Details

sample22.0ms

Algorithm

intervals

Results

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

simplify76.0ms

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: 3.4b

localize12.0ms

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))
3.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite114.0ms

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:

8.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
19.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
39.0ms	(/ (/ (/ (+ (+ (+ 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))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
141.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
146.0ms	(/ (/ (/ (+ (+ (+ 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))
75.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify131.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune963.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
0.1b	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
58×	`*-un-lft-identity`
55×	`add-sqr-sqrt`
53×	`times-frac`
38×	`add-cube-cbrt` `add-cbrt-cube`
28×	`div-exp`
18×	`associate-l`
16×	`prod-exp`
15×	`cbrt-undiv` `associate-r`
10×	`associate-/r*` `associate-/r/`
9×	`distribute-lft-out`
8×	`cbrt-unprod` `associate-/l*`
7×	`pow1`
6×	`flip3-+` `flip-+` `associate-/l/` `unswap-sqr`
5×	`rec-exp` `1-exp` `div-inv`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`frac-times` `associate-r/` `associate-l/` `un-div-inv`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 171

Calls

4 calls:

7.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
27.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
26.0ms	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
138.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
142.0ms	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
74.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify116.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	758	2684
1	4240	2303
2	5001	2270

prune357.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.6b	(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
0.7b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
3.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

2502×	`times-frac`
1611×	`*-un-lft-identity`
1043×	`add-sqr-sqrt` `add-cube-cbrt`
507×	`sqrt-prod`
460×	`cbrt-prod`
284×	`distribute-lft-out`
160×	`associate-/l*`
144×	`associate-/r/`
75×	`flip3-+` `flip-+`
69×	`div-inv`
42×	`add-exp-log`
25×	`add-cbrt-cube`
22×	`sqrt-div` `div-exp`
17×	`associate-/r*`
16×	`cbrt-undiv`
14×	`cbrt-div`
5×	`associate-/l/`
4×	`pow1` `frac-times` `frac-2neg` `prod-exp` `clear-num` `add-log-exp`
2×	`rec-exp` `1-exp` `associate-r/` `associate-l/` `cbrt-unprod`

Counts

4 → 1202

Calls

4 calls:

22.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
28.0ms	(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
60.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series982.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
248.0ms	(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
445.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
82.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify390.0ms

Algorithm

egg-herbie

Counts

1214 → 1214

Iterations

Useful iterations: 1 (51.0ms)

Iter	Nodes	Cost
0	3185	41871
1	5001	41317

prune3.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.5b

localize26.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
3.3b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.3b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.3b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite863.0ms

Algorithm

rewrite-expression-head

Rules

1973×	`times-frac`
1066×	`*-un-lft-identity`
1026×	`add-sqr-sqrt`
779×	`cbrt-prod`
720×	`add-cube-cbrt`
615×	`associate-r`
173×	`distribute-lft-out`
97×	`associate-l`
84×	`add-exp-log`
74×	`associate-/r/`
63×	`unswap-sqr`
44×	`cbrt-undiv` `div-exp`
40×	`flip3-+` `add-cbrt-cube` `flip-+`
37×	`div-inv`
24×	`cbrt-div`
20×	`prod-exp` `cbrt-unprod`
6×	`pow1`
4×	`add-log-exp`
3×	`pow1/3`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 861

Calls

4 calls:

746.0ms	(* (/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series356.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
65.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
58.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
68.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify335.0ms

Algorithm

egg-herbie

Counts

873 → 873

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5001	40817

prune3.7s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.5b

regimes65.0ms

Accuracy

45.4% (1.3b remaining)

Error of 2.3b against oracle of 1.0b and baseline of 3.4b

bsearch62.0ms

Steps

Iters	Range		Point
9	1.22827826888528e+120	2.4605251711493492e+126	2.3222667041145293e+126

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	34
1	40	34

end0.0ms

sample517.0ms

Algorithm

intervals

Results

284.0ms	8000×	body	80	valid
98.0ms	8000×	pre	80	true