Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	207×	body	80	valid
4.0ms	256×	pre	80	true
2.0ms	18×	body	1280	valid
2.0ms	17×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	7×	body	160	valid

simplify82.0ms

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: 11.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.5b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite134.0ms

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:

25.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
104.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series107.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
62.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify38.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (30.0ms)

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

prune222.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite169.0ms

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:

20.0ms	(/ alpha (+ (+ alpha beta) 2.0))
19.0ms	(/ beta (+ (+ alpha beta) 2.0))
121.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series175.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ alpha (+ (+ alpha beta) 2.0))
46.0ms	(/ beta (+ (+ alpha beta) 2.0))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify59.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (42.0ms)

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

prune333.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt beta)
0.6b	(cbrt beta)
0.6b	(cbrt beta)
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite131.0ms

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)
0.0ms	(cbrt beta)
1.0ms	(cbrt beta)
122.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series616.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt beta)
185.0ms	(cbrt beta)
177.0ms	(cbrt beta)
76.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (34.0ms)

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

prune311.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt beta))
0.6b	(cbrt (cbrt beta))
0.6b	(cbrt (cbrt beta))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

129×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
67×	`add-cube-cbrt`
63×	`prod-diff`
61×	`times-frac`
36×	`distribute-lft-out`
27×	`cbrt-prod`
21×	`fma-neg`
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 → 149

Calls

4 calls:

1.0ms	(cbrt (cbrt beta))
1.0ms	(cbrt (cbrt beta))
1.0ms	(cbrt (cbrt beta))
121.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series953.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(cbrt (cbrt beta))
387.0ms	(cbrt (cbrt beta))
245.0ms	(cbrt (cbrt beta))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	399	1554
1	1123	1098
2	5001	1039

prune364.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.4b

regimes60.0ms

Accuracy

77.8% (3.0b remaining)

Error of 5.7b against oracle of 2.7b and baseline of 16.0b

bsearch62.0ms

Steps

Iters	Range		Point
9	5.840411952416047	26520870.86331656	20359646.53319541

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	41
1	44	41

end0.0ms

sample627.0ms

Algorithm

intervals

Results

155.0ms	5830×	body	80	valid
113.0ms	872×	body	1280	valid
99.0ms	8000×	pre	80	true
69.0ms	706×	body	640	valid
32.0ms	394×	body	320	valid
10.0ms	198×	body	160	valid