Details

sample23.0ms

Algorithm

intervals

Results

6.0ms	57×	body	640	valid
4.0ms	134×	body	80	valid
2.0ms	31×	body	320	valid
2.0ms	17×	body	1280	valid
1.0ms	17×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	7
1	31	7
2	43	7
3	57	7
4	73	7
5	92	7
6	126	7
7	158	7
8	207	7
9	209	7
10	209	7
done	209	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.0b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite390.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
47×	`times-frac`
43×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
14×	`distribute-lft-out--`
13×	`distribute-lft-out`
11×	`add-log-exp`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `associate-+l+` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 114

Calls

4 calls:

12.0ms	(/ 1.0 (- x 1.0))
12.0ms	(/ 1.0 (+ x 1.0))
64.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
296.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1.0 (- x 1.0))
24.0ms	(/ 1.0 (+ x 1.0))
46.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
212.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify50.0ms

Counts

126 → 126

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	496	865
1	1681	827
2	5002	816
done	5002	816

prune238.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ x 1.0) (cbrt 1.0)))
0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ x 1.0) (cbrt 1.0))) (/ 2.0 x))
2.0b	(+ (- (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ x 1.0) (cbrt 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite615.0ms

Algorithm

rewrite-expression-head

Rules

105×	`times-frac`
83×	`*-un-lft-identity`
76×	`add-sqr-sqrt`
44×	`add-cube-cbrt`
33×	`associate-/r*`
26×	`cbrt-prod`
18×	`add-exp-log`
14×	`distribute-lft-out`
12×	`add-cbrt-cube` `difference-of-squares`
11×	`add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`distribute-lft-out--`
4×	`pow1` `div-inv` `associate-/l*`
3×	`flip3--` `frac-add` `associate-/r/` `flip--`
2×	`sub-neg` `associate-+l+` `frac-2neg` `diff-log` `prod-exp` `clear-num` `sum-log` `frac-sub` `cbrt-unprod`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+`

Counts

4 → 155

Calls

4 calls:

25.0ms	(/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ x 1.0) (cbrt 1.0)))
11.0ms	(/ 1.0 (- x 1.0))
102.0ms	(- (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ x 1.0) (cbrt 1.0))) (/ 2.0 x))
470.0ms	(+ (- (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ x 1.0) (cbrt 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ x 1.0) (cbrt 1.0)))
26.0ms	(/ 1.0 (- x 1.0))
69.0ms	(- (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ x 1.0) (cbrt 1.0))) (/ 2.0 x))
245.0ms	(+ (- (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (+ x 1.0) (cbrt 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify77.0ms

Counts

167 → 167

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	772	1816
1	3265	1731
2	5001	1693
done	5001	1693

prune361.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0)) (- x 1.0))
0.0b	(/ (+ (* (- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) x) 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) x) (- x 1.0)))
0.1b	(* (* (/ (+ x 1.0) (cbrt 1.0)) x) (- x 1.0))
19.5b	(+ (* (- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) x) 1.0))

rewrite415.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

118.0ms	(* (- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0)) (- x 1.0))
172.0ms	(/ (+ (* (- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) x) 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) x) (- x 1.0)))
62.0ms	(* (* (/ (+ x 1.0) (cbrt 1.0)) x) (- x 1.0))
58.0ms	(+ (* (- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) x) 1.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

199.0ms	(* (- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0)) (- x 1.0))
693.0ms	(/ (+ (* (- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) x) 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) x) (- x 1.0)))
175.0ms	(* (* (/ (+ x 1.0) (cbrt 1.0)) x) (- x 1.0))
210.0ms	(+ (* (- (* (* (cbrt 1.0) (cbrt 1.0)) x) (* (/ (+ x 1.0) (cbrt 1.0)) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) (cbrt 1.0)) x) 1.0))

simplify147.0ms

Counts

138 → 138

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	881	3150
1	4856	2803
2	5001	2803
done	5001	2803

prune418.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (/ 1 (pow x 3))))
0.2b	(/ 1 (pow x 5))
0.2b	(/ 1 (pow x 7))
0.2b	(/ 1 (pow x 3))

rewrite276.0ms

Algorithm

rewrite-expression-head

Rules

88×	`*-un-lft-identity`
87×	`times-frac`
64×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`unpow-prod-down`
31×	`add-exp-log`
26×	`associate-/r*`
24×	`distribute-lft-out`
18×	`div-exp`
16×	`div-inv`
12×	`cube-prod` `sqr-pow`
10×	`add-cbrt-cube`
9×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*` `add-log-exp`
4×	`pow1` `cube-mult` `unpow3` `frac-add`
3×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `sum-log` `inv-pow`
2×	`flip3-+` `flip-+`
1×	`+-commutative` `associate-+r+`

Counts

4 → 208

Calls

4 calls:

240.0ms	(+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (/ 1 (pow x 3))))
9.0ms	(/ 1 (pow x 5))
9.0ms	(/ 1 (pow x 7))
10.0ms	(/ 1 (pow x 3))

series189.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (/ 1 (pow x 7)) (+ (/ 1 (pow x 5)) (/ 1 (pow x 3))))
50.0ms	(/ 1 (pow x 5))
54.0ms	(/ 1 (pow x 7))
37.0ms	(/ 1 (pow x 3))

simplify79.0ms

Counts

220 → 220

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	586	1177
1	3298	983
2	5001	983
done	5001	983

prune311.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes29.0ms

Accuracy

99.7% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 9.4b

bsearch108.0ms

Steps

Iters	Range		Point
9	7.055123656280252	892369.0132880388	109.89750468235896
10	-1.8070707071506563e+17	-0.15939393977811658	-111.02026224228146

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	21
1	42	21
done	42	21

end0.0ms

sample609.0ms

Algorithm

intervals

Results

184.0ms	1861×	body	640	valid
119.0ms	4112×	body	80	valid
78.0ms	598×	body	1280	valid
75.0ms	938×	body	320	valid
25.0ms	491×	body	160	valid