Details

sample22.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify77.0ms

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: 2.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
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))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite623.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 463

Calls

4 calls:

13.0ms	(+ (+ alpha beta) (* beta alpha))
172.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
257.0ms	(/ (/ (/ (+ (+ (+ 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))
146.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series373.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ alpha beta) (* beta alpha))
136.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
145.0ms	(/ (/ (/ (+ (+ (+ 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))
77.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify146.0ms

Algorithm

egg-herbie

Counts

475 → 475

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1512	13008
1	5001	12540

prune953.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.0b	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(* (/ 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)))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite765.0ms

Algorithm

rewrite-expression-head

Rules

297×	`times-frac`
277×	`*-un-lft-identity`
168×	`add-sqr-sqrt`
138×	`add-cube-cbrt`
78×	`associate-r`
68×	`distribute-lft-out`
54×	`add-exp-log`
34×	`add-cbrt-cube`
28×	`associate-/r/`
25×	`associate-/l*`
24×	`div-exp`
15×	`flip3-+` `associate-l` `flip-+`
14×	`cbrt-undiv` `div-inv`
12×	`prod-exp`
10×	`associate-/r*`
9×	`unswap-sqr`
7×	`pow1`
6×	`cbrt-unprod`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 311

Calls

4 calls:

217.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
17.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
370.0ms	(* (/ 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)))
144.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
35.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
150.0ms	(* (/ 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)))
77.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify88.0ms

Algorithm

egg-herbie

Counts

323 → 323

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1147	6185
1	5001	5763

prune694.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(* (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

1513×	`times-frac`
1098×	`*-un-lft-identity`
685×	`add-sqr-sqrt`
651×	`sqrt-prod`
602×	`add-cube-cbrt`
249×	`associate-l`
248×	`distribute-lft-out`
89×	`associate-/l*`
88×	`associate-/r/`
81×	`associate-r`
46×	`flip3-+` `flip-+`
44×	`div-inv`
20×	`unswap-sqr`
15×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*`
6×	`pow1`
5×	`associate-/l/`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`frac-2neg` `sqrt-div` `clear-num`
2×	`prod-exp` `cbrt-unprod`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 778

Calls

4 calls:

257.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
894.0ms	(* (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
143.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
145.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
154.0ms	(* (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (/ (/ (+ (+ (+ 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)))
80.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify276.0ms

Algorithm

egg-herbie

Counts

790 → 790

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1922	25450
1	5001	24792

prune2.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
2.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite563.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
49×	`add-sqr-sqrt`
37×	`times-frac`
31×	`add-cube-cbrt`
29×	`sqrt-prod`
27×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
10×	`distribute-lft-out`
8×	`pow1` `sqrt-div`
7×	`flip3-+` `associate-l` `flip-+`
6×	`unswap-sqr`
4×	`associate-/r/` `associate-/l*` `add-log-exp`
3×	`associate-/r*`
2×	`cbrt-undiv` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 125

Calls

4 calls:

291.0ms	(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
60.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
61.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
145.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))))
45.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
52.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
77.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify71.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	506	1798
1	2285	1606
2	5001	1550

prune463.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.8b

regimes84.0ms

Accuracy

51.2% (1.2b remaining)

Error of 2.4b against oracle of 1.2b and baseline of 3.6b

bsearch50.0ms

Steps

Iters	Range		Point
7	2.928539913264705e+160	1.678957329733711e+162	7.014666408001456e+160

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	40
1	34	40

end0.0ms

sample522.0ms

Algorithm

intervals

Results

294.0ms	8000×	body	80	valid
91.0ms	8000×	pre	80	true