Details

sample78.0ms

Algorithm

intervals

Results

39.0ms	256×	body	80	valid
18.0ms	256×	pre	80	true

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5011
3	1567
2	267
1	58
0	17

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.5b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.6b	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
48.3b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite17.9s

Algorithm

rewrite-expression-head

Rules

98841×	`*-un-lft-identity`
45731×	`distribute-lft-out`
39648×	`times-frac`
39139×	`associate-l`
26853×	`add-sqr-sqrt`
13506×	`swap-sqr`
12217×	`associate-r`
7974×	`distribute-lft-out--`
7376×	`add-cube-cbrt`
6645×	`difference-of-squares`
4800×	`unswap-sqr`
3290×	`*-commutative`
1384×	`associate-/l*`
130×	`associate-/r/`
120×	`flip3-+` `flip-+`
108×	`associate-/r*`
102×	`associate-/l/`
80×	`frac-times`
61×	`add-cbrt-cube` `add-exp-log`
58×	`associate-*r/`
40×	`associate-*l/`
22×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
17×	`div-inv`
16×	`pow1` `associate-+r+`
14×	`+-commutative`
12×	`associate-+l+`
4×	`pow-prod-down` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`pow2` `pow-plus` `flip3--` `pow-sqr` `pow-prod-up` `flip--`

Counts

4 → 21617

Calls

4 calls:

303.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
1.3s	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
7.7s	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
3.7s	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

series1.6s

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
138.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.1s	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
262.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify17.4s

Counts

21629 → 21629

Iterations

Iter	Nodes
done	5001
0	3596

prune15.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 32.4b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0)))
0.1b	(* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i))
0.1b	(* (/ (* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i)) (+ (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0))))
33.4b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite10.3s

Algorithm

rewrite-expression-head

Rules

24494×	`*-un-lft-identity`
11566×	`distribute-lft-out`
9572×	`associate-/l*`
9431×	`frac-times`
8437×	`associate-l`
7796×	`times-frac`
5321×	`associate-/l/`
4998×	`add-sqr-sqrt`
3703×	`add-cube-cbrt`
3285×	`associate-/r*`
1472×	`flip3-+` `flip-+`
1192×	`associate-*l/`
781×	`associate-r`
520×	`clear-num`
518×	`frac-2neg`
398×	`difference-of-squares`
388×	`associate-/r/`
253×	`associate-*r/`
199×	`sqrt-prod` `distribute-lft-out--`
196×	`unswap-sqr`
194×	`div-inv`
90×	`*-commutative`
70×	`add-cbrt-cube` `add-exp-log`
29×	`cbrt-undiv` `div-exp`
20×	`prod-exp` `cbrt-unprod`
8×	`pow1` `un-div-inv`
4×	`distribute-rgt-in` `+-commutative` `associate-+l+` `distribute-lft-in` `insert-posit16` `add-log-exp`
2×	`flip3--` `pow-prod-down` `flip--`

Counts

4 → 8547

Calls

4 calls:

1.3s	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0)))
359.0ms	(* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i))
6.1s	(* (/ (* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i)) (+ (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0))))
990.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series9.9s

Counts

4 → 12

Calls

4 calls:

2.3s	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0)))
142.0ms	(* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i))
7.3s	(* (/ (* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i)) (+ (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0))))
155.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify10.7s

Counts

8559 → 8559

Iterations

Iter	Nodes
done	5000
0	3787

prune20.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.1b

localize93.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i)) (+ (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0))) (/ (+ (* 1/2 i) (* 1/4 (+ beta alpha))) (- (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0))))
0.0b	(/ i (+ (+ alpha beta) (* 2 i)))
0.0b	(/ (* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i)) (+ (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0)))
0.1b	(* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i))

rewrite4.5s

Algorithm

rewrite-expression-head

Rules

3639×	`*-un-lft-identity`
2112×	`frac-times`
1633×	`associate-l`
1593×	`associate-/l*`
1489×	`distribute-lft-out`
1364×	`add-sqr-sqrt`
1056×	`associate-/r*`
1025×	`times-frac`
996×	`associate-/l/`
807×	`add-cube-cbrt`
414×	`flip3-+` `flip-+`
360×	`associate-*l/`
193×	`associate-r`
190×	`difference-of-squares`
173×	`clear-num`
172×	`frac-2neg`
95×	`sqrt-prod` `distribute-lft-out--`
70×	`unswap-sqr`
66×	`associate-/r/`
60×	`associate-*r/`
52×	`add-cbrt-cube` `add-exp-log`
33×	`div-inv`
30×	`*-commutative`
18×	`cbrt-undiv` `div-exp`
16×	`prod-exp` `cbrt-unprod`
8×	`pow1`
6×	`un-div-inv`
4×	`distribute-rgt-in` `+-commutative` `associate-+l+` `distribute-lft-in` `insert-posit16` `add-log-exp`
2×	`pow-prod-down`
1×	`flip3--` `flip--`

