Details

sample60.0ms

Algorithm

intervals

Results

28.0ms	256×	body	80	valid
10.0ms	256×	pre	80	true

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	1615
2	280
1	60
0	17

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(* i (+ (+ alpha beta) i))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
39.2b	(/ (/ (* (* 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))
46.7b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite581.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-cbrt-cube` `add-exp-log`
58×	`times-frac`
50×	`associate-/r/`
49×	`flip3-+` `flip-+`
42×	`add-sqr-sqrt`
32×	`frac-times`
31×	`*-un-lft-identity`
30×	`associate-*r/`
26×	`add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
16×	`associate-*l/`
14×	`associate-/l*` `difference-of-squares`
11×	`pow1`
9×	`associate-/l/`
8×	`associate-r`
7×	`div-inv`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-out`
2×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `*-commutative`
1×	`flip3--` `flip--` `unswap-sqr`

Counts

4 → 201

Calls

4 calls:

93.0ms	(* i (+ (+ alpha beta) i))
122.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
251.0ms	(/ (/ (* (* 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))
109.0ms	(/ (* (* 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:

44.0ms	(* i (+ (+ alpha beta) i))
141.0ms	(* (* 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))
278.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify1.9s

Counts

213 → 213

Iterations

Iter	Nodes
done	5001
1	1299
0	359

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 36.6b

localize67.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
37.0b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
38.2b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

366×	`times-frac`
300×	`add-sqr-sqrt`
235×	`*-un-lft-identity`
155×	`add-cube-cbrt`
96×	`associate-r`
70×	`add-cbrt-cube` `add-exp-log`
62×	`difference-of-squares`
44×	`associate-/r/`
42×	`associate-l`
33×	`cbrt-undiv` `div-exp`
31×	`sqrt-prod` `distribute-lft-out--`
22×	`flip3-+` `flip-+` `div-inv`
19×	`associate-/l*`
16×	`prod-exp` `cbrt-unprod`
12×	`associate-/r*`
9×	`distribute-lft-out`
6×	`pow1` `unswap-sqr`
5×	`associate-/l/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*r/`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 376

Calls

4 calls:

253.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
785.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
80.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
127.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series4.1s

Counts

4 → 12

Calls

4 calls:

539.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
3.2s	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
126.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
168.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify1.8s

Counts

388 → 388

Iterations

Iter	Nodes
done	5000
1	1744
0	511

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 36.5b

localize85.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.0b	(/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))
0.1b	(* (/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
38.2b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

1714×	`times-frac`
1388×	`*-un-lft-identity`
773×	`add-sqr-sqrt`
659×	`add-cube-cbrt`
392×	`distribute-lft-out`
278×	`associate-l`
96×	`associate-r`
85×	`associate-/r/`
74×	`associate-/l*`
71×	`add-cbrt-cube` `add-exp-log`
47×	`div-inv`
39×	`flip3-+` `flip-+`
38×	`cbrt-undiv` `div-exp`
30×	`difference-of-squares`
15×	`sqrt-prod` `distribute-lft-out--`
12×	`associate-/r*` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`pow1`
5×	`associate-/l/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`frac-times` `flip3--` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--`

Counts

4 → 867

Calls

4 calls:

180.0ms	(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
98.0ms	(/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))
811.0ms	(* (/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
564.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.4s

Counts

4 → 12

Calls

4 calls:

333.0ms	(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
69.0ms	(/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))
2.9s	(* (/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
153.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify3.0s

Counts

879 → 879

Iterations

Iter	Nodes
done	5001
1	3261
0	967

prune5.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.5b

localize62.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.0b

(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

0.0b

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

rewrite391.0ms

Algorithm

rewrite-expression-head

Rules

950×	`times-frac`
828×	`*-un-lft-identity`
385×	`add-sqr-sqrt` `add-cube-cbrt`
252×	`distribute-lft-out`
74×	`associate-/l*`
48×	`associate-/r/`
30×	`associate-/r*`
27×	`div-inv`
22×	`flip3-+` `flip-+`
19×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`

Counts

3 → 513

Calls

3 calls:

52.0ms

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

240.0ms

(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

70.0ms

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

series546.0ms

Counts

3 → 9

Calls

3 calls:

122.0ms

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

346.0ms

(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))

77.0ms

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

simplify1.8s

Counts

522 → 522

Iterations

Iter	Nodes
done	5000
1	1563
0	578

prune2.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 1.4b

regimes391.0ms

Accuracy

43.3% (9.2b remaining)

Error of 11.1b against oracle of 1.9b and baseline of 18.1b

bsearch100.0ms

Steps

Iters	Range		Point
7	4.180155208905662e+119	1.7530375893929083e+121	2.495505368754722e+120

simplify17.0ms

Iterations

Iter	Nodes
done	45
1	45
0	34

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.2s	8000×	body	80	valid
396.0ms	8000×	pre	80	true