Details

sample98.0ms

Algorithm

intervals

Results

25.0ms	188×	body	80	valid
18.0ms	16×	body	640	valid
15.0ms	23×	body	1280	valid
11.0ms	256×	pre	80	true
8.0ms	21×	body	320	valid
2.0ms	8×	body	160	valid

simplify398.0ms

Counts

1 → 1

Iterations

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize49.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

2.1b

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

23.3b

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

rewrite512.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
47×	`*-un-lft-identity`
25×	`add-sqr-sqrt` `add-cube-cbrt`
17×	`add-cbrt-cube` `add-exp-log`
14×	`associate-/r/`
11×	`flip3-+` `flip-+` `distribute-lft-out`
10×	`associate-/l*`
9×	`associate-/l/`
7×	`cbrt-undiv` `associate-/r*` `div-exp` `div-inv`
5×	`add-log-exp`
4×	`frac-times`
3×	`pow1` `flip3--` `insert-posit16` `flip--`
2×	`clear-num` `frac-2neg` `associate-l/` `prod-exp` `associate-r/` `cbrt-unprod`
1×	`+-commutative` `sum-log`

Counts

3 → 114

Calls

3 calls:

114.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

356.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

40.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series678.0ms

Counts

3 → 9

Calls

3 calls:

236.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

343.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

99.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify488.0ms

Counts

123 → 123

Iterations

Iter	Nodes
done	2001
1	697
0	228

prune636.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
0.1b	(/ (/ (- 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)))
3.3b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

rewrite450.0ms

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:

28.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
115.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
231.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
69.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series935.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
231.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
329.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
282.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify799.0ms

Counts

311 → 311

Iterations

Iter	Nodes
done	2004
1	1128
0	389

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.6b

localize78.0ms

Local error

Found 4 expressions with local error:

2.5b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
3.3b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
3.3b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
3.3b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

rewrite543.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 154

Calls

4 calls:

326.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
72.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
61.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
81.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series1.4s

Counts

4 → 12

Calls

4 calls:

277.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
393.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
345.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
343.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify740.0ms

Counts

166 → 166

Iterations

Iter	Nodes
done	2000
1	867
0	276

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.6b

localize102.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.6b	(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
2.5b	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
4.8b	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)

rewrite3.2s

Algorithm

rewrite-expression-head

Rules

207×	`add-exp-log`
94×	`prod-exp`
87×	`div-exp`
84×	`add-cbrt-cube`
58×	`cbrt-unprod`
51×	`cbrt-undiv`
13×	`*-un-lft-identity`
12×	`1-exp`
9×	`frac-times` `pow1`
8×	`cbrt-prod`
7×	`add-sqr-sqrt` `flip3-+` `add-cube-cbrt` `flip-+`
6×	`associate-*r/` `add-log-exp`
5×	`associate-*l/`
4×	`cbrt-div` `associate-l` `insert-posit16`
3×	`pow-prod-down` `distribute-lft-out`
2×	`pow1/3`
1×	`+-commutative` `sum-log` `associate-r` `*-commutative`

Counts

4 → 125

Calls

4 calls:

43.0ms	(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
42.0ms	(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
1.6s	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
1.5s	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)

series1.2s

Counts

4 → 12

Calls

4 calls:

267.0ms	(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
227.0ms	(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
306.0ms	(* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
383.0ms	(+ (* (+ alpha beta) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) 1.0)

simplify1.1s

Counts

137 → 137

Iterations

Iter	Nodes
done	2000
1	1041
0	340

prune786.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.6b

regimes593.0ms

Accuracy

6.8% (5.9b remaining)

Error of 11.9b against oracle of 6.0b and baseline of 12.3b

bsearch311.0ms

Steps

Iters	Range		Point
2	7.657638831517088e+174	9.353867177132027e+174	8.621431291668078e+174
9	1.838882238404714e+84	2.5987397470618154e+89	1.8551287992761453e+84
9	2.567854176142929e+45	4.791523621903145e+52	5.841782349532883e+51

simplify46.0ms

Iterations

Iter	Nodes
done	83
1	83
0	63

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.3s	6370×	body	80	valid
884.0ms	8000×	pre	80	true
430.0ms	529×	body	1280	valid
358.0ms	551×	body	640	valid
195.0ms	346×	body	320	valid
61.0ms	204×	body	160	valid