Counts

4 → 2323

Calls

4 calls:

2.9s	(* (/ (* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i)) (+ (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0))) (/ (+ (* 1/2 i) (* 1/4 (+ beta alpha))) (- (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0))))
54.0ms	(/ i (+ (+ alpha beta) (* 2 i)))
829.0ms	(/ (* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i)) (+ (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0)))
381.0ms	(* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i))

series7.0s

Counts

4 → 12

Calls

4 calls:

4.0s	(* (/ (* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i)) (+ (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0))) (/ (+ (* 1/2 i) (* 1/4 (+ beta alpha))) (- (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0))))
89.0ms	(/ i (+ (+ alpha beta) (* 2 i)))
2.7s	(/ (* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i)) (+ (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0)))
151.0ms	(* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i))

simplify5.3s

Counts

2335 → 2335

Iterations

Iter	Nodes
done	5000
0	1842

prune9.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 1.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ i (+ (+ alpha beta) (* 2 i)))
0.0b	(/ (* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i)) (+ (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0)))
0.1b	(* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i))
1.8b	(exp (log (* (/ (* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i)) (+ (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0))) (/ (+ (* 1/2 i) (* 1/4 (+ beta alpha))) (- (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0))))))

rewrite6.6s

Algorithm

rewrite-expression-head

Rules

3641×	`*-un-lft-identity`
2112×	`frac-times`
1677×	`log-div` `exp-diff`
1633×	`associate-l`
1593×	`associate-/l*`
1489×	`distribute-lft-out`
1366×	`add-sqr-sqrt`
1056×	`associate-/r*`
1025×	`times-frac`
996×	`associate-/l/`
809×	`add-cube-cbrt`
414×	`flip3-+` `flip-+`
360×	`associate-*l/`
223×	`log-prod` `exp-sum`
193×	`associate-r`
190×	`difference-of-squares`
173×	`clear-num`
172×	`frac-2neg`
95×	`sqrt-prod` `distribute-lft-out--`
70×	`unswap-sqr`
66×	`associate-/r/`
60×	`associate-*r/`
33×	`div-inv`
30×	`*-commutative`
20×	`add-cbrt-cube` `add-exp-log`
9×	`pow1`
6×	`cbrt-undiv` `div-exp` `un-div-inv`
5×	`exp-prod` `add-log-exp`
4×	`distribute-rgt-in` `+-commutative` `associate-+l+` `distribute-lft-in` `prod-exp` `cbrt-unprod` `insert-posit16`
2×	`pow-prod-down` `log-pow` `rem-exp-log`
1×	`flip3--` `flip--`

Counts

4 → 2317

Calls

4 calls:

58.0ms	(/ i (+ (+ alpha beta) (* 2 i)))
733.0ms	(/ (* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i)) (+ (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0)))
351.0ms	(* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i))
5.2s	(exp (log (* (/ (* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i)) (+ (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0))) (/ (+ (* 1/2 i) (* 1/4 (+ beta alpha))) (- (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0))))))

series6.9s

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ i (+ (+ alpha beta) (* 2 i)))
2.6s	(/ (* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i)) (+ (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0)))
139.0ms	(* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i))
4.1s	(exp (log (* (/ (* (/ i (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) i)) (+ (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0))) (/ (+ (* 1/2 i) (* 1/4 (+ beta alpha))) (- (fabs (+ (+ alpha beta) (* 2 i))) (sqrt 1.0))))))

simplify9.0s

Counts

2329 → 2329

Iterations

Iter	Nodes
done	5000
0	4657

prune13.4s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 1.1b

regimes449.0ms

Accuracy

48.4% (8.6b remaining)

Error of 10.2b against oracle of 1.6b and baseline of 18.3b

bsearch59.0ms

Steps

Iters	Range		Point
5	5.4039666828126895e+146	1.5043712263133658e+147	6.263709625600619e+146

simplify15.0ms

Iterations

Iter	Nodes
done	48
1	48
0	35

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
391.0ms	8000×	pre	80	true