Details

sample31.0ms

Algorithm

intervals

Results

9.0ms	188×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	24×	body	1280	valid
2.0ms	21×	body	640	valid
1.0ms	15×	body	320	valid
0.0ms	8×	body	160	valid

simplify79.0ms

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

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: 15.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.2b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite35.0ms

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:

10.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
20.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series107.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
62.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify44.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (31.0ms)

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

prune199.0ms

Filtered

106 candidates to 68 candidates (64.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	94	12	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	12	107

Merged error: 15.0b

Counts

107 → 12

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

182×	`*-un-lft-identity`
91×	`times-frac`
85×	`add-sqr-sqrt`
80×	`add-cube-cbrt`
63×	`prod-diff`
60×	`distribute-lft-out`
21×	`fma-neg`
12×	`associate-/r/`
10×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube`
6×	`flip3-+` `flip-+` `div-inv` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

3 → 179

Calls

3 calls:

8.0ms	(/ beta (+ (+ alpha beta) 2.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
16.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series169.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ beta (+ (+ alpha beta) 2.0))
49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
76.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify62.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	493	1766
1	1623	1302
2	5002	1263

prune298.0ms

Filtered

188 candidates to 97 candidates (51.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	180	8	188
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	190	10	200

Merged error: 3.2b

Counts

200 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt beta)
0.6b	(cbrt beta)
0.6b	(cbrt beta)
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 140

Calls

4 calls:

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

series617.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt beta)
178.0ms	(cbrt beta)
184.0ms	(cbrt beta)
76.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	386	1443
1	1119	993
2	5001	940

prune286.0ms

Filtered

152 candidates to 82 candidates (53.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	147	5	152
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	151	11	162

Merged error: 3.2b

Counts

162 → 11

localize14.0ms

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))
2.2b	(- (/ 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:

6.0ms	(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)

series376.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(cbrt (+ (+ alpha beta) 2.0))
99.0ms	(cbrt (+ (+ alpha beta) 2.0))
101.0ms	(cbrt (+ (+ alpha beta) 2.0))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify61.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (38.0ms)

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

prune296.0ms

Filtered

164 candidates to 90 candidates (54.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	161	3	164
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	165	10	175

Merged error: 3.2b

Counts

175 → 10

regimes94.0ms

Accuracy

78.1% (2.9b remaining)

Error of 5.9b against oracle of 3.0b and baseline of 16.4b

bsearch56.0ms

Steps

Iters	Range		Point
8	165808724399.22992	2174182153969134.0	184229630314.30515

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	34
1	42	34

end0.0ms

sample720.0ms

Algorithm

intervals

Results

189.0ms	5833×	body	80	valid
131.0ms	861×	body	1280	valid
124.0ms	8000×	pre	80	true
86.0ms	704×	body	640	valid
37.0ms	393×	body	320	valid
12.0ms	209×	body	160	valid