Details

sample197.0ms

Algorithm

intervals

Results

91.0ms	91×	body	2560	valid
48.0ms	91×	body	1280	valid
17.0ms	45×	body	640	valid
6.0ms	314×	pre	80	true
4.0ms	58×	body	80	overflowed
2.0ms	11×	body	320	valid
1.0ms	15×	body	80	valid
0.0ms	3×	body	160	valid

simplify95.0ms

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

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 60.3b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.2b	(- (exp (* b eps)) 1.0)
5.2b	(- (exp (* a eps)) 1.0)
7.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite23.0ms

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

series196.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
41.0ms	(- (exp (* b eps)) 1.0)
42.0ms	(- (exp (* a eps)) 1.0)
54.0ms	(- (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

prune467.0ms

Filtered

88 candidates to 66 candidates (25.0%)

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: 49.0b

Counts

89 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

4.0b	(+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps)))
7.1b	(- (exp (* (+ a b) eps)) 1.0)
17.6b	(* (pow a 2) (pow eps 2))
17.8b	(* (pow a 3) (pow eps 3))

rewrite39.0ms

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)
10.0ms	(* (pow a 2) (pow eps 2))
9.0ms	(* (pow a 3) (pow eps 3))

series296.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps)))
55.0ms	(- (exp (* (+ a b) eps)) 1.0)
38.0ms	(* (pow a 2) (pow eps 2))
79.0ms	(* (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

prune1.1s

Filtered

149 candidates to 79 candidates (47.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	145	4	149
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	147	7	154

Merged error: 48.5b

Counts

154 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps)) (- (exp (* b eps)) 1.0))
3.2b	(- (exp (* b eps)) 1.0)
7.1b	(- (exp (* (+ a b) eps)) 1.0)
17.6b	(* (pow a 2) (pow eps 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

12.0ms	(* (+ (* 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)
7.0ms	(* (pow a 2) (pow eps 2))

series235.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps)) (- (exp (* b eps)) 1.0))
40.0ms	(- (exp (* b eps)) 1.0)
55.0ms	(- (exp (* (+ a b) eps)) 1.0)
38.0ms	(* (pow a 2) (pow eps 2))

simplify83.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	545	1039
1	2595	923
2	5001	919

prune822.0ms

Filtered

123 candidates to 79 candidates (35.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	117	6	123
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	122	8	130

Merged error: 48.1b

Counts

130 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

7.1b	(- (exp (* (+ a b) eps)) 1.0)
17.6b	(* (pow a 2) (pow eps 2))
17.6b	(* (pow a 2) (pow eps 2))
17.6b	(* (pow a 2) (pow eps 2))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
48×	`unswap-sqr`
42×	`unpow-prod-down`
40×	`add-exp-log`
30×	`unpow2` `sqr-pow`
27×	`prod-exp`
24×	`associate-r` `associate-l`
18×	`pow-to-exp` `*-un-lft-identity` `pow-exp`
16×	`add-cube-cbrt`
10×	`add-cbrt-cube`
6×	`add-log-exp`
4×	`pow1`
3×	`pow-prod-down` `*-commutative` `cbrt-unprod`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 167

Calls

4 calls:

4.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow a 2) (pow eps 2))
7.0ms	(* (pow a 2) (pow eps 2))
10.0ms	(* (pow a 2) (pow eps 2))

series167.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (exp (* (+ a b) eps)) 1.0)
37.0ms	(* (pow a 2) (pow eps 2))
40.0ms	(* (pow a 2) (pow eps 2))
37.0ms	(* (pow a 2) (pow eps 2))

simplify184.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	243	954
1	973	695
2	4873	660
3	5001	660

prune876.0ms

Filtered

179 candidates to 90 candidates (49.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	179	8	187

Merged error: 48.1b

Counts

187 → 8

regimes304.0ms

Accuracy

56.8% (3.4b remaining)

Error of 53.0b against oracle of 49.6b and baseline of 57.4b

bsearch246.0ms

Steps

Iters	Range		Point
9	1.3289269437910574e+52	1.8348536167988354e+59	8.497467814633822e+55
5	-4.365930467263021e+104	-1.800310994331996e+104	-1.8286874142428294e+104

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	62
1	68	62
2	68	62

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.7s	2603×	body	2560	valid
1.9s	3429×	body	1280	valid
341.0ms	1065×	body	640	valid
187.0ms	10027×	pre	80	true
134.0ms	2026×	body	80	overflowed
72.0ms	336×	body	320	valid
28.0ms	426×	body	80	valid
20.0ms	142×	body	160	valid

Details

sample197.0ms

simplify95.0ms

prune5.0ms

localize16.0ms

rewrite23.0ms

series196.0ms

simplify43.0ms

prune467.0ms

localize28.0ms

rewrite39.0ms

series296.0ms

simplify97.0ms

prune1.1s

localize24.0ms

rewrite30.0ms

series235.0ms

simplify83.0ms

prune822.0ms

localize27.0ms

rewrite34.0ms

series167.0ms

simplify184.0ms

prune876.0ms

regimes304.0ms

bsearch246.0ms

simplify2.0ms

end0.0ms

sample5.8s

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