Details

sample35.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify78.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	17
1	114	17
2	563	17
3	4164	17
4	5002	17

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite676.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
586×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`sum-log`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+`

Counts

4 → 465

Calls

4 calls:

56.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
177.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
262.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
147.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
137.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
151.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
83.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify142.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune998.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
0.0b	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
0.1b	(/ (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

18109×	`times-frac`
9724×	`*-un-lft-identity`
6724×	`add-sqr-sqrt` `add-cube-cbrt`
1500×	`distribute-lft-out`
792×	`associate-/l*`
684×	`div-inv`
572×	`associate-/r/`
245×	`flip3-+` `flip-+`
154×	`add-exp-log`
134×	`div-exp`
84×	`associate-/r*`
61×	`add-cbrt-cube`
41×	`cbrt-undiv`
30×	`1-exp`
12×	`rec-exp`
6×	`associate-/l/`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

4 → 4911

Calls

4 calls:

115.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
265.0ms	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
408.0ms	(/ (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
148.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
135.0ms	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
146.0ms	(/ (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
76.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.7s

Algorithm

egg-herbie

Counts

4923 → 4923

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5274	182635

prune13.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite362.0ms

Algorithm

rewrite-expression-head

Rules

112×	`sqrt-prod`
98×	`*-un-lft-identity`
84×	`times-frac`
68×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
16×	`distribute-lft-out`
14×	`associate-/l*`
12×	`sqrt-div` `associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `flip3-+` `flip-+`
4×	`associate-/r/` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 176

Calls

4 calls:

113.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
114.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
62.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
65.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series313.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
105.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
46.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
52.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify107.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	325	2980
1	1021	2792
2	4270	2720
3	5001	2720

prune476.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite442.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
80×	`sqrt-prod`
70×	`times-frac`
56×	`add-sqr-sqrt`
54×	`add-cube-cbrt`
22×	`distribute-lft-out`
13×	`associate-/r*`
11×	`associate-/l*`
10×	`sqrt-div`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `flip3-+` `flip-+`
4×	`associate-/r/` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`
1×	`sqrt-undiv`

Counts

4 → 159

Calls

4 calls:

196.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
114.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
61.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
63.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series411.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
105.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
52.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
47.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify73.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	507	2617
1	1942	2448
2	5003	2394

prune437.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes76.0ms

Accuracy

39.1% (2.4b remaining)

Error of 2.5b against oracle of 0.0b and baseline of 4.0b

bsearch74.0ms

Steps

Iters	Range		Point
8	1.1571551707290985e+116	4.188171874707301e+119	3.5039397066266325e+117

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	40
1	40	40

end0.0ms

sample917.0ms

Algorithm

intervals

Results

630.0ms	8000×	body	80	valid
136.0ms	8000×	pre	80	true