Details

sample33.0ms

Algorithm

intervals

Results

9.0ms	51×	body	1280	valid
6.0ms	43×	body	640	valid
5.0ms	134×	body	80	valid
2.0ms	21×	body	320	valid
0.0ms	7×	body	160	valid

simplify2.4s

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.8b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
1.7b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite268.0ms

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:

20.0ms	(/ x (+ x 1.0))
25.0ms	(/ (+ x 1.0) (- x 1.0))
158.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series290.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(/ x (+ x 1.0))
62.0ms	(/ (+ x 1.0) (- x 1.0))
166.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify2.6s

Counts

605 → 605

Iterations

Useful iterations: 2 (937.0ms)

Iter	Nodes	Cost
0	523	34216
1	1254	30941
2	4643	23743
done	5000	23743

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- x 1.0))
0.2b	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
0.2b	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
19.4b	(- (* x (/ 1 (+ x 1.0))) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

160×	`times-frac`
148×	`*-un-lft-identity`
141×	`cbrt-prod`
136×	`add-sqr-sqrt`
134×	`prod-diff`
124×	`cbrt-div`
70×	`add-cube-cbrt`
66×	`associate-/r/`
63×	`flip3--` `flip--`
40×	`frac-times`
29×	`distribute-lft-out--`
25×	`difference-of-squares`
21×	`associate-*r/`
20×	`swap-sqr` `associate-*l/`
18×	`pow1`
16×	`associate-r` `associate-l`
13×	`pow1/3`
9×	`div-inv`
8×	`add-exp-log` `distribute-lft-out` `unswap-sqr`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow-prod-down` `pow-sqr` `pow-prod-up` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow2` `pow-plus` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod`
1×	`sub-neg` `fma-neg` `diff-log` `un-div-inv`

Counts

4 → 284

Calls

4 calls:

4.0ms	(cbrt (- x 1.0))
45.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
40.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
132.0ms	(- (* x (/ 1 (+ x 1.0))) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

series696.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(cbrt (- x 1.0))
180.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
184.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
189.0ms	(- (* x (/ 1 (+ x 1.0))) (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0))))

simplify1.4s

Counts

296 → 296

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	917	19643
1	2738	18362
done	5000	16196

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- x 1.0))
0.2b	(cbrt (- x 1.0))
0.2b	(cbrt (- x 1.0))
0.2b	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

43×	`cbrt-prod`
37×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
9×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 109

Calls

4 calls:

8.0ms	(cbrt (- x 1.0))
6.0ms	(cbrt (- x 1.0))
5.0ms	(cbrt (- x 1.0))
64.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(cbrt (- x 1.0))
103.0ms	(cbrt (- x 1.0))
124.0ms	(cbrt (- x 1.0))
164.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))

simplify889.0ms

Counts

121 → 121

Iterations

Useful iterations: done (886.0ms)

Iter	Nodes	Cost
0	171	1613
1	413	1452
2	1491	1384
done	5000	1339

prune573.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
0.5b	(/ 3.0 (pow x 3))
0.9b	(/ (- 1.0) (* x x))
8.2b	(- (/ (- 1.0) (* x x)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

rewrite365.0ms

Algorithm

rewrite-expression-head

Rules

406×	`times-frac`
387×	`*-un-lft-identity`
182×	`prod-diff`
176×	`add-sqr-sqrt`
172×	`add-cube-cbrt`
79×	`unpow3`
76×	`distribute-lft-out`
60×	`distribute-rgt-out`
48×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
47×	`div-inv`
16×	`neg-mul-1`
15×	`distribute-rgt1-in`
14×	`add-exp-log` `fma-neg`
13×	`fma-def` `associate-/r` `associate-/l`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube` `add-log-exp`
5×	`div-exp`
4×	`pow1` `expm1-log1p-u` `cube-mult` `log1p-expm1-u` `sqr-pow`
3×	`cbrt-undiv` `frac-sub`
2×	`neg-sub0` `frac-2neg` `flip3-+` `diff-log` `div-sub` `frac-add` `clear-num` `sum-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `pow-to-exp` `sub-neg` `flip3--` `distribute-frac-neg` `pow-exp` `prod-exp` `flip--` `cbrt-unprod` `associate--r+`

Counts

4 → 363

Calls

4 calls:

63.0ms	(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
14.0ms	(/ 3.0 (pow x 3))
17.0ms	(/ (- 1.0) (* x x))
241.0ms	(- (/ (- 1.0) (* x x)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

series232.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
55.0ms	(/ 3.0 (pow x 3))
28.0ms	(/ (- 1.0) (* x x))
35.0ms	(- (/ (- 1.0) (* x x)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

simplify656.0ms

Counts

375 → 375

Iterations

Useful iterations: done (631.0ms)

Iter	Nodes	Cost
0	447	13415
1	1161	11149
done	5000	9840

prune1.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes59.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.5b

bsearch191.0ms

Steps

Iters	Range		Point
11	0.022891638200552334	5.118117448855024e+31	6174.270166505639
10	-911936.9907706906	-4.3470241882695893e-07	-11192.062083074488

simplify9.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	34	97
1	49	82
2	52	82
done	52	82

end0.0ms

sample1.8s

Algorithm

intervals

Results

840.0ms	1707×	body	1280	valid
316.0ms	4136×	body	80	valid
287.0ms	1227×	body	640	valid
77.0ms	613×	body	320	valid
31.0ms	317×	body	160	valid