Details

sample42.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
4	2152
3	441
2	102
1	35
0	15

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha 2) beta) 1.0)
0.0b	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (+ (+ alpha 2) beta))
0.1b	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (+ (+ alpha 2) beta)) (+ (+ (+ alpha 2) beta) 1.0))
3.6b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

4332×	`*-un-lft-identity`
2696×	`times-frac`
2173×	`distribute-lft-out`
778×	`add-sqr-sqrt` `add-cube-cbrt`
166×	`associate-/l*`
102×	`associate-/r/`
53×	`flip3-+` `flip-+`
51×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp`
6×	`sum-log`
4×	`pow1` `insert-posit16` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 1221

Calls

4 calls:

116.0ms	(+ (+ (+ alpha 2) beta) 1.0)
213.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (+ (+ alpha 2) beta))
496.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (+ (+ alpha 2) beta)) (+ (+ (+ alpha 2) beta) 1.0))
134.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))

series524.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (+ (+ alpha 2) beta) 1.0)
178.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (+ (+ alpha 2) beta))
211.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (+ (+ alpha 2) beta)) (+ (+ (+ alpha 2) beta) 1.0))
115.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))

simplify2.2s

Counts

1233 → 1233

Iterations

Iter	Nodes
2	4099
1	1397
0	607

prune14.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.1b

localize65.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha 2) beta))
0.1b	(* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (/ 1 (+ (+ alpha 2) beta)))
0.1b	(/ (* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (/ 1 (+ (+ alpha 2) beta))) (+ (+ (+ alpha 2) beta) 1.0))
3.6b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))

rewrite714.0ms

Algorithm

rewrite-expression-head

Rules

168×	`*-un-lft-identity`
83×	`times-frac`
71×	`distribute-lft-out`
64×	`add-exp-log`
63×	`add-sqr-sqrt`
46×	`add-cube-cbrt`
38×	`add-cbrt-cube`
28×	`div-exp`
26×	`associate-l`
21×	`associate-r`
16×	`associate-/r*` `prod-exp`
15×	`cbrt-undiv`
10×	`associate-/r/`
8×	`cbrt-unprod` `associate-/l*`
7×	`pow1`
6×	`flip3-+` `flip-+` `unswap-sqr` `associate-/l/`
5×	`rec-exp` `1-exp` `div-inv`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`frac-times` `associate-l/` `associate-r/` `un-div-inv`
1×	`pow-prod-down` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 211

Calls

4 calls:

44.0ms	(/ 1 (+ (+ alpha 2) beta))
290.0ms	(* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (/ 1 (+ (+ alpha 2) beta)))
174.0ms	(/ (* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (/ 1 (+ (+ alpha 2) beta))) (+ (+ (+ alpha 2) beta) 1.0))
200.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))

series567.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ 1 (+ (+ alpha 2) beta))
183.0ms	(* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (/ 1 (+ (+ alpha 2) beta)))
213.0ms	(/ (* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta)) (/ 1 (+ (+ alpha 2) beta))) (+ (+ (+ alpha 2) beta) 1.0))
110.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))

simplify1.0s

Counts

223 → 223

Iterations

Iter	Nodes
2	3504
1	773
0	256

prune2.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha 2) beta))
0.0b	(/ (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ (+ alpha 2) beta))) (+ (+ alpha 2) beta))
0.1b	(/ (/ (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ (+ alpha 2) beta))) (+ (+ alpha 2) beta)) (+ (+ (+ alpha 2) beta) 1.0))
3.7b	(* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ (+ alpha 2) beta)))

rewrite632.0ms

Algorithm

rewrite-expression-head

Rules

243×	`*-un-lft-identity`
138×	`times-frac`
121×	`distribute-lft-out`
59×	`add-sqr-sqrt`
54×	`add-exp-log`
52×	`add-cube-cbrt`
34×	`add-cbrt-cube`
24×	`div-exp`
22×	`associate-/r/`
21×	`associate-r`
16×	`associate-/r*`
15×	`flip3-+` `flip-+` `associate-/l*`
14×	`cbrt-undiv`
12×	`prod-exp`
11×	`div-inv`
7×	`pow1` `associate-/l/`
6×	`cbrt-unprod`
4×	`frac-times` `rec-exp` `1-exp` `associate-l` `associate-*l/` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `unswap-sqr`
2×	`associate-*r/` `un-div-inv`
1×	`pow-prod-down` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 237

Calls

4 calls:

34.0ms	(/ 1 (+ (+ alpha 2) beta))
96.0ms	(/ (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ (+ alpha 2) beta))) (+ (+ alpha 2) beta))
220.0ms	(/ (/ (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ (+ alpha 2) beta))) (+ (+ alpha 2) beta)) (+ (+ (+ alpha 2) beta) 1.0))
277.0ms	(* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ (+ alpha 2) beta)))

series554.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ 1 (+ (+ alpha 2) beta))
162.0ms	(/ (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ (+ alpha 2) beta))) (+ (+ alpha 2) beta))
207.0ms	(/ (/ (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ (+ alpha 2) beta))) (+ (+ alpha 2) beta)) (+ (+ (+ alpha 2) beta) 1.0))
117.0ms	(* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ (+ alpha 2) beta)))

simplify1.4s

Counts

249 → 249

Iterations

Iter	Nodes
2	3773
1	839
0	289

prune3.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))) (cbrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))))
3.6b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))
3.6b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))
3.6b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))

rewrite973.0ms

Algorithm

rewrite-expression-head

Rules

582×	`*-un-lft-identity`
249×	`distribute-lft-out`
238×	`times-frac`
208×	`cbrt-prod`
121×	`add-sqr-sqrt`
97×	`add-cube-cbrt`
75×	`swap-sqr`
29×	`associate-r` `associate-l`
15×	`associate-/r*`
14×	`associate-/r/`
12×	`add-exp-log` `associate-/l*`
11×	`pow1`
10×	`flip3-+` `add-cbrt-cube` `flip-+`
9×	`unswap-sqr`
7×	`div-inv`
6×	`pow1/3` `associate-/l/`
4×	`cbrt-div` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 302

Calls

4 calls:

395.0ms	(* (cbrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))) (cbrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))))
200.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))
159.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))
211.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))

series595.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(* (cbrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))) (cbrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))))
136.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))
142.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))
100.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ (+ alpha 2) beta))

simplify2.4s

Counts

314 → 314

Iterations

Iter	Nodes
3	5929
2	1459
1	493
0	225

prune4.5s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 1.1b

regimes158.0ms

Accuracy

46.3% (1.4b remaining)

Error of 2.6b against oracle of 1.2b and baseline of 3.7b

bsearch73.0ms

Steps

Iters	Range		Point
6	3.996480357247039e+140	3.990983090279907e+141	3.292108726261348e+141

simplify10.0ms

Iterations

Iter	Nodes
2	38
1	38
0	27

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.3s	8000×	body	80	valid
337.0ms	8000×	pre	80	true