Details

sample205.0ms

Algorithm

intervals

Results

97.0ms	87×	body	2560	valid
61.0ms	108×	body	1280	valid
10.0ms	29×	body	640	valid
8.0ms	65×	body	80	overflowed
7.0ms	321×	pre	80	true
3.0ms	13×	body	320	valid
1.0ms	15×	body	80	valid
1.0ms	4×	body	160	valid

simplify100.0ms

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

prune3.0ms

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: 60.3b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
2.4b	(- (exp (* b eps)) 1.0)
3.6b	(- (exp (* a eps)) 1.0)
4.8b	(- (exp (* (+ a b) eps)) 1.0)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `flip3--` `*-un-lft-identity` `flip--` `add-log-exp`
8×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `frac-times` `add-cube-cbrt` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod`
3×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/` `associate-/l/`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 73

Calls

4 calls:

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

series320.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
37.0ms	(- (exp (* b eps)) 1.0)
34.0ms	(- (exp (* a eps)) 1.0)
49.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify59.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	488	957
1	2299	794
2	5001	789

prune298.0ms

Filtered

85 candidates to 63 candidates (74.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	81	4	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	4	86

Merged error: 0.1b

Counts

86 → 4

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite13.0ms

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:

12.0ms

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

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

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

simplify70.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (28.0ms)

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

prune47.0ms

Filtered

22 candidates to 14 candidates (63.6%)

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

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 b) b)
0.2b	(/ (neg (/ 1 a)) a)
3.8b	(+ (/ (neg (/ 1 a)) a) (/ (/ 1 b) b))
31.0b	(/ (+ (/ (neg (/ 1 a)) a) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

rewrite379.0ms

Algorithm

rewrite-expression-head

Rules

1240×	`times-frac`
1158×	`*-un-lft-identity`
577×	`add-sqr-sqrt`
241×	`add-cube-cbrt`
210×	`distribute-lft-out`
199×	`distribute-rgt-neg-in`
176×	`div-inv`
126×	`difference-of-squares`
98×	`distribute-lft-out--`
56×	`associate-/l*`
52×	`distribute-lft-neg-in`
25×	`associate-/r*`
17×	`add-exp-log`
13×	`add-cbrt-cube`
8×	`div-exp`
7×	`pow1`
6×	`add-log-exp`
5×	`cbrt-undiv` `associate-/l/`
4×	`neg-mul-1` `div-sub`
3×	`neg-sub0` `frac-2neg` `clear-num` `associate-/r/`
2×	`associate-+l-` `flip3-+` `frac-add` `flip-+` `pow-div`
1×	`+-commutative` `rec-exp` `flip3--` `pow-flip` `1-exp` `distribute-frac-neg` `sum-log` `frac-sub` `flip--` `distribute-neg-frac` `inv-pow`

Counts

4 → 533

Calls

4 calls:

6.0ms	(/ (/ 1 b) b)
9.0ms	(/ (neg (/ 1 a)) a)
143.0ms	(+ (/ (neg (/ 1 a)) a) (/ (/ 1 b) b))
163.0ms	(/ (+ (/ (neg (/ 1 a)) a) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

series110.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ (/ 1 b) b)
25.0ms	(/ (neg (/ 1 a)) a)
31.0ms	(+ (/ (neg (/ 1 a)) a) (/ (/ 1 b) b))
38.0ms	(/ (+ (/ (neg (/ 1 a)) a) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

simplify99.0ms

Algorithm

egg-herbie

Counts

545 → 545

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1343	6800
1	5002	5779

prune491.0ms

Filtered

545 candidates to 180 candidates (33.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	544	1	545
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	544	6	550

Merged error: 0.1b

Counts

550 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (pow b 2))
3.8b	(- (/ 1 (pow b 2)) (/ 1 (pow a 2)))
19.8b	(cbrt (pow (- (/ 1 (pow b 2)) (/ 1 (pow a 2))) 3))
31.0b	(/ (cbrt (pow (- (/ 1 (pow b 2)) (/ 1 (pow a 2))) 3)) (- (/ 1 b) (/ 1 a)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

14039×	`times-frac`
12588×	`add-sqr-sqrt`
7822×	`*-un-lft-identity`
5265×	`difference-of-squares`
4074×	`cbrt-prod`
3792×	`unpow-prod-down`
1974×	`cube-prod`
1816×	`distribute-lft-out--`
1573×	`sqr-pow`
1552×	`unpow2`
966×	`div-inv`
870×	`add-cube-cbrt`
200×	`associate-/l*`
27×	`associate-/r*`
21×	`cube-mult` `unpow3`
15×	`add-exp-log`
7×	`div-exp` `add-cbrt-cube`
6×	`cube-div` `cbrt-div` `add-log-exp`
4×	`pow1` `flip3--` `frac-sub` `flip--`
3×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/r/` `associate-/l/`
2×	`cbrt-undiv` `frac-2neg` `clear-num`
1×	`sub-neg` `pow-flip` `pow1/3` `diff-log` `rem-cbrt-cube` `inv-pow`

Counts

4 → 4344

Calls

4 calls:

5.0ms	(/ 1 (pow b 2))
36.0ms	(- (/ 1 (pow b 2)) (/ 1 (pow a 2)))
54.0ms	(cbrt (pow (- (/ 1 (pow b 2)) (/ 1 (pow a 2))) 3))
165.0ms	(/ (cbrt (pow (- (/ 1 (pow b 2)) (/ 1 (pow a 2))) 3)) (- (/ 1 b) (/ 1 a)))

series115.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1 (pow b 2))
25.0ms	(- (/ 1 (pow b 2)) (/ 1 (pow a 2)))
26.0ms	(cbrt (pow (- (/ 1 (pow b 2)) (/ 1 (pow a 2))) 3))
46.0ms	(/ (cbrt (pow (- (/ 1 (pow b 2)) (/ 1 (pow a 2))) 3)) (- (/ 1 b) (/ 1 a)))

simplify1.0s

Algorithm

egg-herbie

Counts

4356 → 4356

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5001	96907

prune4.8s

Filtered

4356 candidates to 1019 candidates (23.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	4356	0	4356
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	4356	6	4362

Merged error: 0.1b

Counts

4362 → 6

regimes146.0ms

Accuracy

92.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 3.3b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	73
1	43	73

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.8s	2582×	body	2560	valid
2.0s	3518×	body	1280	valid
349.0ms	1027×	body	640	valid
204.0ms	9937×	pre	80	true
130.0ms	1932×	body	80	overflowed
71.0ms	307×	body	320	valid
31.0ms	446×	body	80	valid
19.0ms	125×	body	160	valid

Details

sample205.0ms

simplify100.0ms

prune3.0ms

localize17.0ms

rewrite28.0ms

series320.0ms

simplify59.0ms

prune298.0ms

localize5.0ms

rewrite13.0ms

series11.0ms

simplify70.0ms

prune47.0ms

localize11.0ms

rewrite379.0ms

series110.0ms

simplify99.0ms

prune491.0ms

localize22.0ms

rewrite1.3s

series115.0ms

simplify1.0s

prune4.8s

regimes146.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample5.9s

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