Details

sample225.0ms

Algorithm

intervals

Results

84.0ms	116×	body	1280	valid
83.0ms	63×	body	2560	valid
15.0ms	32×	body	640	valid
8.0ms	59×	body	80	overflowed
8.0ms	315×	pre	80	true
7.0ms	20×	body	320	valid
3.0ms	20×	body	80	valid
1.0ms	5×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
5.2b	(- (exp (* b eps)) 1.0)
5.6b	(- (exp (* a eps)) 1.0)
9.0b	(- (exp (* (+ a b) eps)) 1.0)

rewrite32.0ms

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:

19.0ms	(/ (* 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)

series305.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
36.0ms	(- (exp (* b eps)) 1.0)
32.0ms	(- (exp (* a eps)) 1.0)
45.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify57.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (48.0ms)

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

prune322.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite17.0ms

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:

16.0ms

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

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify70.0ms

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

prune48.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))
0.1b	(sqrt (+ (/ 1 b) (/ 1 a)))
0.1b	(sqrt (+ (/ 1 b) (/ 1 a)))
0.3b	(* (sqrt (+ (/ 1 b) (/ 1 a))) (sqrt (+ (/ 1 b) (/ 1 a))))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

138×	`*-un-lft-identity`
106×	`sqrt-prod`
81×	`distribute-lft-out`
60×	`div-inv`
42×	`add-sqr-sqrt` `times-frac`
35×	`swap-sqr`
30×	`sqrt-div`
28×	`add-cube-cbrt`
21×	`pow1`
13×	`associate-r` `associate-l`
11×	`flip3-+` `frac-add` `flip-+`
10×	`sqrt-pow1` `pow1/2`
9×	`frac-times`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`unswap-sqr`
3×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr`
2×	`rem-sqrt-square`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 170

Calls

4 calls:

17.0ms	(+ (/ 1 b) (/ 1 a))
27.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
28.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
121.0ms	(* (sqrt (+ (/ 1 b) (/ 1 a))) (sqrt (+ (/ 1 b) (/ 1 a))))

series169.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (/ 1 b) (/ 1 a))
68.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
68.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
22.0ms	(* (sqrt (+ (/ 1 b) (/ 1 a))) (sqrt (+ (/ 1 b) (/ 1 a))))

simplify64.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	321	1208
1	1520	1045
2	5001	1029

prune258.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (/ 1 b) (/ 1 a)))
0.1b	(sqrt (+ (/ 1 b) (/ 1 a)))
0.3b	(* (sqrt (sqrt (+ (/ 1 b) (/ 1 a)))) (sqrt (sqrt (+ (/ 1 b) (/ 1 a)))))
0.3b	(* (* (sqrt (sqrt (+ (/ 1 b) (/ 1 a)))) (sqrt (sqrt (+ (/ 1 b) (/ 1 a))))) (sqrt (+ (/ 1 b) (/ 1 a))))

rewrite424.0ms

Algorithm

rewrite-expression-head

Rules

294×	`sqrt-div`
234×	`sqrt-prod`
144×	`*-un-lft-identity`
91×	`sqrt-pow1`
90×	`frac-times`
81×	`distribute-lft-out`
73×	`pow1`
70×	`add-sqr-sqrt`
60×	`div-inv`
58×	`flip3-+` `frac-add` `flip-+`
51×	`pow1/2`
44×	`swap-sqr`
43×	`pow-prod-up`
42×	`times-frac`
34×	`add-cube-cbrt`
30×	`associate-*l/`
29×	`associate-r`
18×	`associate-*r/`
17×	`associate-l`
13×	`pow-sqr`
12×	`pow-prod-down`
11×	`add-exp-log` `add-cbrt-cube` `unswap-sqr`
7×	`pow-plus`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`sqrt-unprod`
2×	`rem-sqrt-square` `*-commutative`
1×	`pow2` `rem-square-sqrt`

Counts

4 → 299

Calls

4 calls:

29.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
27.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
132.0ms	(* (sqrt (sqrt (+ (/ 1 b) (/ 1 a)))) (sqrt (sqrt (+ (/ 1 b) (/ 1 a)))))
214.0ms	(* (* (sqrt (sqrt (+ (/ 1 b) (/ 1 a)))) (sqrt (sqrt (+ (/ 1 b) (/ 1 a))))) (sqrt (+ (/ 1 b) (/ 1 a))))

series224.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
67.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
69.0ms	(* (sqrt (sqrt (+ (/ 1 b) (/ 1 a)))) (sqrt (sqrt (+ (/ 1 b) (/ 1 a)))))
21.0ms	(* (* (sqrt (sqrt (+ (/ 1 b) (/ 1 a)))) (sqrt (sqrt (+ (/ 1 b) (/ 1 a))))) (sqrt (+ (/ 1 b) (/ 1 a))))

simplify119.0ms

Algorithm

egg-herbie

Counts

311 → 311

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	792	3765
1	3255	3120
2	5002	3098

prune536.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes95.0ms

Accuracy

0% (3.4b remaining)

Error of 3.5b against oracle of 0.1b and baseline of 3.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample7.1s

Algorithm

intervals

Results

3.1s	2469×	body	2560	valid
2.5s	3487×	body	1280	valid
495.0ms	1063×	body	640	valid
268.0ms	2013×	body	80	overflowed
256.0ms	10014×	pre	80	true
127.0ms	376×	body	320	valid
61.0ms	466×	body	80	valid
34.0ms	140×	body	160	valid