Details

sample15.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	11
1	11	11
2	12	11
done	12	11

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.0b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
35×	`times-frac`
30×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `distribute-lft-out--`
5×	`add-log-exp`
4×	`associate-/r/` `difference-of-squares`
3×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`
1×	`+-commutative` `flip3--` `frac-add` `sum-log` `flip--`

Counts

3 → 87

Calls

3 calls:

28.0ms	(+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))
6.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ x (+ x 1.0))

series13.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))
3.0ms	(/ 1.0 (- x 1.0))
3.0ms	(/ x (+ x 1.0))

simplify824.0ms

Counts

96 → 96

Iterations

Useful iterations: done (821.0ms)

Iter	Nodes	Cost
0	169	1135
1	393	1062
2	1124	996
3	2783	996
done	5001	995

prune135.0ms

Filtered

70 candidates to 96 candidates (-37.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	3	97

Merged error: 0b

Counts

97 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(/ x (+ x 1.0))
0.2b	(/ 1.0 (- (* x x) (* 1.0 1.0)))
14.5b	(* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 128

Calls

4 calls:

16.0ms	(+ (* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0)) (/ x (+ x 1.0)))
5.0ms	(/ x (+ x 1.0))
6.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
12.0ms	(* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0))

series21.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0)) (/ x (+ x 1.0)))
3.0ms	(/ x (+ x 1.0))
4.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
4.0ms	(* (/ 1.0 (- (* x x) (* 1.0 1.0))) (+ x 1.0))

simplify731.0ms

Counts

140 → 140

Iterations

Useful iterations: 2 (257.0ms)

Iter	Nodes	Cost
0	251	2406
1	788	2290
2	3147	2112
done	5001	2112

prune231.0ms

Filtered

113 candidates to 140 candidates (-23.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	140	3	143

Merged error: 0b

Counts

143 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(cbrt (pow (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))) 3))
0.0b	(/ x (+ x 1.0))
0.0b	(pow (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))) 3)

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

133×	`*-un-lft-identity`
59×	`times-frac`
37×	`add-sqr-sqrt`
32×	`distribute-lft-out`
29×	`add-cube-cbrt`
22×	`cbrt-prod`
16×	`unpow-prod-down` `cube-prod`
12×	`distribute-lft-out--`
9×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
6×	`cube-div` `associate-/l*`
5×	`pow1`
4×	`associate-/r/` `add-log-exp` `difference-of-squares`
3×	`pow-unpow` `cbrt-div` `flip3-+` `flip-+`
2×	`cbrt-undiv` `cube-mult` `frac-2neg` `unpow3` `div-exp` `frac-add` `clear-num` `div-inv` `sqr-pow`
1×	`pow-to-exp` `flip3--` `pow-pow` `pow1/3` `pow-exp` `flip--` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 140

Calls

4 calls:

6.0ms	(/ 1.0 (- x 1.0))
30.0ms	(cbrt (pow (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))) 3))
6.0ms	(/ x (+ x 1.0))
27.0ms	(pow (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))) 3)

series22.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ 1.0 (- x 1.0))
9.0ms	(cbrt (pow (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))) 3))
3.0ms	(/ x (+ x 1.0))
8.0ms	(pow (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))) 3)

simplify466.0ms

Counts

152 → 152

Iterations

Useful iterations: 2 (153.0ms)

Iter	Nodes	Cost
0	237	2491
1	566	2126
2	1799	1956
done	5001	1956

prune205.0ms

Filtered

92 candidates to 152 candidates (-65.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	152	3	155

Merged error: 0b

Counts

155 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

277×	`*-un-lft-identity`
116×	`times-frac`
78×	`distribute-lft-out`
64×	`cbrt-prod`
47×	`add-sqr-sqrt`
39×	`add-cube-cbrt`
25×	`swap-sqr`
24×	`cbrt-div`
20×	`distribute-lft-out--`
12×	`add-exp-log` `associate-/r*`
11×	`pow1` `flip3-+` `associate-r` `associate-l` `flip-+`
10×	`add-cbrt-cube`
9×	`frac-times` `associate-/l*`
8×	`frac-add`
6×	`pow1/3` `associate-/r/`
4×	`add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `frac-2neg` `associate-r/` `div-exp` `associate-l/` `clear-num` `div-inv`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 183

Calls

4 calls:

59.0ms	(* (cbrt (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))) (cbrt (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))))
6.0ms	(/ x (+ x 1.0))
7.0ms	(/ x (+ x 1.0))
6.0ms	(/ x (+ x 1.0))

series28.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (cbrt (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))) (cbrt (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))))
3.0ms	(/ x (+ x 1.0))
3.0ms	(/ x (+ x 1.0))
3.0ms	(/ x (+ x 1.0))

simplify739.0ms

Counts

195 → 195

Iterations

Useful iterations: 3 (328.0ms)

Iter	Nodes	Cost
0	194	4101
1	418	3673
2	1195	3514
3	3335	3069
done	5000	3069

prune417.0ms

Filtered

116 candidates to 195 candidates (-68.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	195	3	198

Merged error: 0b

Counts

198 → 3

regimes82.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	13	19
done	13	19

end0.0ms

sample391.0ms

Algorithm

intervals

Results

251.0ms

8000×

body

valid

Details

sample15.0ms

simplify4.0ms

prune2.0ms

localize6.0ms

rewrite42.0ms

series13.0ms

simplify824.0ms

prune135.0ms

localize12.0ms

rewrite44.0ms

series21.0ms

simplify731.0ms

prune231.0ms

localize10.0ms

rewrite74.0ms

series22.0ms

simplify466.0ms

prune205.0ms

localize11.0ms

rewrite89.0ms

series28.0ms

simplify739.0ms

prune417.0ms

regimes82.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample391.0ms

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