Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	202×	body	80	valid
5.0ms	25×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	14×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	7×	body	160	valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	14
1	103	14
2	454	14
3	2127	14
4	5001	14
done	5001	14

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b

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

1.7b

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

21.3b

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

rewrite789.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 111

Calls

3 calls:

178.0ms

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

555.0ms

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

50.0ms

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

series634.0ms

Counts

3 → 9

Calls

3 calls:

250.0ms

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

298.0ms

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

86.0ms

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

simplify300.0ms

Counts

120 → 120

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	681	1905
1	3622	1789
2	5003	1789
done	5003	1789

prune338.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.7b	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite771.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
35×	`times-frac`
26×	`add-cube-cbrt`
21×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
8×	`flip3-+` `flip-+`
7×	`associate-/r*` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/r/` `associate-/l*` `add-log-exp`
4×	`frac-times` `associate-l` `associate-*l/` `prod-exp` `cbrt-unprod` `distribute-lft-out`
3×	`div-inv`
2×	`frac-2neg` `associate-*r/` `clear-num` `unswap-sqr`
1×	`+-commutative` `flip3--` `div-sub` `pow-prod-down` `sum-log` `*-commutative` `flip--`

Counts

4 → 129

Calls

4 calls:

43.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
151.0ms	(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
114.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
458.0ms	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series711.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
249.0ms	(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
83.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
298.0ms	(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify93.0ms

Counts

141 → 141

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	657	1569
1	3554	1429
2	5001	1429
done	5001	1429

prune362.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.1b	(pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3)
1.6b	(+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
2.6b	(- 1.0 (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
24×	`times-frac`
21×	`associate-r`
19×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
14×	`unpow-prod-down` `cube-prod`
8×	`distribute-lft-out` `add-log-exp`
7×	`pow1`
6×	`flip3-+` `associate-/r/` `flip-+`
5×	`cbrt-undiv` `div-exp`
4×	`associate-l` `pow-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares`
3×	`pow-unpow` `div-inv`
2×	`frac-times` `associate-*l/` `unswap-sqr`
1×	`+-commutative` `cube-div` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `unpow3` `associate-r/` `pow-prod-down` `sum-log` `sum-cubes` `-commutative` `flip--` `sqr-pow`

Counts

4 → 120

Calls

4 calls:

101.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
153.0ms	(pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3)
877.0ms	(+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
188.0ms	(- 1.0 (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series8.2s

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
3.1s	(pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3)
4.8s	(+ (pow (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
192.0ms	(- 1.0 (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify123.0ms

Counts

132 → 132

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	771	1892
1	4175	1722
2	5002	1718
done	5002	1718

prune484.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (+ alpha beta) (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(* (+ alpha beta) (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))))
0.2b	(* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))
3.4b	(+ (/ (* (+ alpha beta) (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite918.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
38×	`frac-times`
32×	`add-cbrt-cube`
26×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
22×	`prod-exp`
20×	`associate-/l/`
19×	`associate-*r/`
18×	`associate-*l/`
17×	`flip3-+` `flip-+`
16×	`associate-r`
15×	`add-cube-cbrt` `times-frac`
14×	`flip3--` `flip--`
12×	`div-exp` `cbrt-unprod`
11×	`pow1`
9×	`associate-l`
7×	`cbrt-undiv` `un-div-inv`
6×	`add-log-exp`
4×	`pow-prod-down` `associate-/r*` `associate-/r/` `distribute-lft-out`
3×	`rec-exp` `1-exp` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `frac-2neg` `clear-num` `sum-log` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 150

Calls

4 calls:

212.0ms	(/ (* (+ alpha beta) (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
103.0ms	(* (+ alpha beta) (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))))
91.0ms	(* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))
505.0ms	(+ (/ (* (+ alpha beta) (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series728.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(/ (* (+ alpha beta) (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
89.0ms	(* (+ alpha beta) (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))))
83.0ms	(* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))
304.0ms	(+ (/ (* (+ alpha beta) (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify42.0ms

Counts

162 → 162

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	850	1900
1	5001	1675
done	5001	1675

prune426.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

regimes190.0ms

Accuracy

13.7% (5.4b remaining)

Error of 11.2b against oracle of 5.8b and baseline of 12.1b

bsearch83.0ms

Steps

Iters	Range		Point
10	3.6798278606000456e+102	4.598624050959069e+119	2.148651077263628e+115

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	25
1	46	25
done	46	25

end0.0ms

sample862.0ms

Algorithm

intervals

Results

248.0ms	6386×	body	80	valid
112.0ms	8000×	pre	80	true
106.0ms	523×	body	1280	valid
84.0ms	563×	body	640	valid
40.0ms	334×	body	320	valid
15.0ms	194×	body	160	valid