Details

sample74.0ms

Algorithm

intervals

Results

19.0ms	201×	body	80	valid
8.0ms	16×	body	1280	valid
8.0ms	256×	pre	80	true
7.0ms	17×	body	640	valid
4.0ms	12×	body	320	valid
2.0ms	10×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	2483
3	453
2	102
1	31
0	15

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.4b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b

(* (+ (+ alpha (* 2.0 i)) beta) (+ (+ 2.0 (+ beta alpha)) (* 2.0 i)))

2.1b

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

18.8b

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

rewrite500.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-cbrt-cube` `add-exp-log`
16×	`flip3-+` `flip-+`
12×	`frac-times`
9×	`*-un-lft-identity`
8×	`associate-/r/` `associate-/l/`
7×	`add-sqr-sqrt`
6×	`associate-l/` `associate-r/`
5×	`pow1` `prod-exp` `add-cube-cbrt` `cbrt-unprod` `add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-l`
3×	`flip3--` `associate-r` `flip--`
2×	`distribute-lft-out`
1×	`distribute-rgt-in` `+-commutative` `clear-num` `associate-/r` `sum-log` `frac-2neg` `distribute-lft-in` `times-frac` `pow-prod-down` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

3 → 78

Calls

3 calls:

331.0ms

(* (+ (+ alpha (* 2.0 i)) beta) (+ (+ 2.0 (+ beta alpha)) (* 2.0 i)))

52.0ms

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

114.0ms

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

series760.0ms

Counts

3 → 9

Calls

3 calls:

148.0ms

(* (+ (+ alpha (* 2.0 i)) beta) (+ (+ 2.0 (+ beta alpha)) (* 2.0 i)))

269.0ms

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

342.0ms

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

simplify454.0ms

Counts

87 → 87

Iterations

Iter	Nodes
done	5001
1	739
0	188

prune648.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.3b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ 1.0 (* (/ (+ alpha beta) (+ (* 2.0 i) (+ alpha beta))) (/ (- beta alpha) (+ (+ alpha (+ beta 2.0)) (* 2.0 i))))))
0.1b	(* (/ (+ alpha beta) (+ (* 2.0 i) (+ alpha beta))) (/ (- beta alpha) (+ (+ alpha (+ beta 2.0)) (* 2.0 i))))
2.1b	(+ 1.0 (* (/ (+ alpha beta) (+ (* 2.0 i) (+ alpha beta))) (/ (- beta alpha) (+ (+ alpha (+ beta 2.0)) (* 2.0 i)))))
2.1b	(log (exp (+ 1.0 (* (/ (+ alpha beta) (+ (* 2.0 i) (+ alpha beta))) (/ (- beta alpha) (+ (+ alpha (+ beta 2.0)) (* 2.0 i)))))))

rewrite412.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
31×	`times-frac`
24×	`add-cube-cbrt`
21×	`associate-r`
18×	`associate-l`
16×	`add-cbrt-cube` `add-exp-log`
9×	`add-log-exp`
7×	`pow1`
6×	`exp-prod`
4×	`cbrt-undiv` `log-prod` `div-exp` `prod-exp` `associate-/r/` `log-pow` `cbrt-unprod` `unswap-sqr`
3×	`flip3-+` `flip-+` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
2×	`sum-log` `exp-sum` `div-inv` `rem-exp-log`
1×	`frac-times` `+-commutative` `rem-log-exp` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 103

Calls

4 calls:

14.0ms	(exp (+ 1.0 (* (/ (+ alpha beta) (+ (* 2.0 i) (+ alpha beta))) (/ (- beta alpha) (+ (+ alpha (+ beta 2.0)) (* 2.0 i))))))
372.0ms	(* (/ (+ alpha beta) (+ (* 2.0 i) (+ alpha beta))) (/ (- beta alpha) (+ (+ alpha (+ beta 2.0)) (* 2.0 i))))
6.0ms	(+ 1.0 (* (/ (+ alpha beta) (+ (* 2.0 i) (+ alpha beta))) (/ (- beta alpha) (+ (+ alpha (+ beta 2.0)) (* 2.0 i)))))
16.0ms	(log (exp (+ 1.0 (* (/ (+ alpha beta) (+ (* 2.0 i) (+ alpha beta))) (/ (- beta alpha) (+ (+ alpha (+ beta 2.0)) (* 2.0 i)))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

349.0ms	(exp (+ 1.0 (* (/ (+ alpha beta) (+ (* 2.0 i) (+ alpha beta))) (/ (- beta alpha) (+ (+ alpha (+ beta 2.0)) (* 2.0 i))))))
353.0ms	(* (/ (+ alpha beta) (+ (* 2.0 i) (+ alpha beta))) (/ (- beta alpha) (+ (+ alpha (+ beta 2.0)) (* 2.0 i))))
429.0ms	(+ 1.0 (* (/ (+ alpha beta) (+ (* 2.0 i) (+ alpha beta))) (/ (- beta alpha) (+ (+ alpha (+ beta 2.0)) (* 2.0 i)))))
400.0ms	(log (exp (+ 1.0 (* (/ (+ alpha beta) (+ (* 2.0 i) (+ alpha beta))) (/ (- beta alpha) (+ (+ alpha (+ beta 2.0)) (* 2.0 i)))))))

