Details

sample28.0ms

Algorithm

intervals

Results

6.0ms	256×	pre	80	true
5.0ms	190×	body	80	valid
3.0ms	24×	body	1280	valid
3.0ms	28×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	6×	body	160	valid

simplify77.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	6
1	34	6
2	52	6
3	73	6
4	123	6
5	172	6
6	224	6
7	261	6
8	323	6
9	411	6
10	532	6
11	612	6
12	654	6
13	697	6
14	922	6
15	980	6
16	1007	6
17	1027	6
18	1035	6
19	1035	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.4b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
19×	`distribute-lft-out`
14×	`add-cube-cbrt`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 65

Calls

2 calls:

43.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
142.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series97.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
56.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify35.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	320	535
1	1022	510
2	5001	502

prune231.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
61×	`add-sqr-sqrt`
56×	`times-frac`
36×	`add-cube-cbrt`
24×	`distribute-lft-out`
13×	`associate-/r` `associate-/l` `distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`add-log-exp`
4×	`pow1` `associate-/r/` `associate-/l/`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
2×	`flip3-+` `frac-sub` `flip-+`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 137

Calls

4 calls:

918.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
33.0ms	(/ beta (+ (+ alpha beta) 2.0))
32.0ms	(/ alpha (+ (+ alpha beta) 2.0))
162.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series211.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
43.0ms	(/ beta (+ (+ alpha beta) 2.0))
40.0ms	(/ alpha (+ (+ alpha beta) 2.0))
69.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	544	1336
1	1910	1268
2	5001	1268

prune638.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
1.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`cbrt-prod`
12×	`add-sqr-sqrt`
9×	`distribute-lft-out`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

14.0ms	(cbrt (+ (+ alpha beta) 2.0))
14.0ms	(cbrt (+ (+ alpha beta) 2.0))
16.0ms	(cbrt (+ (+ alpha beta) 2.0))
163.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series339.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (+ (+ alpha beta) 2.0))
90.0ms	(cbrt (+ (+ alpha beta) 2.0))
91.0ms	(cbrt (+ (+ alpha beta) 2.0))
69.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify68.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	278	567
1	708	537
2	2658	521
3	5001	512

prune648.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (pow (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)) (+ (* (/ (- beta alpha) (+ (+ alpha beta) 2.0)) (- (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)))
0.1b	(pow (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 3)
1.4b	(+ (pow (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
1.7b	(- (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

163×	`*-un-lft-identity`
78×	`times-frac`
66×	`add-sqr-sqrt`
55×	`distribute-lft-out`
51×	`unpow-prod-down` `cube-prod`
41×	`add-cube-cbrt`
12×	`difference-of-squares`
11×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
8×	`add-log-exp`
6×	`associate-/r/`
5×	`pow1` `flip3-+` `sum-cubes` `flip-+`
3×	`pow-unpow` `associate-/r*` `div-inv`
2×	`cbrt-undiv` `div-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt`
1×	`+-commutative` `cube-div` `associate--l-` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `clear-num` `sum-log` `flip--` `sqr-pow`

Counts

4 → 170

Calls

4 calls:

981.0ms	(/ (+ (pow (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)) (+ (* (/ (- beta alpha) (+ (+ alpha beta) 2.0)) (- (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)))
43.0ms	(pow (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 3)
317.0ms	(+ (pow (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
194.0ms	(- (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series713.0ms

Counts

4 → 12

Calls

4 calls:

316.0ms	(/ (+ (pow (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)) (+ (* (/ (- beta alpha) (+ (+ alpha beta) 2.0)) (- (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)))
70.0ms	(pow (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 3)
235.0ms	(+ (pow (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
91.0ms	(- (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify115.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	787	2964
1	3428	2733
2	5002	2723

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.9b

regimes188.0ms

Accuracy

98% (0.3b remaining)

Error of 3.3b against oracle of 3.0b and baseline of 16.1b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	54
1	56	54

end0.0ms

sample638.0ms

Algorithm

intervals

Results

161.0ms	5856×	body	80	valid
115.0ms	833×	body	1280	valid
97.0ms	8000×	pre	80	true
75.0ms	701×	body	640	valid
31.0ms	398×	body	320	valid
14.0ms	212×	body	160	valid