Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	45×	body	1280	valid
5.0ms	45×	body	640	valid
4.0ms	138×	body	80	valid
2.0ms	19×	body	320	valid
0.0ms	9×	body	160	valid

simplify2.2s

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	79	13
9	183	13
10	535	13
11	1706	13
12	3584	13
done	5000	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ 1.0 x) (- x 1.0))
0.0b	(/ x (+ x 1.0))
2.7b	(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

rewrite225.0ms

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:

28.0ms	(/ (+ 1.0 x) (- x 1.0))
12.0ms	(/ x (+ x 1.0))
126.0ms	(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

series239.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ (+ 1.0 x) (- x 1.0))
52.0ms	(/ x (+ x 1.0))
133.0ms	(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

simplify2.5s

Counts

605 → 605

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	536	34216
1	1303	30941
2	4759	23491
done	5000	23490

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(log1p (expm1 (/ (+ 1.0 x) (- x 1.0))))
0.5b	(expm1 (/ (+ 1.0 x) (- x 1.0)))
2.7b	(- (/ x (+ x 1.0)) (log1p (expm1 (/ (+ 1.0 x) (- x 1.0)))))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

97×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
16×	`distribute-lft-out`
10×	`associate-/r/`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+` `log1p-expm1-u` `div-inv`
4×	`pow1` `expm1-log1p-u` `associate-/r*`
3×	`associate-/l*`
2×	`log1p-udef` `diff-log` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `expm1-log1p` `flip3--` `frac-2neg` `log1p-expm1` `div-exp` `clear-num` `flip--` `distribute-lft-out--` `expm1-udef`

Counts

4 → 147

Calls

4 calls:

19.0ms	(/ x (+ x 1.0))
0.0ms	(log1p (expm1 (/ (+ 1.0 x) (- x 1.0))))
1.0ms	(expm1 (/ (+ 1.0 x) (- x 1.0)))
102.0ms	(- (/ x (+ x 1.0)) (log1p (expm1 (/ (+ 1.0 x) (- x 1.0)))))

series671.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ x (+ x 1.0))
198.0ms	(log1p (expm1 (/ (+ 1.0 x) (- x 1.0))))
98.0ms	(expm1 (/ (+ 1.0 x) (- x 1.0)))
315.0ms	(- (/ x (+ x 1.0)) (log1p (expm1 (/ (+ 1.0 x) (- x 1.0)))))

simplify1.7s

Counts

159 → 159

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	220	5730
1	516	3388
2	1979	2736
done	5000	2178

prune455.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))
0.0b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
2.7b	(- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))

rewrite683.0ms

Algorithm

rewrite-expression-head

Rules

2049×	`*-un-lft-identity`
1567×	`times-frac`
1304×	`add-sqr-sqrt`
1114×	`cbrt-prod`
1098×	`prod-diff`
947×	`add-cube-cbrt`
524×	`unpow-prod-down` `cube-prod`
390×	`distribute-lft-out`
206×	`associate-/r/`
174×	`difference-of-squares`
161×	`distribute-lft-out--`
103×	`div-inv`
63×	`flip3-+` `flip-+`
41×	`flip3--` `flip--`
22×	`sqr-pow`
20×	`cube-mult` `unpow3`
18×	`fma-neg`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`cube-div` `pow-unpow` `associate-/l*`
2×	`cbrt-undiv` `cbrt-div` `div-exp` `pow-exp` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `clear-num` `frac-sub` `rem-cbrt-cube`

Counts

4 → 1325

Calls

4 calls:

14.0ms	(/ x (+ x 1.0))
36.0ms	(cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))
38.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
351.0ms	(- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ x (+ x 1.0))
55.0ms	(cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3))
89.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
188.0ms	(- (/ x (+ x 1.0)) (cbrt (pow (/ (+ x 1.0) (- x 1.0)) 3)))

simplify1.2s

Counts

1337 → 1337

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	813	100406
1	2026	71299
done	5000	60563

prune1.9s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (+ x 1.0)) (- x 1.0))
0.1b	(* (/ (sqrt (+ x 1.0)) (- x 1.0)) (- (sqrt (+ x 1.0))))
5.7b	(/ x (+ (pow x 3) (pow 1.0 3)))
17.7b	(fma (/ x (+ (pow x 3) (pow 1.0 3))) (fma x x (* 1.0 (- 1.0 x))) (* (/ (sqrt (+ x 1.0)) (- x 1.0)) (- (sqrt (+ x 1.0)))))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

157×	`*-un-lft-identity`
99×	`add-sqr-sqrt` `times-frac`
61×	`add-cube-cbrt`
53×	`sqrt-prod`
41×	`associate-l`
33×	`distribute-lft-out`
18×	`associate-r`
16×	`unpow-prod-down` `cube-prod`
15×	`distribute-lft-out--` `difference-of-squares`
14×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/l*`
7×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
6×	`pow1` `sqrt-div` `associate-/r/`
4×	`expm1-log1p-u` `flip3-+` `sum-cubes` `flip-+` `log1p-expm1-u` `distribute-neg-frac` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `div-inv` `unswap-sqr`
2×	`frac-times` `flip3--` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `associate-/l/`
1×	`neg-mul-1` `pow-prod-down` `associate-l/` `-commutative` `distribute-rgt-neg-out` `fma-udef`

Counts

4 → 213

Calls

4 calls:

30.0ms	(/ (sqrt (+ x 1.0)) (- x 1.0))
123.0ms	(* (/ (sqrt (+ x 1.0)) (- x 1.0)) (- (sqrt (+ x 1.0))))
65.0ms	(/ x (+ (pow x 3) (pow 1.0 3)))
1.0ms	(fma (/ x (+ (pow x 3) (pow 1.0 3))) (fma x x (* 1.0 (- 1.0 x))) (* (/ (sqrt (+ x 1.0)) (- x 1.0)) (- (sqrt (+ x 1.0)))))

series497.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (sqrt (+ x 1.0)) (- x 1.0))
48.0ms	(* (/ (sqrt (+ x 1.0)) (- x 1.0)) (- (sqrt (+ x 1.0))))
142.0ms	(/ x (+ (pow x 3) (pow 1.0 3)))
167.0ms	(fma (/ x (+ (pow x 3) (pow 1.0 3))) (fma x x (* 1.0 (- 1.0 x))) (* (/ (sqrt (+ x 1.0)) (- x 1.0)) (- (sqrt (+ x 1.0)))))

simplify2.3s

Counts

225 → 225

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	323	3892
1	878	3623
2	4335	3400
done	5000	3387

prune1.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes51.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.6b

bsearch104.0ms

Steps

Iters	Range		Point
10	15.006088268796836	293663098603.6372	12089.166307002173
8	-28361.394281441724	-101.50163225226844	-13119.887251887727

simplify13.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	26	55
1	34	40
2	41	40
3	44	40
done	44	40

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.1s	1750×	body	1280	valid
212.0ms	1258×	body	640	valid
189.0ms	4055×	body	80	valid
78.0ms	613×	body	320	valid
28.0ms	324×	body	160	valid