Details

sample32.0ms

Algorithm

intervals

Results

7.0ms	193×	body	80	valid
5.0ms	25×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	19×	body	640	valid
2.0ms	14×	body	320	valid
0.0ms	5×	body	160	valid

simplify750.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	29
1	31	29
2	101	29
3	408	29
4	1437	29
done	5000	29

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize12.0ms

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))

1.6b

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

21.8b

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

rewrite419.0ms

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:

91.0ms

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

296.0ms

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

27.0ms

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

series567.0ms

Counts

3 → 9

Calls

3 calls:

223.0ms

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

266.0ms

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

77.0ms

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

simplify959.0ms

Counts

120 → 120

Iterations

Useful iterations: 2 (363.0ms)

Iter	Nodes	Cost
0	225	4035
1	677	3821
2	2928	3577
done	5000	3577

prune349.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
0.1b	(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
1.6b	(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite729.0ms

Algorithm

rewrite-expression-head

Rules

1250×	`times-frac`
1055×	`*-un-lft-identity`
619×	`add-sqr-sqrt`
461×	`add-cube-cbrt`
218×	`distribute-lft-out`
96×	`associate-/l*`
79×	`distribute-lft-out--` `difference-of-squares`
60×	`associate-/r/`
33×	`div-inv`
30×	`associate-/r*`
26×	`flip3--` `flip--`
20×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`associate-/l/`
4×	`pow1` `flip3-+` `flip-+`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `sum-log`

Counts

4 → 645

Calls

4 calls:

37.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
119.0ms	(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
31.0ms	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
484.0ms	(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series702.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
225.0ms	(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
81.0ms	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
276.0ms	(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify841.0ms

Counts

657 → 657

Iterations

Useful iterations: done (809.0ms)

Iter	Nodes	Cost
0	705	27143
1	1787	26008
done	5000	25878

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
0.1b	(* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
1.5b	(/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))))
1.6b	(+ (/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) 1.0)

rewrite370.0ms

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`
9×	`associate-/r/`
7×	`flip3-+` `flip-+` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/r*` `add-log-exp`
4×	`frac-times` `associate-l` `associate-*l/` `prod-exp` `cbrt-unprod` `associate-/l/` `distribute-lft-out`
3×	`div-inv`
2×	`flip3--` `frac-2neg` `associate-*r/` `clear-num` `flip--` `unswap-sqr`
1×	`+-commutative` `pow-prod-down` `sum-log` `*-commutative`

Counts

4 → 128

Calls

4 calls:

35.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
202.0ms	(* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
51.0ms	(/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))))
77.0ms	(+ (/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) 1.0)

series777.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
149.0ms	(* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
234.0ms	(/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))))
278.0ms	(+ (/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) 1.0)

simplify1.0s

Counts

140 → 140

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	243	3772
1	688	3615
2	2944	3247
done	5000	3245

prune398.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (log (+ (/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) 1.0)))
1.5b	(/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))))
1.6b	(+ (/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) 1.0)
1.7b	(log (+ (/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) 1.0))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
14×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`log-prod`
6×	`pow1` `flip3-+` `flip-+` `add-log-exp`
5×	`associate-/r/` `distribute-lft-out`
4×	`cbrt-undiv` `log-div` `exp-prod` `times-frac` `div-exp` `exp-sum` `associate-/l*`
2×	`frac-times` `exp-diff` `associate-*l/` `prod-exp` `log-pow` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `frac-2neg` `associate-r/` `rem-log-exp` `clear-num` `associate-/r` `sum-log` `div-inv` `rem-exp-log`

Counts

4 → 77

Calls

4 calls:

63.0ms	(exp (log (+ (/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) 1.0)))
50.0ms	(/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))))
78.0ms	(+ (/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) 1.0)
60.0ms	(log (+ (/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) 1.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

278.0ms	(exp (log (+ (/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) 1.0)))
234.0ms	(/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))))
274.0ms	(+ (/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) 1.0)
276.0ms	(log (+ (/ (+ alpha beta) (* (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))) 1.0))

simplify653.0ms

Counts

89 → 89

Iterations

Useful iterations: 2 (182.0ms)

Iter	Nodes	Cost
0	188	3337
1	515	3206
2	1864	2752
done	5001	2752

prune274.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.0b

regimes192.0ms

Accuracy

12.1% (7.1b remaining)

Error of 11.3b against oracle of 4.2b and baseline of 12.3b

bsearch56.0ms

Steps

Iters	Range		Point
6	3.59071787844819e+176	1.6241016216736652e+177	1.6068051754302115e+177

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	52
1	38	52
done	38	52

end0.0ms

sample777.0ms

Algorithm

intervals

Results

235.0ms	6362×	body	80	valid
126.0ms	8000×	pre	80	true
100.0ms	502×	body	1280	valid
83.0ms	557×	body	640	valid
43.0ms	361×	body	320	valid
16.0ms	218×	body	160	valid