Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	189×	body	80	valid
2.0ms	24×	body	640	valid
2.0ms	27×	body	320	valid
1.0ms	11×	body	1280	valid
0.0ms	5×	body	160	valid

simplify6.6s

Counts

1 → 1

Iterations

Useful iterations: 4 (21.0ms)

Iter	Nodes	Cost
0	8	11
1	16	11
2	35	11
3	72	11
4	137	10
5	243	10
6	316	10
7	381	10
8	417	10
9	499	10
10	573	10
11	582	10
12	601	10
13	640	10
14	740	10
15	1002	10
16	1312	10
17	1800	10
18	2290	10
19	2369	10
20	2375	10
done	2375	10

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- x 1.0) (+ y 1.0))
16.2b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
20×	`times-frac`
13×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-sub` `div-exp` `clear-num` `flip--` `flip-+` `fma-udef` `div-inv`

Counts

2 → 58

Calls

2 calls:

13.0ms	(/ (- x 1.0) (+ y 1.0))
0.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series100.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(/ (- x 1.0) (+ y 1.0))
68.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify2.7s

Counts

64 → 64

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	114	834
1	277	799
2	678	745
3	1667	740
4	4688	736
done	5001	736

prune168.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ (- x 1.0) (+ y 1.0)))
0.5b	(cbrt (/ (- x 1.0) (+ y 1.0)))
0.5b	(cbrt (/ (- x 1.0) (+ y 1.0)))
16.0b	(fma (* (* (cbrt (/ (- x 1.0) (+ y 1.0))) (cbrt (/ (- x 1.0) (+ y 1.0)))) (cbrt (/ (- x 1.0) (+ y 1.0)))) y 1.0)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

88×	`*-un-lft-identity`
78×	`cbrt-prod`
60×	`times-frac`
58×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
15×	`distribute-lft-out`
12×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
1×	`fma-udef`

Counts

4 → 121

Calls

4 calls:

6.0ms	(cbrt (/ (- x 1.0) (+ y 1.0)))
6.0ms	(cbrt (/ (- x 1.0) (+ y 1.0)))
6.0ms	(cbrt (/ (- x 1.0) (+ y 1.0)))
0.0ms	(fma (* (* (cbrt (/ (- x 1.0) (+ y 1.0))) (cbrt (/ (- x 1.0) (+ y 1.0)))) (cbrt (/ (- x 1.0) (+ y 1.0)))) y 1.0)

series386.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(cbrt (/ (- x 1.0) (+ y 1.0)))
103.0ms	(cbrt (/ (- x 1.0) (+ y 1.0)))
100.0ms	(cbrt (/ (- x 1.0) (+ y 1.0)))
84.0ms	(fma (* (* (cbrt (/ (- x 1.0) (+ y 1.0))) (cbrt (/ (- x 1.0) (+ y 1.0)))) (cbrt (/ (- x 1.0) (+ y 1.0)))) y 1.0)

simplify1.9s

Counts

133 → 133

Iterations

Useful iterations: 4 (895.0ms)

Iter	Nodes	Cost
0	156	2618
1	327	2488
2	674	2184
3	1516	2067
4	4371	1989
done	5000	1989

prune395.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x 1.0) (+ y 1.0))
0.1b	(* (/ (- x 1.0) (+ y 1.0)) y)
4.4b	(+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
41×	`times-frac`
26×	`associate-l`
25×	`add-cube-cbrt`
11×	`distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `associate-/l*` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`expm1-log1p-u` `flip3-+` `associate-r` `flip-+` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `flip3--` `fma-def` `frac-2neg` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative` `flip--`

Counts

3 → 109

Calls

3 calls:

13.0ms	(/ (- x 1.0) (+ y 1.0))
25.0ms	(* (/ (- x 1.0) (+ y 1.0)) y)
9.0ms	(+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0)

series155.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(/ (- x 1.0) (+ y 1.0))
51.0ms	(* (/ (- x 1.0) (+ y 1.0)) y)
72.0ms	(+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0)

simplify3.0s

Counts

118 → 118

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	172	1520
1	460	1433
2	1300	1340
3	4433	1328
done	5000	1327

prune254.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y y) (- (* 1.0 1.0) (* y 1.0)))
1.8b	(/ (- x 1.0) (+ (pow y 3) (pow 1.0 3)))
16.2b	(fma (* (/ (- x 1.0) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))) y 1.0)
19.0b	(* (/ (- x 1.0) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

184×	`*-un-lft-identity`
91×	`times-frac`
79×	`add-sqr-sqrt`
55×	`distribute-lft-out`
51×	`associate-l`
44×	`unpow-prod-down` `cube-prod`
36×	`add-cube-cbrt`
19×	`distribute-lft-out--` `difference-of-squares`
11×	`add-exp-log` `sum-cubes` `add-cbrt-cube`
9×	`associate-/r*` `add-log-exp`
6×	`pow1`
5×	`flip3-+` `flip-+` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`associate-+r+` `associate-r`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `sum-log` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `associate-+r-` `sub-neg` `flip3--` `fma-def` `frac-2neg` `distribute-lft-in` `diff-log` `div-sub` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `flip--` `fma-udef`

Counts

4 → 185

Calls

4 calls:

8.0ms	(+ (* y y) (- (* 1.0 1.0) (* y 1.0)))
34.0ms	(/ (- x 1.0) (+ (pow y 3) (pow 1.0 3)))
0.0ms	(fma (* (/ (- x 1.0) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))) y 1.0)
105.0ms	(* (/ (- x 1.0) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (* y y) (- (* 1.0 1.0) (* y 1.0)))
71.0ms	(/ (- x 1.0) (+ (pow y 3) (pow 1.0 3)))
135.0ms	(fma (* (/ (- x 1.0) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))) y 1.0)
88.0ms	(* (/ (- x 1.0) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

simplify1.2s

Counts

197 → 197

Iterations

Useful iterations: 2 (527.0ms)

Iter	Nodes	Cost
0	228	4361
1	753	3795
2	2880	3523
done	5001	3523

prune559.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.2b

regimes93.0ms

Accuracy

99.2% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 14.3b

bsearch112.0ms

Steps

Iters	Range		Point
9	4368.076441928604	211806068951.26135	115382551.39706199
9	-1.7466667409204087e+24	-6567036909727156.0	-6690123426642433.0

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	27	54
1	36	45
done	36	45

end0.0ms

sample453.0ms

Algorithm

intervals

Results

153.0ms	6102×	body	80	valid
63.0ms	706×	body	640	valid
49.0ms	363×	body	1280	valid
39.0ms	512×	body	320	valid
14.0ms	317×	body	160	valid