Details

sample265.0ms

Algorithm

intervals

Results

94.0ms	89×	body	2560	valid
77.0ms	83×	body	10240	exit
53.0ms	103×	body	1280	valid
9.0ms	31×	body	640	valid
6.0ms	340×	pre	80	true
6.0ms	13×	body	320	valid
1.0ms	19×	body	80	valid
0.0ms	2×	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

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: 59.4b

Counts

2 → 1

localize16.0ms

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)))
1.4b	(- (exp (* b eps)) 1.0)
2.9b	(- (exp (* a eps)) 1.0)
3.0b	(- (exp (* (+ a b) eps)) 1.0)

rewrite29.0ms

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

series319.0ms

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)))
33.0ms	(- (exp (* b eps)) 1.0)
35.0ms	(- (exp (* a eps)) 1.0)
51.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify57.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (47.0ms)

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

prune277.0ms

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: 0.3b

Counts

86 → 4

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite15.0ms

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:

15.0ms

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

series11.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify64.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	101	104
1	345	94
2	1153	91
3	2775	90
4	5001	90

prune46.0ms

Filtered

22 candidates to 14 candidates (63.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	19	3	22
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	19	7	26

Merged error: 0.2b

Counts

26 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
0.5b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.5b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.5b	(cbrt (+ (/ 1 b) (/ 1 a)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

139×	`*-un-lft-identity`
114×	`cbrt-prod`
81×	`distribute-lft-out`
60×	`div-inv`
42×	`times-frac`
37×	`add-sqr-sqrt`
33×	`cbrt-div` `swap-sqr`
29×	`add-cube-cbrt`
13×	`associate-r` `associate-l`
11×	`pow1` `flip3-+` `frac-add` `flip-+`
9×	`frac-times` `pow1/3`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`associate-r/` `associate-l/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 159

Calls

4 calls:

34.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
12.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
11.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
11.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
78.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
81.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
84.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

simplify64.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	389	1813
1	1557	1563
2	5001	1403

prune287.0ms

Filtered

171 candidates to 87 candidates (50.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	171	7	178

Merged error: 0.2b

Counts

178 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 b) b)
0.1b	(/ (- (/ 1 a)) a)
4.7b	(+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b))
31.3b	(/ (+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

rewrite382.0ms

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	(/ (- (/ 1 a)) a)
144.0ms	(+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b))
166.0ms	(/ (+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

series113.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (/ 1 b) b)
25.0ms	(/ (- (/ 1 a)) a)
24.0ms	(+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b))
46.0ms	(/ (+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

simplify99.0ms

Algorithm

egg-herbie

Counts

545 → 545

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1343	6820
1	5001	5868

prune483.0ms

Filtered

545 candidates to 181 candidates (33.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	545	0	545
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	545	7	552

Merged error: 0.2b

Counts

552 → 7

regimes103.0ms

Accuracy

0% (3.1b remaining)

Error of 3.2b against oracle of 0.1b 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	2624×	body	2560	valid
1.7s	3392×	body	1280	valid
1.6s	1884×	body	10240	exit
300.0ms	1088×	body	640	valid
164.0ms	9887×	pre	80	true
63.0ms	352×	body	320	valid
22.0ms	425×	body	80	valid
14.0ms	122×	body	160	valid