Details

sample214.0ms

Algorithm

intervals

Results

84.0ms	84×	body	2560	valid
50.0ms	105×	body	1280	valid
45.0ms	48×	body	10240	exit
9.0ms	32×	body	640	valid
5.0ms	304×	pre	80	true
3.0ms	17×	body	320	valid
1.0ms	14×	body	80	valid
0.0ms	4×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
2.1b	(- (exp (* a eps)) 1.0)
4.9b	(- (exp (* b eps)) 1.0)
5.6b	(- (exp (* (+ a b) eps)) 1.0)

rewrite30.0ms

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:

17.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series310.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
33.0ms	(- (exp (* a eps)) 1.0)
37.0ms	(- (exp (* b eps)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify62.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (48.0ms)

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

prune319.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite20.0ms

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:

19.0ms

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

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify67.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (27.0ms)

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

prune42.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
0.6b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.6b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.6b	(cbrt (+ (/ 1 b) (/ 1 a)))

rewrite161.0ms

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:

112.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
13.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
13.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
13.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
84.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
84.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
82.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

simplify70.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (45.0ms)

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

prune299.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (/ 1 a)) a)
0.1b	(/ (/ 1 b) b)
4.3b	(+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b))
30.8b	(/ (+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

rewrite789.0ms

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:

13.0ms	(/ (- (/ 1 a)) a)
6.0ms	(/ (/ 1 b) b)
176.0ms	(+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b))
533.0ms	(/ (+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

series108.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (- (/ 1 a)) a)
21.0ms	(/ (/ 1 b) b)
24.0ms	(+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b))
37.0ms	(/ (+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

simplify104.0ms

Algorithm

egg-herbie

Counts

545 → 545

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1347	6821
1	5001	5869

prune564.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes73.0ms

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

sample6.8s

Algorithm

intervals

Results

2.5s	2608×	body	2560	valid
1.8s	1980×	body	10240	exit
1.7s	3394×	body	1280	valid
299.0ms	1079×	body	640	valid
170.0ms	9980×	pre	80	true
61.0ms	342×	body	320	valid
27.0ms	465×	body	80	valid
13.0ms	112×	body	160	valid