Details

sample31.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
3.0ms	82×	body	80	nan

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8
done	8	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`distribute-lft-out`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 45

Calls

2 calls:

29.0ms	(+ 1.0 (sqrt (+ x 1.0)))
73.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series307.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(+ 1.0 (sqrt (+ x 1.0)))
240.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify2.0s

Counts

51 → 51

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	117	739
1	277	693
2	831	636
3	3565	630
done	5000	628

prune224.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b	(pow (sqrt (+ x 1.0)) 3)
4.5b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.1b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
62×	`sqrt-div`
43×	`add-sqr-sqrt`
34×	`sqrt-prod`
32×	`flip3-+` `flip-+`
31×	`add-cube-cbrt`
28×	`associate-*r/` `distribute-lft-out`
27×	`times-frac`
23×	`unpow-prod-down` `cube-prod`
21×	`pow1`
16×	`frac-sub`
12×	`frac-times`
11×	`swap-sqr`
9×	`add-exp-log` `sqrt-pow1` `pow1/2` `associate-/r*` `add-cbrt-cube`
8×	`associate-*l/`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`pow-prod-up`
4×	`sum-cubes` `sub-div` `unswap-sqr`
3×	`pow-unpow` `pow-pow` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cube-div` `associate-/r/`
1×	`cbrt-undiv` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `pow-plus` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 184

Calls

4 calls:

78.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
10.0ms	(pow (sqrt (+ x 1.0)) 3)
39.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
103.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
100.0ms	(pow (sqrt (+ x 1.0)) 3)
118.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
248.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify2.2s

Counts

196 → 196

Iterations

Useful iterations: 2 (681.0ms)

Iter	Nodes	Cost
0	313	4015
1	746	2931
2	2743	2700
done	5000	2700

prune737.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (/ x (+ (- (+ 1.0 x) (* 1.0 (sqrt (+ x 1.0)))) (* 1.0 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
4.5b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
4.5b	(- (+ 1.0 x) (* 1.0 (sqrt (+ x 1.0))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
99×	`times-frac`
78×	`add-sqr-sqrt`
73×	`associate-l`
64×	`sqrt-div`
57×	`add-cube-cbrt`
41×	`flip3-+` `flip-+`
34×	`associate-*r/`
26×	`sqrt-prod`
21×	`pow1` `distribute-lft-out`
20×	`frac-sub`
15×	`add-exp-log` `add-cbrt-cube`
14×	`frac-times`
11×	`swap-sqr` `add-log-exp`
10×	`associate-r` `associate-/r/`
9×	`associate-*l/`
8×	`sqrt-pow1` `pow1/2`
7×	`unswap-sqr`
5×	`pow-prod-up` `div-inv`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod` `sub-div`
3×	`cbrt-undiv` `diff-log` `div-exp` `pow-sqr`
2×	`sub-neg` `flip3--` `*-commutative` `flip--`
1×	`pow2` `distribute-rgt-in` `distribute-rgt-out--` `distribute-lft-in` `pow-plus` `sqrt-unprod` `associate--l+` `sum-log` `rem-square-sqrt`

Counts

4 → 207

Calls

4 calls:

983.0ms	(* (/ (/ x (+ (- (+ 1.0 x) (* 1.0 (sqrt (+ x 1.0)))) (* 1.0 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
68.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
38.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
94.0ms	(- (+ 1.0 x) (* 1.0 (sqrt (+ x 1.0))))

series427.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(* (/ (/ x (+ (- (+ 1.0 x) (* 1.0 (sqrt (+ x 1.0)))) (* 1.0 1.0))) (+ 1.0 (sqrt (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
18.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
118.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
98.0ms	(- (+ 1.0 x) (* 1.0 (sqrt (+ x 1.0))))

simplify992.0ms

Counts

219 → 219

Iterations

Useful iterations: done (983.0ms)

Iter	Nodes	Cost
0	430	8007
1	1424	6403
done	5000	5530

prune903.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ (- (+ 1.0 x) (* 1.0 (sqrt (+ x 1.0)))) (* 1.0 1.0)))
0.2b	(/ (- (+ 1.0 x) (* 1.0 (- (sqrt (+ x 1.0)) 1.0))) (+ 1.0 (sqrt (+ x 1.0))))
4.5b	(- (sqrt (+ x 1.0)) 1.0)
4.5b	(- (+ 1.0 x) (* 1.0 (sqrt (+ x 1.0))))

rewrite513.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `times-frac`
11×	`add-log-exp`
8×	`add-exp-log` `flip3-+` `associate-*r/` `frac-sub` `add-cbrt-cube` `flip-+`
7×	`associate-/r*`
6×	`associate-/l/` `associate-/l*`
5×	`flip3--` `flip--`
4×	`pow1` `sqrt-div` `associate-/r/` `distribute-lft-out`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `div-exp` `clear-num` `div-inv` `difference-of-squares`
1×	`div-sub` `associate--l+` `sum-log` `sqrt-prod` `distribute-lft-out--`

Counts

4 → 102

Calls

4 calls:

216.0ms	(/ x (+ (- (+ 1.0 x) (* 1.0 (sqrt (+ x 1.0)))) (* 1.0 1.0)))
167.0ms	(/ (- (+ 1.0 x) (* 1.0 (- (sqrt (+ x 1.0)) 1.0))) (+ 1.0 (sqrt (+ x 1.0))))
52.0ms	(- (sqrt (+ x 1.0)) 1.0)
73.0ms	(- (+ 1.0 x) (* 1.0 (sqrt (+ x 1.0))))

series810.0ms

Counts

4 → 12

Calls

4 calls:

306.0ms	(/ x (+ (- (+ 1.0 x) (* 1.0 (sqrt (+ x 1.0)))) (* 1.0 1.0)))
356.0ms	(/ (- (+ 1.0 x) (* 1.0 (- (sqrt (+ x 1.0)) 1.0))) (+ 1.0 (sqrt (+ x 1.0))))
51.0ms	(- (sqrt (+ x 1.0)) 1.0)
97.0ms	(- (+ 1.0 x) (* 1.0 (sqrt (+ x 1.0))))

simplify2.2s

Counts

114 → 114

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	330	3018
1	864	2874
2	3225	2596
done	5001	2584

prune608.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes27.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	44
1	21	44
done	21	44

end0.0ms

sample809.0ms

Algorithm

intervals

Results

440.0ms	8000×	body	80	valid
84.0ms	2751×	body	80	nan