Details

sample79.0ms

Algorithm

intervals

Results

23.0ms	197×	body	80	valid
15.0ms	19×	body	640	valid
12.0ms	20×	body	1280	valid
9.0ms	256×	pre	80	true
5.0ms	16×	body	320	valid
1.0ms	4×	body	160	valid

simplify922.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2042
4	2042
3	440
2	95
1	32
0	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha beta) (- beta alpha))
0.1b	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
1.8b	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
21.2b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

rewrite853.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity` `times-frac`
32×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
14×	`flip3-+` `associate-/r/` `flip-+`
12×	`distribute-lft-out`
10×	`associate-/l*`
9×	`associate-/l/`
8×	`frac-times`
7×	`cbrt-undiv` `associate-/r*` `div-exp` `div-inv`
6×	`pow1` `flip3--` `flip--` `add-log-exp`
5×	`associate-r`
4×	`associate-l` `associate-l/` `associate-r/` `insert-posit16`
3×	`prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in`
1×	`+-commutative` `sum-log` `pow-prod-down` `*-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 148

Calls

4 calls:

24.0ms	(* (+ alpha beta) (- beta alpha))
172.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
590.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
64.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series929.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (+ alpha beta) (- beta alpha))
382.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
385.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
107.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify1.3s

Counts

160 → 160

Iterations

Iter	Nodes
done	2000
2	2000
1	789
0	267

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
1.6b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
2.5b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

rewrite647.0ms

Algorithm

rewrite-expression-head

Rules

321×	`times-frac`
290×	`*-un-lft-identity`
211×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
31×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/l*`
24×	`associate-/r/`
20×	`add-cbrt-cube` `add-exp-log`
15×	`flip3-+` `flip-+`
12×	`div-inv`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`pow1` `add-log-exp`
4×	`associate-l` `insert-posit16`
3×	`div-sub` `prod-exp` `cbrt-unprod` `unswap-sqr` `associate-/l/`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*l/`
1×	`+-commutative` `sum-log` `flip3--` `pow-prod-down` `associate-r/` `-commutative` `flip--`

Counts

4 → 299

Calls

4 calls:

168.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
29.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
351.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
90.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series1.0s

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
100.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
298.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
406.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify1.5s

Counts

311 → 311

Iterations

Iter	Nodes
done	2000
2	2000
1	1128
0	389

prune3.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
1.6b	(* (+ alpha beta) (/ (cbrt (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
2.5b	(+ (* (+ alpha beta) (/ (cbrt (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
11.5b	(cbrt (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))

rewrite721.0ms

Algorithm

rewrite-expression-head

Rules

106×	`*-un-lft-identity`
95×	`add-sqr-sqrt`
93×	`times-frac`
54×	`add-cube-cbrt`
43×	`associate-r`
27×	`swap-sqr`
25×	`associate-l`
21×	`add-exp-log`
20×	`add-cbrt-cube`
18×	`distribute-lft-out--`
13×	`pow1`
12×	`difference-of-squares`
10×	`associate-/r/`
8×	`frac-times` `flip3-+` `associate-*l/` `flip-+`
7×	`cbrt-div`
6×	`prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
5×	`cbrt-prod` `cbrt-undiv` `div-exp` `associate-*r/` `div-inv` `distribute-lft-out`
4×	`insert-posit16`
2×	`pow-prod-down` `*-commutative`
1×	`pow2` `+-commutative` `sum-log` `pow-plus` `pow1/3` `pow3` `pow-sqr` `pow-prod-up` `rem-cbrt-cube`

Counts

4 → 175

Calls

4 calls:

151.0ms	(* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
290.0ms	(* (+ alpha beta) (/ (cbrt (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
84.0ms	(+ (* (+ alpha beta) (/ (cbrt (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
189.0ms	(cbrt (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

178.0ms	(* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
396.0ms	(* (+ alpha beta) (/ (cbrt (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
403.0ms	(+ (* (+ alpha beta) (/ (cbrt (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
157.0ms	(cbrt (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))

simplify1.4s

Counts

187 → 187

Iterations

Iter	Nodes
done	2000
2	2000
1	1055
0	321

prune2.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)))
1.6b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
2.5b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
4.9b	(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))

rewrite622.0ms

Algorithm

rewrite-expression-head

Rules

147×	`times-frac`
134×	`*-un-lft-identity`
99×	`add-sqr-sqrt`
90×	`associate-r`
66×	`add-cube-cbrt`
22×	`distribute-lft-out`
14×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`distribute-lft-out--` `difference-of-squares`
10×	`flip3-+` `associate-/r/` `flip-+`
8×	`pow1`
6×	`log-prod` `add-log-exp`
5×	`div-inv`
4×	`log-div` `exp-prod` `associate-l` `insert-posit16`
3×	`cbrt-undiv` `div-exp` `exp-sum` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `exp-diff` `associate-*l/` `log-pow`
1×	`+-commutative` `sum-log` `rem-log-exp` `pow-prod-down` `associate-r/` `-commutative` `rem-exp-log`

Counts

4 → 163

Calls

4 calls:

80.0ms	(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)))
349.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
77.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
112.0ms	(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

442.0ms	(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)))
349.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
372.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
405.0ms	(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))

simplify1.3s

Counts

175 → 175

Iterations

Iter	Nodes
done	2002
2	2002
1	977
0	332

prune2.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

regimes457.0ms

Accuracy

13.5% (7.3b remaining)

Error of 11.7b against oracle of 4.3b and baseline of 12.8b

bsearch103.0ms

Steps

Iters	Range		Point
6	2.310233354129206e+149	1.637278862402389e+150	1.0312336573895782e+150

simplify17.0ms

Iterations

Iter	Nodes
done	39
1	39
0	31

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.2s	6303×	body	80	valid
827.0ms	494×	body	1280	valid
480.0ms	8000×	pre	80	true
463.0ms	636×	body	640	valid
231.0ms	373×	body	320	valid
62.0ms	194×	body	160	valid