Details

sample43.0ms

Algorithm

intervals

Results

19.0ms

277×

body

valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	23	17
2	37	17
3	55	17
4	72	17
5	84	17
6	108	17
7	177	17
8	326	17
9	605	17
10	1389	17
11	3953	17
done	5001	17

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 25.1b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.0b	(* z (- t a))
0.5b	(+ (* x y) (* z (- t a)))
24.5b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

7.0ms	(* z (- b y))
7.0ms	(* z (- t a))
5.0ms	(+ (* x y) (* z (- t a)))
8.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series135.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* z (- b y))
10.0ms	(* z (- t a))
15.0ms	(+ (* x y) (* z (- t a)))
102.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify695.0ms

Counts

110 → 110

Iterations

Useful iterations: 2 (134.0ms)

Iter	Nodes	Cost
0	168	1522
1	398	1454
2	1274	1348
done	5000	1348

prune155.0ms

Filtered

74 candidates to 110 candidates (-48.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	101	9	110
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	101	10	111

Merged error: 24.5b

Counts

111 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.2b	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
0.5b	(+ (* x y) (* z (- t a)))
24.5b	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
62×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
58×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube`
11×	`associate-/r/`
8×	`div-exp`
7×	`pow1` `flip3-+` `flip-+`
6×	`div-inv` `associate-/l*` `add-log-exp`
5×	`associate-r`
4×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `associate-+r+` `distribute-lft-in`
3×	`associate-l`
2×	`rec-exp` `frac-2neg` `1-exp` `associate-*r/` `clear-num` `associate-/l/`
1×	`+-commutative` `flip3--` `pow-flip` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 156

Calls

4 calls:

7.0ms	(* z (- t a))
9.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
5.0ms	(+ (* x y) (* z (- t a)))
8.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

series287.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* z (- t a))
188.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
15.0ms	(+ (* x y) (* z (- t a)))
76.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

simplify773.0ms

Counts

168 → 168

Iterations

Useful iterations: 2 (191.0ms)

Iter	Nodes	Cost
0	240	4169
1	570	3885
2	1586	3574
done	5000	3574

prune160.0ms

Filtered

99 candidates to 168 candidates (-69.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	1	7	8
Picked	0	1	1
Done	1	0	1
Total	168	10	178

Merged error: 24.5b

Counts

178 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.5b	(+ (* x y) (* z (- t a)))
1.2b	(/ 1 (+ y (* z (- b y))))
23.8b	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
22×	`add-cube-cbrt`
20×	`times-frac` `associate-r`
19×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`flip3-+` `prod-exp` `flip-+`
4×	`distribute-rgt-in` `sub-neg` `associate-+r+` `distribute-lft-in` `div-exp` `associate-/r/` `unswap-sqr`
3×	`associate-r/` `associate-/r` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `flip3--` `pow-flip` `frac-2neg` `clear-num` `sum-log` `un-div-inv` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 116

Calls

4 calls:

7.0ms	(* z (- t a))
5.0ms	(+ (* x y) (* z (- t a)))
5.0ms	(/ 1 (+ y (* z (- b y))))
11.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

series144.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* z (- t a))
15.0ms	(+ (* x y) (* z (- t a)))
18.0ms	(/ 1 (+ y (* z (- b y))))
103.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

simplify806.0ms

Counts

128 → 128

Iterations

Useful iterations: 2 (155.0ms)

Iter	Nodes	Cost
0	173	2024
1	446	1838
2	1490	1656
done	5000	1656

prune140.0ms

Filtered

81 candidates to 128 candidates (-58.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	128	10	138

Merged error: 24.5b

Counts

138 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x y) (* z (- t a)))
1.0b	(/ 1 (+ (* x y) (* z (- t a))))
1.2b	(/ 1 (+ (* z (- b y)) y))
22.9b	(/ (/ 1 (+ (* z (- b y)) y)) (/ 1 (+ (* x y) (* z (- t a)))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

531×	`times-frac`
244×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
69×	`associate-/r/`
52×	`add-exp-log`
36×	`div-exp`
35×	`flip3-+` `flip-+` `div-inv`
21×	`associate-/r` `associate-/l`
20×	`add-cbrt-cube`
10×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`pow1` `add-log-exp`
4×	`associate-+r+`
3×	`frac-2neg` `clear-num`
2×	`distribute-rgt-in` `sub-neg` `pow-flip` `distribute-lft-in` `inv-pow`
1×	`+-commutative` `sum-log` `associate-/l/`

Counts

4 → 368

Calls

4 calls:

5.0ms	(+ (* x y) (* z (- t a)))
6.0ms	(/ 1 (+ (* x y) (* z (- t a))))
8.0ms	(/ 1 (+ (* z (- b y)) y))
24.0ms	(/ (/ 1 (+ (* z (- b y)) y)) (/ 1 (+ (* x y) (* z (- t a)))))

series167.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (* x y) (* z (- t a)))
22.0ms	(/ 1 (+ (* x y) (* z (- t a))))
13.0ms	(/ 1 (+ (* z (- b y)) y))
117.0ms	(/ (/ 1 (+ (* z (- b y)) y)) (/ 1 (+ (* x y) (* z (- t a)))))

simplify1.5s

Counts

380 → 380

Iterations

Useful iterations: 2 (983.0ms)

Iter	Nodes	Cost
0	541	14402
1	1663	12544
2	3644	11708
done	5001	11708

prune206.0ms

Filtered

134 candidates to 380 candidates (-183.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	377	3	380
Fresh	3	4	7
Picked	0	1	1
Done	1	1	2
Total	381	9	390

Merged error: 11.0b

Counts

390 → 9

regimes859.0ms

Accuracy

34.4% (8.3b remaining)

Error of 19.5b against oracle of 11.2b and baseline of 23.9b

bsearch52.0ms

Steps

Iters	Range		Point
8	6.577918230926644e+72	2.1915949522273947e+76	7.033569036513191e+75
7	-9.385494182443387e+61	-1.5762786805130549e+60	-1.2023829244883378e+61

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	25	41
1	35	35
done	35	35

end0.0ms

sample1.0s

Algorithm

intervals

Results

461.0ms

8384×

body

valid

Details

sample43.0ms

simplify2.9s

prune4.0ms

localize13.0ms

rewrite29.0ms

series135.0ms

simplify695.0ms

prune155.0ms

localize14.0ms

rewrite35.0ms

series287.0ms

simplify773.0ms

prune160.0ms

localize14.0ms

rewrite34.0ms

series144.0ms

simplify806.0ms

prune140.0ms

localize15.0ms

rewrite66.0ms

series167.0ms

simplify1.5s

prune206.0ms

regimes859.0ms

bsearch52.0ms

simplify3.0ms

end0.0ms

sample1.0s

Profiling