Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	197×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	27×	body	1280	valid
2.0ms	19×	body	640	valid
0.0ms	8×	body	160	valid
0.0ms	5×	body	320	valid

simplify77.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	34	6
2	52	6
3	73	6
4	123	6
5	184	6
6	250	6
7	287	6
8	349	6
9	437	6
10	574	6
11	654	6
12	712	6
13	785	6
14	1075	6
15	1150	6
16	1193	6
17	1213	6
18	1221	6
19	1221	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.1b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

104×	`*-un-lft-identity`
50×	`times-frac`
47×	`add-sqr-sqrt`
34×	`distribute-lft-out`
31×	`fma-def`
25×	`add-cube-cbrt`
11×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `associate-/r/` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--`

Counts

2 → 100

Calls

2 calls:

11.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
21.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series113.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
63.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	335	555
1	1087	529
2	5002	525

prune228.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.3b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

512×	`*-un-lft-identity`
328×	`add-sqr-sqrt`
263×	`times-frac`
252×	`prod-diff`
213×	`add-cube-cbrt`
150×	`distribute-lft-out`
65×	`associate--r+`
46×	`difference-of-squares`
42×	`fma-neg`
32×	`associate-/r/`
25×	`distribute-lft-out--`
16×	`flip3-+` `flip-+` `div-inv`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub`
1×	`associate--r-`

Counts

4 → 413

Calls

4 calls:

37.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
11.0ms	(/ beta (+ (+ alpha beta) 2.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
17.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series232.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
51.0ms	(/ beta (+ (+ alpha beta) 2.0))
50.0ms	(/ alpha (+ (+ alpha beta) 2.0))
74.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify139.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	977	8429
1	3143	6259
2	5002	6131

prune765.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.4b

localize18.0ms

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))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

141×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
63×	`prod-diff`
61×	`times-frac`
45×	`distribute-lft-out`
21×	`fma-neg`
15×	`cbrt-prod`
8×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 152

Calls

4 calls:

5.0ms	(cbrt (+ (+ alpha beta) 2.0))
5.0ms	(cbrt (+ (+ alpha beta) 2.0))
5.0ms	(cbrt (+ (+ alpha beta) 2.0))
16.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series510.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt (+ (+ alpha beta) 2.0))
240.0ms	(cbrt (+ (+ alpha beta) 2.0))
98.0ms	(cbrt (+ (+ alpha beta) 2.0))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify52.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	460	1755
1	1302	1290
2	5001	1240

prune427.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.4b

localize18.0ms

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))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

141×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
63×	`prod-diff`
61×	`times-frac`
45×	`distribute-lft-out`
21×	`fma-neg`
15×	`cbrt-prod`
8×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 152

Calls

4 calls:

5.0ms	(cbrt (+ (+ alpha beta) 2.0))
5.0ms	(cbrt (+ (+ alpha beta) 2.0))
6.0ms	(cbrt (+ (+ alpha beta) 2.0))
16.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series359.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt (+ (+ alpha beta) 2.0))
95.0ms	(cbrt (+ (+ alpha beta) 2.0))
94.0ms	(cbrt (+ (+ alpha beta) 2.0))
75.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify56.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	460	1755
1	1302	1290
2	5001	1240

prune434.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.4b

regimes159.0ms

Accuracy

97.7% (0.3b remaining)

Error of 3.5b against oracle of 3.2b and baseline of 15.9b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	28
1	38	28

end0.0ms

sample604.0ms

Algorithm

intervals

Results

141.0ms	5810×	body	80	valid
104.0ms	886×	body	1280	valid
99.0ms	8000×	pre	80	true
71.0ms	708×	body	640	valid
27.0ms	385×	body	320	valid
10.0ms	211×	body	160	valid