Details

sample25.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
3.0ms	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: 3.6b

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))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.2s

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:

108.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
334.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
483.0ms	(/ (/ (/ (+ (+ (+ 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))
284.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
122.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
135.0ms	(/ (/ (/ (+ (+ (+ 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))
66.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify134.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune922.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.0b	(* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ 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))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.0s

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

Counts

4 → 169

Calls

4 calls:

35.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
408.0ms	(* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
290.0ms	(/ (* (/ 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))
286.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
126.0ms	(* (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
140.0ms	(/ (* (/ 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))
69.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify51.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	764	2679
1	5001	2305

prune373.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.0b	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
2.1b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

297×	`times-frac`
216×	`*-un-lft-identity`
161×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
78×	`associate-l`
38×	`distribute-lft-out`
37×	`difference-of-squares`
34×	`add-exp-log` `add-cbrt-cube`
28×	`associate-/r/`
25×	`associate-/l*`
18×	`associate-r`
14×	`cbrt-undiv` `div-exp` `div-inv`
13×	`flip3-+` `flip-+`
11×	`associate-/r*`
6×	`pow1` `prod-exp` `cbrt-unprod` `unswap-sqr`
5×	`associate-/l/`
4×	`add-log-exp`
3×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`frac-times` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 308

Calls

4 calls:

181.0ms	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
813.0ms	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
342.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
285.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series453.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
197.0ms	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 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))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
70.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify97.0ms

Algorithm

egg-herbie

Counts

320 → 320

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1417	7781
1	5001	7281

prune899.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))) (- (+ alpha beta) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
0.1b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))) (- (+ alpha beta) (* 2.0 1.0))))
16.7b	(/ (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))) (- (+ alpha beta) (* 2.0 1.0)))
16.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

1985×	`times-frac`
1037×	`*-un-lft-identity`
766×	`add-sqr-sqrt`
725×	`add-cube-cbrt`
401×	`associate-l`
292×	`difference-of-squares`
172×	`associate-/r/`
156×	`distribute-lft-out`
87×	`div-inv`
85×	`flip3--` `flip--`
61×	`add-exp-log` `add-cbrt-cube`
31×	`cbrt-undiv` `div-exp`
30×	`associate-/l*`
25×	`associate-/r*`
18×	`associate-r`
10×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`pow1`
5×	`associate-/l/`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`flip3-+` `flip-+`
1×	`frac-times` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 993

Calls

4 calls:

1.0s	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))) (- (+ alpha beta) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
398.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))) (- (+ alpha beta) (* 2.0 1.0))))
80.0ms	(/ (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))) (- (+ alpha beta) (* 2.0 1.0)))
287.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

series533.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))) (- (+ alpha beta) (* 2.0 1.0)))) (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
156.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))) (- (+ alpha beta) (* 2.0 1.0))))
53.0ms	(/ (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))) (- (+ alpha beta) (* 2.0 1.0)))
103.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

simplify374.0ms

Algorithm

egg-herbie

Counts

1005 → 1005

Iterations

Useful iterations: 1 (69.0ms)

Iter	Nodes	Cost
0	4364	37773
1	5003	37560

prune3.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.8b

regimes71.0ms

Accuracy

31.7% (1.7b remaining)

Error of 3.1b against oracle of 1.3b and baseline of 3.9b

bsearch75.0ms

Steps

Iters	Range		Point
9	3.3557133720855566e+147	1.592759335520542e+154	1.3363296163984674e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	46
1	43	46

end0.0ms

sample571.0ms

Algorithm

intervals

Results

287.0ms	8000×	body	80	valid
95.0ms	8000×	pre	80	true