Details

sample9.0ms

Algorithm

intervals

Results

4.0ms

256×

body

valid

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	7
1	6	7
done	6	7

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize4.0ms

Local error

Found 1 expressions with local error:

15.6b

(/ x (+ (* x x) 1.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 29

Calls

1 calls:

6.0ms

(/ x (+ (* x x) 1.0))

series59.0ms

Counts

1 → 3

Calls

1 calls:

59.0ms

(/ x (+ (* x x) 1.0))

simplify945.0ms

Counts

32 → 32

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	74	428
1	174	413
2	554	373
3	1721	373
done	5001	373

prune62.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ 1 (+ (* x x) 1.0))
15.4b	(* x (/ 1 (+ (* x x) 1.0)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`times-frac`
19×	`*-un-lft-identity`
18×	`add-cube-cbrt`
15×	`add-exp-log` `associate-r`
9×	`add-cbrt-cube`
5×	`pow1`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

2 → 71

Calls

2 calls:

7.0ms	(/ 1 (+ (* x x) 1.0))
18.0ms	(* x (/ 1 (+ (* x x) 1.0)))

series99.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ 1 (+ (* x x) 1.0))
55.0ms	(* x (/ 1 (+ (* x x) 1.0)))

simplify752.0ms

Counts

77 → 77

Iterations

Useful iterations: 2 (124.0ms)

Iter	Nodes	Cost
0	128	985
1	324	863
2	1199	727
done	5000	727

prune111.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
3.9b	(/ (cbrt x) (+ (pow x 2) 1.0))
11.5b	(* (* (cbrt x) (cbrt x)) (/ (cbrt x) (+ (pow x 2) 1.0)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
50×	`times-frac`
43×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
34×	`cbrt-prod`
30×	`associate-r`
18×	`add-exp-log`
13×	`distribute-lft-out`
11×	`add-cbrt-cube`
9×	`pow1`
6×	`prod-exp` `cbrt-unprod` `associate-/l*`
4×	`associate-/r*` `associate-/r/` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `unswap-sqr`
2×	`flip3-+` `pow1/3` `flip-+` `div-inv`
1×	`frac-2neg` `associate-r/` `associate-l` `clear-num` `-commutative`

Counts

4 → 123

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
13.0ms	(/ (cbrt x) (+ (pow x 2) 1.0))
45.0ms	(* (* (cbrt x) (cbrt x)) (/ (cbrt x) (+ (pow x 2) 1.0)))

series554.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt x)
175.0ms	(cbrt x)
130.0ms	(/ (cbrt x) (+ (pow x 2) 1.0))
74.0ms	(* (* (cbrt x) (cbrt x)) (/ (cbrt x) (+ (pow x 2) 1.0)))

simplify886.0ms

Counts

135 → 135

Iterations

Useful iterations: 2 (182.0ms)

Iter	Nodes	Cost
0	188	1929
1	528	1819
2	2221	1506
done	5000	1506

prune284.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 x) (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))))
0.2b	(/ 1.0 (pow x 5))
0.2b	(/ 1.0 (pow x 3))
19.2b	(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
97×	`times-frac`
69×	`*-un-lft-identity`
47×	`add-cube-cbrt`
33×	`unpow-prod-down`
20×	`difference-of-squares`
19×	`associate-/r*`
17×	`sqr-pow`
16×	`cube-prod`
14×	`add-exp-log`
11×	`add-log-exp`
8×	`add-cbrt-cube` `distribute-lft-out--`
6×	`div-exp` `div-inv` `associate-/l*`
5×	`distribute-lft-out`
4×	`pow1` `cube-mult` `unpow3`
3×	`frac-add`
2×	`cbrt-undiv` `pow-to-exp` `sub-neg` `associate-+r+` `flip3--` `frac-2neg` `diff-log` `pow-exp` `clear-num` `sum-log` `frac-sub` `flip--`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 171

Calls

4 calls:

193.0ms	(+ (/ 1 x) (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))))
4.0ms	(/ 1.0 (pow x 5))
5.0ms	(/ 1.0 (pow x 3))
67.0ms	(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (/ 1 x) (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))))
52.0ms	(/ 1.0 (pow x 5))
41.0ms	(/ 1.0 (pow x 3))
128.0ms	(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

simplify1.9s

Counts

183 → 183

Iterations

Useful iterations: 2 (221.0ms)

Iter	Nodes	Cost
0	257	2827
1	580	2514
2	2583	2418
done	5000	2418

prune357.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes24.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.2b

bsearch60.0ms

Steps

Iters	Range		Point
11	0.08347146558812443	3.320253512051989e+22	509.7156046843299
10	-5.276190702543451e+18	-14583263.309321204	-62379821099783.21

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	22	47
1	30	33
done	30	33

end0.0ms

sample225.0ms

Algorithm

intervals

Results

139.0ms

8000×

body

valid