Details

sample210.0ms

Algorithm

intervals

Results

97.0ms	87×	body	2560	valid
60.0ms	104×	body	1280	valid
12.0ms	39×	body	640	valid
6.0ms	308×	pre	80	true
5.0ms	15×	body	1280	overflowed
3.0ms	4×	body	2560	overflowed
3.0ms	10×	body	640	overflowed
2.0ms	9×	body	320	valid
1.0ms	17×	body	80	overflowed
1.0ms	5×	body	320	overflowed
1.0ms	14×	body	80	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	160	overflowed

simplify97.0ms

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

prune6.0ms

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

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.4b	(- (exp (* b eps)) 1.0)
2.7b	(- (exp (* a eps)) 1.0)
4.0b	(- (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))
4.0ms	(- (exp (* b eps)) 1.0)
3.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series40.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
7.0ms	(- (exp (* b eps)) 1.0)
7.0ms	(- (exp (* a eps)) 1.0)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (8.0ms)

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

prune152.0ms

Filtered

66 candidates to 88 candidates (-33.3%)

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: 49.3b

Counts

89 → 5

localize30.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (exp (* (+ a b) eps)) 1.0)
4.6b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
11.3b	(* (pow eps 2) (pow b 2))
13.2b	(* (pow eps 3) (pow b 3))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
40×	`add-exp-log`
32×	`unswap-sqr`
28×	`unpow-prod-down`
22×	`prod-exp`
20×	`associate-r` `associate-l` `add-cbrt-cube` `sqr-pow`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt` `cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`associate-/r/`
6×	`cbrt-unprod` `add-log-exp`
5×	`flip3--` `flip--`
4×	`pow1` `cbrt-undiv` `frac-times` `associate-*r/` `div-exp`
3×	`flip3-+` `flip-+`
2×	`cube-mult` `unpow3` `pow-prod-down` `associate-l/` `-commutative` `associate-/l/`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 155

Calls

4 calls:

4.0ms	(- (exp (* (+ a b) eps)) 1.0)
21.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
7.0ms	(* (pow eps 2) (pow b 2))
9.0ms	(* (pow eps 3) (pow b 3))

series661.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (exp (* (+ a b) eps)) 1.0)
632.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
6.0ms	(* (pow eps 2) (pow b 2))
10.0ms	(* (pow eps 3) (pow b 3))

simplify41.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	848	1843
1	5001	1499

prune359.0ms

Filtered

96 candidates to 167 candidates (-74.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	168	4	172

Merged error: 0.1b

Counts

172 → 4

localize4.0ms

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))

series3.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify62.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (24.0ms)

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

prune39.0ms

Filtered

14 candidates to 22 candidates (-57.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	21	5	26

Merged error: 0.1b

Counts

26 → 5

localize4.0ms

Local error

Found 1 expressions with local error:

14.3b

(/ (+ b a) (* b a))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`times-frac` `associate-/l*`
3×	`add-sqr-sqrt` `add-cube-cbrt`
2×	`cbrt-undiv` `div-exp` `associate-/l/` `distribute-lft-out`
1×	`pow1` `frac-2neg` `flip3-+` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 25

Calls

1 calls:

6.0ms

(/ (+ b a) (* b a))

series6.0ms

Counts

1 → 3

Calls

1 calls:

6.0ms

(/ (+ b a) (* b a))

simplify45.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	145	134
1	519	113
2	2023	113
3	5001	113

prune23.0ms

Filtered

19 candidates to 28 candidates (-47.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	28	5	33

Merged error: 0.1b

Counts

33 → 5

regimes161.0ms

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

sample6.2s

Algorithm

intervals

Results

2.7s	2584×	body	2560	valid
1.9s	3480×	body	1280	valid
328.0ms	1015×	body	640	valid
271.0ms	668×	body	1280	overflowed
197.0ms	9956×	pre	80	true
115.0ms	173×	body	2560	overflowed
98.0ms	354×	body	640	overflowed
75.0ms	341×	body	320	valid
39.0ms	197×	body	320	overflowed
32.0ms	495×	body	80	overflowed
31.0ms	461×	body	80	valid
17.0ms	120×	body	160	valid
9.0ms	68×	body	160	overflowed

Details

sample210.0ms

simplify97.0ms

prune6.0ms

localize16.0ms

rewrite22.0ms

series40.0ms

simplify43.0ms

prune152.0ms

localize30.0ms

rewrite47.0ms

series661.0ms

simplify41.0ms

prune359.0ms

localize4.0ms

rewrite12.0ms

series3.0ms

simplify62.0ms

prune39.0ms

localize4.0ms

rewrite7.0ms

series6.0ms

simplify45.0ms

prune23.0ms

regimes161.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.2s

Profiling