Details

sample31.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
3.0ms	79×	body	80	nan

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 61

Calls

3 calls:

6.0ms	(sqrt (+ x 1.0))
12.0ms	(+ 1.0 (sqrt (+ x 1.0)))
35.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series250.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(sqrt (+ x 1.0))
50.0ms	(+ 1.0 (sqrt (+ x 1.0)))
168.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify1.2s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	1079
1	316
0	137

prune327.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ x (+ (* 1.0 (* 1.0 1.0)) (* (+ 1.0 x) (sqrt (+ 1.0 x))))) (+ (* 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)))
3.0b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.8b	(/ x (+ (* 1.0 (* 1.0 1.0)) (* (+ 1.0 x) (sqrt (+ 1.0 x)))))

rewrite446.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-div`
54×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
34×	`flip3-+` `flip-+`
30×	`associate-*r/` `add-cube-cbrt`
26×	`sqrt-prod`
25×	`times-frac` `associate-l`
21×	`pow1`
16×	`frac-sub`
14×	`frac-times`
13×	`add-cbrt-cube` `add-exp-log`
11×	`swap-sqr`
10×	`associate-r`
9×	`associate-*l/`
8×	`sqrt-pow1` `pow1/2`
7×	`cube-unmult` `pow3` `sum-cubes`
6×	`distribute-lft-out` `add-log-exp` `unswap-sqr`
5×	`pow-prod-up`
4×	`associate-/r*` `pow-prod-down` `associate-/r/` `sub-div`
3×	`prod-exp` `pow-sqr` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `*-commutative` `div-inv`
1×	`pow2` `distribute-rgt-in` `clear-num` `sub-neg` `rem-square-sqrt` `frac-2neg` `distribute-lft-in` `pow-plus` `flip3--` `distribute-rgt-out--` `sqrt-unprod` `diff-log` `flip--`

Counts

4 → 171

Calls

4 calls:

331.0ms	(* (/ x (+ (* 1.0 (* 1.0 1.0)) (* (+ 1.0 x) (sqrt (+ 1.0 x))))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
35.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
28.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
45.0ms	(/ x (+ (* 1.0 (* 1.0 1.0)) (* (+ 1.0 x) (sqrt (+ 1.0 x)))))

series923.0ms

Counts

4 → 12

Calls

4 calls:

530.0ms	(* (/ x (+ (* 1.0 (* 1.0 1.0)) (* (+ 1.0 x) (sqrt (+ 1.0 x))))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
25.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
87.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
279.0ms	(/ x (+ (* 1.0 (* 1.0 1.0)) (* (+ 1.0 x) (sqrt (+ 1.0 x)))))

simplify3.3s

Counts

183 → 183

Iterations

Iter	Nodes
done	5008
2	4585
1	1201
0	384

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b	(/ 1 (/ (+ (* 1.0 (* 1.0 1.0)) (* (+ x 1.0) (sqrt (+ x 1.0)))) x))
3.0b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.8b	(/ (+ (* 1.0 (* 1.0 1.0)) (* (+ x 1.0) (sqrt (+ x 1.0)))) x)

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
98×	`add-sqr-sqrt`
84×	`*-un-lft-identity`
70×	`add-cube-cbrt`
60×	`sqrt-div`
31×	`flip3-+` `flip-+`
28×	`associate-*r/`
26×	`sqrt-prod`
20×	`pow1`
19×	`associate-/r*` `add-exp-log`
16×	`cube-unmult` `pow3` `sum-cubes` `frac-sub`
13×	`add-cbrt-cube`
12×	`frac-times`
11×	`swap-sqr`
8×	`sqrt-pow1` `pow1/2` `div-exp` `associate-*l/`
7×	`associate-r` `associate-l` `associate-/l*`
6×	`div-inv` `distribute-lft-out` `add-log-exp`
5×	`pow-prod-up`
4×	`cbrt-undiv` `sub-div` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-/l/`
1×	`pow2` `sub-neg` `rem-square-sqrt` `pow-plus` `flip3--` `distribute-rgt-out--` `sqrt-unprod` `diff-log` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `pow-flip` `flip--` `inv-pow`

