Details

sample58.0ms

Algorithm

intervals

Results

19.0ms	203×	body	80	valid
8.0ms	256×	pre	80	true
8.0ms	20×	body	640	valid
6.0ms	14×	body	1280	valid
3.0ms	12×	body	320	valid
1.0ms	7×	body	160	valid

simplify605.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.1b

localize57.0ms

Local error

Found 3 expressions with local error:

0.1b

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

1.5b

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

19.9b

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

rewrite695.0ms

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:

146.0ms

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

500.0ms

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

45.0ms

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

series789.0ms

Counts

3 → 9

Calls

3 calls:

291.0ms

(/ (/ (* (+ 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)

112.0ms

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

simplify866.0ms

Counts

123 → 123

Iterations

Iter	Nodes
2	2969
1	697
0	228

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

localize36.0ms

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))
1.2b	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
2.5b	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

rewrite737.0ms

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:

41.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
199.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
390.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
98.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series1.1s

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
297.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
367.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
270.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify1.9s

Counts

311 → 311

Iterations

Iter	Nodes
2	4557
1	1123
0	385

prune4.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

localize79.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
2.5b	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
2.5b	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
2.5b	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

rewrite647.0ms

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:

368.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
95.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
88.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
88.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series1.2s

Counts

4 → 12

Calls

4 calls:

331.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
283.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
318.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
259.0ms	(+ (* (+ 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

prune3.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize84.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- beta alpha))
0.6b	(cbrt (- beta alpha))
0.6b	(cbrt (- beta alpha))
8.3b	(+ (* (* (+ beta alpha) (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)

rewrite820.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

4 → 60

Calls

4 calls:

6.0ms	(cbrt (- beta alpha))
6.0ms	(cbrt (- beta alpha))
6.0ms	(cbrt (- beta alpha))
802.0ms	(+ (* (* (+ beta alpha) (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)

series1.4s

Counts

4 → 12

Calls

4 calls:

218.0ms	(cbrt (- beta alpha))
198.0ms	(cbrt (- beta alpha))
217.0ms	(cbrt (- beta alpha))
751.0ms	(+ (* (* (+ beta alpha) (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i))))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2 i)))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)

simplify3.1s

Counts

72 → 72

Iterations

Iter	Nodes
3	4124
2	835
1	291
0	121

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

regimes338.0ms

Accuracy

4.7% (6.2b remaining)

Error of 11.7b against oracle of 5.5b and baseline of 12.0b

bsearch115.0ms

Steps

Iters	Range		Point
8	4.6087787816230727e+77	6.329623610556215e+80	6.233799141039502e+80

simplify15.0ms

Iterations

Iter	Nodes
2	41
1	41
0	33

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.5s	6397×	body	80	valid
420.0ms	501×	body	1280	valid
387.0ms	8000×	pre	80	true
369.0ms	558×	body	640	valid
177.0ms	350×	body	320	valid
88.0ms	194×	body	160	valid