Details

sample27.0ms

Algorithm

intervals

Results

7.0ms	49×	body	1280	valid
5.0ms	49×	body	640	valid
4.0ms	119×	body	80	valid
2.0ms	26×	body	320	valid
1.0ms	13×	body	160	valid

simplify154.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	12	13
2	16	13
3	19	13
4	21	13
5	27	13
6	39	13
7	58	13
8	77	13
9	99	13
10	113	13
11	119	13
12	123	13
done	123	13

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.9b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

12.0ms	(/ x (+ x 1.0))
26.0ms	(/ (+ x 1.0) (- x 1.0))
168.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series237.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ x (+ x 1.0))
51.0ms	(/ (+ x 1.0) (- x 1.0))
147.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify3.4s

Counts

605 → 605

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	523	34216
1	1199	30851
2	2823	22735
done	5000	16848

prune646.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 (* x x)) (/ 3.0 x))
0.3b	(/ 1.0 (* x x))
0.4b	(/ 3.0 (pow x 3))
7.0b	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite365.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
42×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-/r*`
12×	`unpow-prod-down` `cube-prod`
11×	`fma-def` `add-cbrt-cube` `add-log-exp`
6×	`associate-/l*`
5×	`div-exp` `frac-add` `distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `sum-log` `log1p-expm1-u` `sqr-pow`
3×	`cbrt-undiv` `flip3-+` `flip-+` `div-inv`
2×	`+-commutative` `frac-2neg` `clear-num`
1×	`pow-to-exp` `associate-+l+` `pow-exp` `prod-exp` `cbrt-unprod`

Counts

4 → 136

Calls

4 calls:

57.0ms	(+ (/ 1.0 (* x x)) (/ 3.0 x))
9.0ms	(/ 1.0 (* x x))
9.0ms	(/ 3.0 (pow x 3))
285.0ms	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series205.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (/ 1.0 (* x x)) (/ 3.0 x))
37.0ms	(/ 1.0 (* x x))
49.0ms	(/ 3.0 (pow x 3))
31.0ms	(+ (+ (/ 1.0 (* x x)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify1.1s

Counts

148 → 148

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	202	1801
1	455	1547
2	1633	1460
done	5001	1457

prune373.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.0b	(fma (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)) (/ x (- x 1.0)))
0.0b	(pow (/ x (+ x 1.0)) 3)
3.9b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite886.0ms

Algorithm

rewrite-expression-head

Rules

4381×	`*-un-lft-identity`
3248×	`times-frac`
2699×	`add-sqr-sqrt`
2436×	`prod-diff`
2258×	`unpow-prod-down` `cube-prod`
1927×	`add-cube-cbrt`
822×	`distribute-lft-out`
412×	`associate-/r/`
397×	`distribute-lft-out--`
380×	`difference-of-squares`
206×	`div-inv`
120×	`flip3-+` `flip-+`
115×	`sqr-pow`
103×	`cube-mult` `unpow3`
87×	`flip3--` `flip--`
42×	`fma-neg`
10×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `pow-unpow` `add-log-exp`
4×	`cube-div` `expm1-log1p-u` `pow-exp` `log1p-expm1-u` `rem-cube-cbrt`
2×	`cbrt-undiv` `pow-to-exp` `pow-pow` `div-exp`
1×	`difference-cubes` `sub-neg` `diff-log` `frac-sub` `fma-udef`

Counts

4 → 2709

Calls

4 calls:

23.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.0ms	(fma (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)) (/ x (- x 1.0)))
15.0ms	(pow (/ x (+ x 1.0)) 3)
470.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series796.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
208.0ms	(fma (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)) (/ x (- x 1.0)))
85.0ms	(pow (/ x (+ x 1.0)) 3)
415.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify2.4s

Counts

2721 → 2721

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	898	213446
1	2127	176057
done	5000	130726

prune2.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
5.9b	(/ x (+ (pow x 3) (pow 1.0 3)))
33.2b	(fma (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (/ (+ x 1.0) (- x 1.0))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

91×	`*-un-lft-identity`
47×	`times-frac`
39×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
26×	`distribute-lft-out`
16×	`unpow-prod-down` `cube-prod`
14×	`associate-/r*`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`pow1` `expm1-log1p-u` `associate-/r/` `sum-cubes` `log1p-expm1-u`
3×	`associate-+r+` `flip3-+` `flip-+`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv` `associate-/l/`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3--` `fma-def` `diff-log` `prod-diff` `flip--` `fma-udef`

Counts

4 → 131

Calls

4 calls:

27.0ms	(/ (+ x 1.0) (- x 1.0))
32.0ms	(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
76.0ms	(/ x (+ (pow x 3) (pow 1.0 3)))
0.0ms	(fma (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (/ (+ x 1.0) (- x 1.0))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (+ x 1.0) (- x 1.0))
29.0ms	(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
145.0ms	(/ x (+ (pow x 3) (pow 1.0 3)))
240.0ms	(fma (/ x (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (/ (+ x 1.0) (- x 1.0))))

simplify1.6s

Counts

143 → 143

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	232	2271
1	551	2008
2	1652	1847
done	5000	1832

prune491.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes42.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 32.0b

bsearch174.0ms

Steps

Iters	Range		Point
10	8.937283511995443e-05	28405617999702.24	12015.494489501321
9	-115102859795.89769	-7465.585501010854	-10364.722782930596

simplify15.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	47	143
1	63	128
2	70	128
3	73	128
done	73	128

end0.0ms

sample1.3s

Algorithm

intervals

Results

478.0ms	1685×	body	1280	valid
288.0ms	4134×	body	80	valid
276.0ms	1271×	body	640	valid
72.0ms	611×	body	320	valid
27.0ms	299×	body	160	valid