (* (+ a b) eps)) 1.0)
32.0ms	(* (pow a 2) (pow eps 2))
65.0ms	(* (pow a 3) (pow eps 3))

simplify97.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	504	927
1	2461	815
2	5002	772

prune529.0ms

Filtered

149 candidates to 79 candidates (53.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	147	7	154

Merged error: 48.2b

Counts

154 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

2.0b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps)) (- (exp (* b eps)) 1.0)))
2.9b	(- (exp (* b eps)) 1.0)
5.3b	(- (exp (* (+ a b) eps)) 1.0)
14.2b	(* (pow a 2) (pow eps 2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log` `add-sqr-sqrt`
18×	`add-cbrt-cube`
16×	`unswap-sqr`
14×	`unpow-prod-down`
13×	`prod-exp`
12×	`*-un-lft-identity`
10×	`unpow2` `sqr-pow`
8×	`add-cube-cbrt` `associate-r` `associate-l` `associate-/r/` `add-log-exp`
6×	`pow-to-exp` `flip3--` `pow-exp` `flip--`
5×	`cbrt-unprod`
4×	`pow1` `cbrt-undiv` `frac-times` `associate-*r/` `div-exp`
3×	`flip3-+` `flip-+`
2×	`sub-neg` `diff-log` `associate-*l/` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`frac-2neg` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 110

Calls

4 calls:

16.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps)) (- (exp (* b eps)) 1.0)))
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
8.0ms	(* (pow a 2) (pow eps 2))

series914.0ms

Counts

4 → 12

Calls

4 calls:

590.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps)) (- (exp (* b eps)) 1.0)))
242.0ms	(- (exp (* b eps)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)
36.0ms	(* (pow a 2) (pow eps 2))

simplify107.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	720	1386
1	3838	1146
2	5002	1146

prune394.0ms

Filtered

122 candidates to 79 candidates (64.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	124	5	129

Merged error: 0.0b

Counts

129 → 5

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 19

Calls

1 calls:

11.0ms

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

series11.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify71.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	101	104
1	345	94
2	1153	91
3	2755	90
4	5001	90

prune29.0ms

Filtered

22 candidates to 14 candidates (63.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	21	6	27

Merged error: 0.0b

Counts

27 → 6

regimes97.0ms

Accuracy

0% (3.3b remaining)

Error of 3.4b against oracle of 0.1b and baseline of 3.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.7s	2570×	body	2560	valid
1.9s	3470×	body	1280	valid
346.0ms	1048×	body	640	valid
209.0ms	9882×	pre	80	true
124.0ms	1880×	body	80	overflowed
74.0ms	327×	body	320	valid
33.0ms	462×	body	80	valid
18.0ms	125×	body	160	valid

Details

sample188.0ms

simplify103.0ms

prune4.0ms

localize20.0ms

rewrite24.0ms

series172.0ms

simplify43.0ms

prune305.0ms

localize27.0ms

rewrite37.0ms

series254.0ms

simplify97.0ms

prune529.0ms

localize22.0ms

rewrite35.0ms

series914.0ms

simplify107.0ms

prune394.0ms

localize5.0ms

rewrite12.0ms

series11.0ms

simplify71.0ms

prune29.0ms

regimes97.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.8s

Profiling