Details

sample111.0ms

Algorithm

intervals

Results

40.0ms	212×	body	80	valid
15.0ms	256×	pre	80	true
14.0ms	18×	body	640	valid
12.0ms	12×	body	1280	valid
5.0ms	9×	body	320	valid
2.0ms	5×	body	160	valid

simplify666.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	2155
3	440
2	95
1	32
0	16

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2 i)) 2.0)
0.1b	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
1.2b	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
18.1b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

rewrite844.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 130

Calls

4 calls:

97.0ms	(+ (+ (+ alpha beta) (* 2 i)) 2.0)
159.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
523.0ms	(+ (/ (/ (* (+ 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)))

series885.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (+ (+ alpha beta) (* 2 i)) 2.0)
313.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
417.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
111.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify889.0ms

Counts

142 → 142

Iterations

Iter	Nodes
2	3139
1	744
0	250

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.7b

localize57.0ms

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))
1.8b	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
3.1b	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

rewrite670.0ms

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:

37.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
157.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
387.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
76.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series924.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
238.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
321.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
253.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify2.0s

Counts

311 → 311

Iterations

Iter	Nodes
2	4557
1	1123
0	385

prune3.8s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.7b

localize93.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
3.1b	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
3.1b	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
3.1b	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

rewrite631.0ms

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:

363.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
81.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
92.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
91.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series1.2s

Counts

4 → 12

Calls

4 calls:

350.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
266.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
298.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
238.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify1.6s

Counts

166 → 166

Iterations

Iter	Nodes
2	3679
1	860
0	274

prune2.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.7b

localize76.0ms

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))
1.2b	(* (* (+ beta alpha) (/ (/ (* (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))))
4.1b	(+ (* (* (+ beta alpha) (/ (/ (* (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)

rewrite3.8s

Algorithm

rewrite-expression-head

Rules

378×	`times-frac`
278×	`*-un-lft-identity`
233×	`cbrt-prod`
216×	`associate-r`
214×	`add-sqr-sqrt` `add-exp-log`
172×	`add-cube-cbrt`
96×	`prod-exp`
90×	`div-exp`
88×	`add-cbrt-cube`
60×	`cbrt-unprod`
54×	`cbrt-undiv`
32×	`distribute-lft-out`
21×	`distribute-lft-out--` `difference-of-squares`
16×	`associate-/r/`
15×	`flip3-+` `flip-+`
12×	`1-exp`
9×	`frac-times` `pow1` `associate-*l/`
8×	`div-inv`
6×	`cbrt-div` `add-log-exp`
4×	`insert-posit16`
3×	`pow-prod-down` `associate-*r/`
2×	`pow1/3`
1×	`+-commutative` `sum-log` `associate-l` `*-commutative`

Counts

4 → 341

Calls

4 calls:

76.0ms	(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
79.0ms	(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
1.8s	(* (* (+ beta alpha) (/ (/ (* (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))))
1.8s	(+ (* (* (+ beta alpha) (/ (/ (* (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)

series1.1s

Counts

4 → 12

Calls

4 calls:

268.0ms	(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
253.0ms	(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
311.0ms	(* (* (+ beta alpha) (/ (/ (* (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))))
241.0ms	(+ (* (* (+ beta alpha) (/ (/ (* (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)

simplify1.3s

Counts

353 → 353

Iterations

Iter	Nodes
1	2387
0	683

prune6.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.7b

regimes386.0ms

Accuracy

14.8% (5.6b remaining)

Error of 11.3b against oracle of 5.8b and baseline of 12.3b

bsearch221.0ms

Steps

Iters	Range		Point
9	6.994450312263042e+191	3.1988988901785705e+198	4.6401313163804604e+197

simplify29.0ms

Iterations

Iter	Nodes
2	48
1	48
0	38

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.5s	6367×	body	80	valid
479.0ms	600×	body	640	valid
446.0ms	8000×	pre	80	true
370.0ms	485×	body	1280	valid
232.0ms	355×	body	320	valid
56.0ms	193×	body	160	valid