Details

sample61.0ms

Algorithm

intervals

Results

35.0ms	256×	body	80	valid
10.0ms	256×	pre	80	true

simplify4.1s

Counts

1 → 1

Iterations

Iter	Nodes
4	11034
3	1567
2	267
1	58
0	17

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 50.1b

localize44.0ms

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))))
35.2b	(/ (/ (* (* 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))
44.1b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite549.0ms

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×	`associate-l` `pow-prod-down` `insert-posit16` `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 → 193

Calls

4 calls:

57.0ms	(* i (+ (+ alpha beta) i))
105.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
231.0ms	(/ (/ (* (* 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))
149.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

series1.5s

Counts

4 → 12

Calls

4 calls:

25.0ms	(* i (+ (+ alpha beta) i))
162.0ms	(* (* 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))
216.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify2.9s

Counts

205 → 205

Iterations

Iter	Nodes
2	6901
1	1224
0	351

prune2.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 33.2b

localize59.0ms

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))))
34.3b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
34.8b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.2s

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×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*r/`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 368

Calls

4 calls:

292.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
679.0ms	(* (/ (/ (* 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))))
64.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
148.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.9s

Counts

4 → 12

Calls

4 calls:

504.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
3.1s	(* (/ (/ (* 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))))
152.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
187.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify4.6s

Counts

380 → 380

Iterations

Iter	Nodes
2	7081
1	1692
0	503

prune6.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 33.1b

localize96.0ms

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)))
0.0b	(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
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))))
34.8b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

1852×	`times-frac`
1455×	`*-un-lft-identity`
892×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
380×	`distribute-lft-out`
278×	`associate-l`
99×	`associate-/r/`
96×	`associate-r`
86×	`associate-/l*`
74×	`add-cbrt-cube` `add-exp-log`
62×	`difference-of-squares`
54×	`div-inv`
44×	`flip3-+` `flip-+`
40×	`cbrt-undiv` `div-exp`
31×	`sqrt-prod` `distribute-lft-out--`
13×	`associate-/r*`
12×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`pow1`
4×	`insert-posit16` `add-log-exp` `associate-/l/`
3×	`clear-num` `frac-2neg`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 948

Calls

4 calls:

269.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
280.0ms	(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
828.0ms	(* (/ (/ 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))))
147.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series4.1s

Counts

4 → 12

Calls

4 calls:

428.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
356.0ms	(/ (/ i (/ (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
3.1s	(* (/ (/ 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))))
175.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify2.2s

Counts

960 → 960

Iterations

Iter	Nodes
1	3364
0	1034

prune17.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.1b

localize44.0ms

Local error

Found 3 expressions with local error:

0.0b

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

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)))

rewrite405.0ms

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×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp` `associate-/l/`

Counts

3 → 507

Calls

3 calls:

122.0ms

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

51.0ms

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

203.0ms

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

series556.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms

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

117.0ms

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

356.0ms

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

simplify2.5s

Counts

516 → 516

Iterations

Iter	Nodes
2	4918
1	1478
0	572

prune8.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 1.1b

regimes421.0ms

Accuracy

36% (10.4b remaining)

Error of 12.5b against oracle of 2.1b and baseline of 18.4b

bsearch385.0ms

Steps

Iters	Range		Point
7	5.10633297233485e+153	4.121021321028831e+155	8.296142771618488e+154
6	3.1819839989364968e+143	1.9564396141384856e+144	1.1670218513000327e+144
7	4.6213351350430846e+131	1.4905430430158114e+133	6.635668102175435e+131
6	4.790332713009464e+113	3.8021573547113504e+114	2.413859403597715e+114

simplify14.0ms

Iterations

Iter	Nodes
2	62
1	62
0	48

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
317.0ms	8000×	pre	80	true