Counts

4 → 216

Calls

4 calls:

41.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
69.0ms	(/ 1 (/ (+ (* 1.0 (* 1.0 1.0)) (* (+ x 1.0) (sqrt (+ x 1.0)))) x))
43.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
79.0ms	(/ (+ (* 1.0 (* 1.0 1.0)) (* (+ x 1.0) (sqrt (+ x 1.0)))) x)

series589.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
256.0ms	(/ 1 (/ (+ (* 1.0 (* 1.0 1.0)) (* (+ x 1.0) (sqrt (+ x 1.0)))) x))
91.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
213.0ms	(/ (+ (* 1.0 (* 1.0 1.0)) (* (+ x 1.0) (sqrt (+ x 1.0)))) x)

simplify2.4s

Counts

228 → 228

Iterations

Iter	Nodes
done	5001
2	3093
1	1063
0	394

prune1.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ (* 1.0 1.0) (- (+ 1.0 x) (* (sqrt (+ 1.0 x)) 1.0))))
0.1b	(* (+ 1.0 x) (sqrt (+ 1.0 x)))
3.0b	(- (+ 1.0 x) (* (sqrt (+ 1.0 x)) 1.0))
10.2b	(/ (* x (+ (* 1.0 1.0) (- (+ 1.0 x) (* (sqrt (+ 1.0 x)) 1.0)))) (+ (* 1.0 (* 1.0 1.0)) (* (+ 1.0 x) (sqrt (+ 1.0 x)))))

rewrite395.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
11×	`pow1` `add-cube-cbrt`
10×	`sqrt-div` `associate-r`
9×	`add-log-exp`
7×	`associate-l`
6×	`associate-l/` `associate-r/`
5×	`sqrt-prod`
4×	`frac-times` `associate-/r*` `times-frac` `frac-sub`
3×	`pow3` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `diff-log` `cube-unmult` `div-exp` `pow-prod-down` `associate-/r/` `sum-cubes` `*-commutative` `pow-prod-up` `distribute-lft-out` `associate-/l/`
1×	`distribute-rgt-in` `clear-num` `sum-log` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `flip3--` `pow1/2` `associate--l+` `div-inv` `flip--` `associate-/l*` `distribute-lft-out--`

Counts

4 → 103

Calls

4 calls:

229.0ms	(* x (+ (* 1.0 1.0) (- (+ 1.0 x) (* (sqrt (+ 1.0 x)) 1.0))))
35.0ms	(* (+ 1.0 x) (sqrt (+ 1.0 x)))
36.0ms	(- (+ 1.0 x) (* (sqrt (+ 1.0 x)) 1.0))
92.0ms	(/ (* x (+ (* 1.0 1.0) (- (+ 1.0 x) (* (sqrt (+ 1.0 x)) 1.0)))) (+ (* 1.0 (* 1.0 1.0)) (* (+ 1.0 x) (sqrt (+ 1.0 x)))))

series873.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(* x (+ (* 1.0 1.0) (- (+ 1.0 x) (* (sqrt (+ 1.0 x)) 1.0))))
73.0ms	(* (+ 1.0 x) (sqrt (+ 1.0 x)))
81.0ms	(- (+ 1.0 x) (* (sqrt (+ 1.0 x)) 1.0))
509.0ms	(/ (* x (+ (* 1.0 1.0) (- (+ 1.0 x) (* (sqrt (+ 1.0 x)) 1.0)))) (+ (* 1.0 (* 1.0 1.0)) (* (+ 1.0 x) (sqrt (+ 1.0 x)))))

simplify2.9s

Counts

115 → 115

Iterations

Iter	Nodes
done	5015
2	3527
1	856
0	299

prune696.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes38.0ms

Accuracy

99.7% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 7.1b

bsearch54.0ms

Steps

Iters	Range		Point
6	16665313893544862.0	1.7505038925535098e+17	16902064928340788.0

simplify10.0ms

Iterations

Iter	Nodes
done	30
1	30
0	22

end0.0ms

sample617.0ms

Algorithm

intervals

Results

360.0ms	7995×	body	80	valid
75.0ms	2741×	body	80	nan
1.0ms	5×	body	1280	valid