Details

sample36.0ms

Algorithm

intervals

Results

15.0ms

267×

body

valid

simplify806.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
9	1412
8	514
7	233
6	164
5	138
4	102
3	65
2	37
1	23
0	14

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.0b	(+ y (* z (- b y)))
1.0b	(+ (* x y) (* z (- t a)))
22.0b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

22.0ms	(* z (- b y))
15.0ms	(+ y (* z (- b y)))
7.0ms	(+ (* x y) (* z (- t a)))
35.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series702.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* z (- b y))
54.0ms	(+ y (* z (- b y)))
66.0ms	(+ (* x y) (* z (- t a)))
517.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify750.0ms

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	1474
1	375
0	146

prune566.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.6b	(/ 1 (+ (* z (- b y)) y))
1.0b	(+ (* x y) (* z (- t a)))
21.7b	(* (+ (* x y) (* z (- t a))) (/ 1 (+ (* z (- b y)) y)))

rewrite195.0ms

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` `associate-+r+` `sub-neg` `distribute-lft-in` `div-exp` `associate-/r/` `unswap-sqr`
3×	`associate-/r` `associate-r/` `cbrt-unprod` `associate-/l*`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `un-div-inv` `pow-flip` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 116

Calls

4 calls:

32.0ms	(* z (- b y))
35.0ms	(/ 1 (+ (* z (- b y)) y))
18.0ms	(+ (* x y) (* z (- t a)))
104.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ (* z (- b y)) y)))

series653.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* z (- b y))
82.0ms	(/ 1 (+ (* z (- b y)) y))
61.0ms	(+ (* x y) (* z (- t a)))
460.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ (* z (- b y)) y)))

simplify1.9s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	2707
1	485
0	176

prune706.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.3b	(/ 1 (/ (+ (* z (- b y)) y) (+ (* z (- t a)) (* x y))))
1.0b	(+ (* z (- t a)) (* x y))
22.0b	(/ (+ (* z (- b y)) y) (+ (* z (- t a)) (* x y)))

rewrite138.0ms

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×	`distribute-rgt-in` `cbrt-undiv` `associate-+l+` `sub-neg` `distribute-lft-in`
3×	`associate-l`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-*r/` `associate-/l/`
1×	`+-commutative` `sum-log` `flip3--` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `pow-flip` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 156

Calls

4 calls:

20.0ms	(* z (- b y))
49.0ms	(/ 1 (/ (+ (* z (- b y)) y) (+ (* z (- t a)) (* x y))))
11.0ms	(+ (* z (- t a)) (* x y))
48.0ms	(/ (+ (* z (- b y)) y) (+ (* z (- t a)) (* x y)))

series906.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* z (- b y))
631.0ms	(/ 1 (/ (+ (* z (- b y)) y) (+ (* z (- t a)) (* x y))))
59.0ms	(+ (* z (- t a)) (* x y))
158.0ms	(/ (+ (* z (- b y)) y) (+ (* z (- t a)) (* x y)))

simplify1.6s

Counts

168 → 168

Iterations

Iter	Nodes
done	5001
2	3746
1	665
0	249

prune903.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 16.4b

localize45.0ms

Local error

Found 4 expressions with local error:

16.5b	(cbrt (* z (- b y)))
16.5b	(cbrt (* z (- b y)))
16.5b	(cbrt (* z (- b y)))
22.0b	(/ (+ (* x y) (* z (- t a))) (+ y (* (* (cbrt (* z (- b y))) (cbrt (* z (- b y)))) (cbrt (* z (- b y))))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`cbrt-div` `add-cbrt-cube` `associate-*r/` `add-exp-log`
4×	`pow1` `add-log-exp`
3×	`cbrt-prod` `associate-/r` `flip3--` `pow1/3` `flip--` `associate-/l`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 64

Calls

4 calls:

6.0ms	(cbrt (* z (- b y)))
6.0ms	(cbrt (* z (- b y)))
6.0ms	(cbrt (* z (- b y)))
25.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* (* (cbrt (* z (- b y))) (cbrt (* z (- b y)))) (cbrt (* z (- b y))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

214.0ms	(cbrt (* z (- b y)))
224.0ms	(cbrt (* z (- b y)))
230.0ms	(cbrt (* z (- b y)))
655.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* (* (cbrt (* z (- b y))) (cbrt (* z (- b y)))) (cbrt (* z (- b y))))))

simplify795.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
2	1100
1	320
0	129

prune576.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 16.4b

regimes762.0ms

Accuracy

37% (5.3b remaining)

Error of 20.4b against oracle of 15.1b and baseline of 23.5b

bsearch125.0ms

Steps

Iters	Range		Point
8	3.988153498496788e+45	4.479251535464297e+48	3.9584922856662595e+48
6	-1.48985545878022e+244	-9.682329788799394e+242	-9.946154013212847e+242

simplify3.0ms

Iterations

Iter	Nodes
done	36
1	36
0	25

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.2s

8403×

body

valid