simplify1.7s

Counts

115 → 115

Iterations

Iter	Nodes
done	5000
2	3663
1	706
0	221

prune913.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (+ (+ alpha beta) (* i 2.0)))
2.3b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (+ (+ alpha beta) (* i 2.0))))
4.3b	(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (+ (+ alpha beta) (* i 2.0)))))
4.3b	(log (exp (+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (+ (+ alpha beta) (* i 2.0)))))))

rewrite477.0ms

Algorithm

rewrite-expression-head

Rules

403×	`*-un-lft-identity`
388×	`times-frac`
235×	`add-sqr-sqrt`
156×	`add-cube-cbrt`
111×	`associate-r`
106×	`distribute-lft-out`
46×	`associate-/r/`
40×	`flip3-+` `flip-+`
35×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
28×	`frac-add`
18×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`log-prod` `associate-l` `log-pow`
3×	`exp-prod` `associate-/r*` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `div-sub` `associate-*l/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `rem-log-exp` `exp-sum` `pow-prod-down` `associate-r/` `-commutative` `associate-/l/`

Counts

4 → 326

Calls

4 calls:

199.0ms	(/ (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (+ (+ alpha beta) (* i 2.0)))
233.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (+ (+ alpha beta) (* i 2.0))))
6.0ms	(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (+ (+ alpha beta) (* i 2.0)))))
14.0ms	(log (exp (+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (+ (+ alpha beta) (* i 2.0)))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

260.0ms	(/ (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (+ (+ alpha beta) (* i 2.0)))
402.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (+ (+ alpha beta) (* i 2.0))))
417.0ms	(+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (+ (+ alpha beta) (* i 2.0)))))
408.0ms	(log (exp (+ 1.0 (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (+ (+ alpha beta) (* i 2.0)))))))

simplify737.0ms

Counts

338 → 338

Iterations

Iter	Nodes
done	5000
1	1458
0	471

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize75.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (/ 1 (+ (+ beta alpha) (* i 2.0))))
2.3b	(* (+ alpha beta) (* (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (/ 1 (+ (+ beta alpha) (* i 2.0)))))
4.3b	(+ 1.0 (* (+ alpha beta) (* (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (/ 1 (+ (+ beta alpha) (* i 2.0))))))
4.3b	(log (exp (+ 1.0 (* (+ alpha beta) (* (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (/ 1 (+ (+ beta alpha) (* i 2.0))))))))

rewrite497.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
58×	`add-exp-log`
52×	`add-sqr-sqrt`
41×	`times-frac`
39×	`associate-l`
34×	`add-cbrt-cube`
25×	`prod-exp` `add-cube-cbrt`
16×	`div-exp` `associate-r` `distribute-lft-out`
13×	`cbrt-unprod`
12×	`frac-times` `pow1` `flip3-+` `flip-+`
8×	`cbrt-undiv` `associate-*r/` `associate-/r/`
6×	`associate-*l/` `add-log-exp` `unswap-sqr`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`rec-exp` `log-prod` `1-exp` `pow-prod-down` `frac-add` `log-pow` `un-div-inv`
3×	`exp-prod`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `sum-log` `rem-log-exp` `exp-sum`

Counts

4 → 151

Calls

4 calls:

223.0ms	(* (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (/ 1 (+ (+ beta alpha) (* i 2.0))))
232.0ms	(* (+ alpha beta) (* (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (/ 1 (+ (+ beta alpha) (* i 2.0)))))
8.0ms	(+ 1.0 (* (+ alpha beta) (* (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (/ 1 (+ (+ beta alpha) (* i 2.0))))))
27.0ms	(log (exp (+ 1.0 (* (+ alpha beta) (* (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (/ 1 (+ (+ beta alpha) (* i 2.0))))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

268.0ms	(* (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (/ 1 (+ (+ beta alpha) (* i 2.0))))
343.0ms	(* (+ alpha beta) (* (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (/ 1 (+ (+ beta alpha) (* i 2.0)))))
420.0ms	(+ 1.0 (* (+ alpha beta) (* (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (/ 1 (+ (+ beta alpha) (* i 2.0))))))
420.0ms	(log (exp (+ 1.0 (* (+ alpha beta) (* (/ (- beta alpha) (+ (+ (* i 2.0) alpha) (+ beta 2.0))) (/ 1 (+ (+ beta alpha) (* i 2.0))))))))

simplify539.0ms

Counts

163 → 163

Iterations

Iter	Nodes
done	5000
1	996
0	298

prune915.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

regimes461.0ms

Accuracy

12% (5.3b remaining)

Error of 11.1b against oracle of 5.8b and baseline of 11.8b

bsearch90.0ms

Steps

Iters	Range		Point
7	4.644949955970094e+210	7.857719149395794e+212	1.244272110236543e+212

simplify8.0ms

Iterations

Iter	Nodes
done	44
1	44
0	35

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.2s	6418×	body	80	valid
298.0ms	8000×	pre	80	true
264.0ms	495×	body	1280	valid
194.0ms	572×	body	640	valid
114.0ms	321×	body	320	valid
33.0ms	194×	body	160	valid