Details

sample70.0ms

Algorithm

intervals

Results

36.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify9.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	35
1	37	35
2	170	35
3	4983	35
done	5002	35

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize35.0ms

Local error

Found 3 expressions with local error:

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))

1.9b

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

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
583×	`*-un-lft-identity`
339×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
28×	`flip3-+` `flip-+`
27×	`div-inv`
19×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
4×	`associate-/l/`
3×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

3 → 450

Calls

3 calls:

578.0ms

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

777.0ms

(/ (/ (/ (+ (+ (+ 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))

443.0ms

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

series629.0ms

Counts

3 → 9

Calls

3 calls:

259.0ms

(/ (/ (+ (+ (+ 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))

108.0ms

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

simplify5.9s

Counts

459 → 459

Iterations

Useful iterations: done (5.9s)

Iter	Nodes	Cost
0	580	25719
1	2857	24955
done	5000	24097

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (* 2.0 1.0) (+ alpha beta)) (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (* 2.0 1.0) (+ alpha beta))))
0.0b	(/ (/ 1 1) (/ (+ (* 2.0 1.0) (+ alpha beta)) (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (* 2.0 1.0) (+ alpha beta)))))
0.1b	(/ (/ (/ 1 1) (/ (+ (* 2.0 1.0) (+ alpha beta)) (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (* 2.0 1.0) (+ alpha beta))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
1.9b	(/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (* 2.0 1.0) (+ alpha beta)))

rewrite2.8s

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:

261.0ms	(/ (+ (* 2.0 1.0) (+ alpha beta)) (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (* 2.0 1.0) (+ alpha beta))))
260.0ms	(/ (/ 1 1) (/ (+ (* 2.0 1.0) (+ alpha beta)) (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (* 2.0 1.0) (+ alpha beta)))))
895.0ms	(/ (/ (/ 1 1) (/ (+ (* 2.0 1.0) (+ alpha beta)) (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (* 2.0 1.0) (+ alpha beta))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
385.0ms	(/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (* 2.0 1.0) (+ alpha beta)))

series762.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (+ (* 2.0 1.0) (+ alpha beta)) (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (* 2.0 1.0) (+ alpha beta))))
212.0ms	(/ (/ 1 1) (/ (+ (* 2.0 1.0) (+ alpha beta)) (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (* 2.0 1.0) (+ alpha beta)))))
251.0ms	(/ (/ (/ 1 1) (/ (+ (* 2.0 1.0) (+ alpha beta)) (/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (* 2.0 1.0) (+ alpha beta))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
106.0ms	(/ (+ 1.0 (+ (+ alpha beta) (* beta alpha))) (+ (* 2.0 1.0) (+ alpha beta)))

simplify3.0s

Counts

4923 → 4923

Iterations

Useful iterations: 0 (760.0ms)

Iter	Nodes	Cost
0	5276	351082
done	5276	351082

prune25.9s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha beta) (+ alpha beta))
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 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))))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 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))
15.8b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

5989×	`times-frac`
3533×	`*-un-lft-identity`
2111×	`add-sqr-sqrt`
2109×	`add-cube-cbrt`
711×	`distribute-lft-out`
458×	`associate-/r/`
369×	`difference-of-squares`
361×	`associate-/l*`
232×	`div-inv`
225×	`flip3--` `flip--`
38×	`add-exp-log` `add-cbrt-cube`
23×	`associate-/r*`
22×	`cbrt-undiv` `div-exp`
11×	`pow1`
8×	`flip3-+` `flip-+`
6×	`swap-sqr`
4×	`frac-times` `associate-r` `associate-l` `associate-/l/` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-r/` `associate-l/`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 2169

Calls

4 calls:

48.0ms	(* (+ alpha beta) (+ alpha beta))
559.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 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))))
925.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 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))
435.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

series950.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ alpha beta) (+ alpha beta))
420.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 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))))
335.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 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))
175.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

simplify2.3s

Counts

2181 → 2181

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	2571	190370
done	5000	183951

prune10.6s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 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))))
1.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
1.9b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

624×	`times-frac`
522×	`sqrt-prod`
425×	`*-un-lft-identity`
325×	`add-sqr-sqrt`
323×	`add-cube-cbrt`
55×	`associate-/l*`
51×	`distribute-lft-out`
24×	`sqrt-div`
18×	`associate-/r/`
12×	`flip3-+` `associate-/r*` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`sqrt-undiv` `associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 464

Calls

4 calls:

441.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
347.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
192.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
165.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series577.0ms

Counts

4 → 12

Calls

4 calls:

303.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
143.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
70.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
61.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify2.9s

Counts

476 → 476

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	455	23023
1	2216	20399
done	5000	19454

prune1.5s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes97.0ms

Accuracy

74% (0.9b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 3.6b

bsearch154.0ms

Steps

Iters	Range		Point
10	3.787217848124224e+152	3.104754081890425e+165	1.1135175582662521e+159

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	28	66
1	38	62
done	38	62

end0.0ms

sample1.3s

Algorithm

intervals

Results

741.0ms	8000×	body	80	valid
235.0ms	8000×	pre	80	true