Details

sample49.0ms

Algorithm

intervals

Results

19.0ms	188×	body	80	valid
6.0ms	27×	body	640	valid
4.0ms	16×	body	1280	valid
2.0ms	15×	body	320	valid
1.0ms	10×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: 4 (56.0ms)

Iter	Nodes	Cost
0	8	11
1	16	11
2	35	11
3	76	11
4	161	10
5	466	10
6	1868	10
done	5000	10

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- x 1.0) (+ y 1.0))
16.0b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite38.0ms

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:

35.0ms	(/ (- x 1.0) (+ y 1.0))
1.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series144.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- x 1.0) (+ y 1.0))
97.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify957.0ms

Counts

64 → 64

Iterations

Useful iterations: done (955.0ms)

Iter	Nodes	Cost
0	114	834
1	282	799
2	1133	747
done	5002	743

prune213.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ y 1.0) (- x 1.0))
0.1b	(/ 1 (/ (+ y 1.0) (- x 1.0)))
16.0b	(fma (/ 1 (/ (+ y 1.0) (- x 1.0))) y 1.0)

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

178×	`times-frac`
175×	`*-un-lft-identity`
123×	`add-sqr-sqrt`
81×	`add-cube-cbrt`
31×	`associate-/r*`
26×	`distribute-lft-out`
21×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`div-inv`
5×	`flip3--` `flip--`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `flip3-+` `flip-+` `fma-udef` `inv-pow`

Counts

3 → 187

Calls

3 calls:

46.0ms	(/ (+ y 1.0) (- x 1.0))
36.0ms	(/ 1 (/ (+ y 1.0) (- x 1.0)))
0.0ms	(fma (/ 1 (/ (+ y 1.0) (- x 1.0))) y 1.0)

series160.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (+ y 1.0) (- x 1.0))
47.0ms	(/ 1 (/ (+ y 1.0) (- x 1.0)))
67.0ms	(fma (/ 1 (/ (+ y 1.0) (- x 1.0))) y 1.0)

simplify2.5s

Counts

196 → 196

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	255	3277
1	654	2809
2	4076	2678
done	5000	2666

prune420.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (- x 1.0) (/ 1 (+ y 1.0)))
16.0b	(fma (* (- x 1.0) (/ 1 (+ y 1.0))) y 1.0)

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`associate-r`
14×	`times-frac`
11×	`add-exp-log` `add-cube-cbrt`
7×	`add-cbrt-cube`
5×	`associate-l`
4×	`pow1` `prod-exp`
3×	`distribute-lft-out` `unswap-sqr`
2×	`expm1-log1p-u` `frac-times` `flip3--` `div-exp` `associate-*l/` `associate-/r/` `flip--` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `flip-+` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 59

Calls

2 calls:

83.0ms	(* (- x 1.0) (/ 1 (+ y 1.0)))
1.0ms	(fma (* (- x 1.0) (/ 1 (+ y 1.0))) y 1.0)

series152.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(* (- x 1.0) (/ 1 (+ y 1.0)))
108.0ms	(fma (* (- x 1.0) (/ 1 (+ y 1.0))) y 1.0)

simplify5.2s

Counts

65 → 65

Iterations

Useful iterations: done (5.2s)

Iter	Nodes	Cost
0	137	866
1	374	785
2	2643	622
done	5000	616

prune199.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x 1.0) (+ y 1.0))
1.3b	(exp (log (fma y (/ (- x 1.0) (+ y 1.0)) 1.0)))
1.7b	(log (fma y (/ (- x 1.0) (+ y 1.0)) 1.0))
16.0b	(fma y (/ (- x 1.0) (+ y 1.0)) 1.0)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
20×	`times-frac`
18×	`add-cube-cbrt`
7×	`add-exp-log`
6×	`pow1` `log-prod` `add-cbrt-cube` `distribute-lft-out`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `exp-prod` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`exp-sum`
2×	`associate-/r/` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-sub` `div-exp` `rem-log-exp` `clear-num` `flip--` `flip-+` `fma-udef` `div-inv` `rem-exp-log`

Counts

4 → 89

Calls

4 calls:

43.0ms	(/ (- x 1.0) (+ y 1.0))
4.0ms	(exp (log (fma y (/ (- x 1.0) (+ y 1.0)) 1.0)))
2.0ms	(log (fma y (/ (- x 1.0) (+ y 1.0)) 1.0))
1.0ms	(fma y (/ (- x 1.0) (+ y 1.0)) 1.0)

series264.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ (- x 1.0) (+ y 1.0))
59.0ms	(exp (log (fma y (/ (- x 1.0) (+ y 1.0)) 1.0)))
87.0ms	(log (fma y (/ (- x 1.0) (+ y 1.0)) 1.0))
68.0ms	(fma y (/ (- x 1.0) (+ y 1.0)) 1.0)

simplify1.2s

Counts

101 → 101

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	160	1436
1	368	1355
2	1325	1214
done	5001	1210

prune454.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

regimes150.0ms

Accuracy

100% (0.0b remaining)

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

bsearch125.0ms

Steps

Iters	Range		Point
9	6123.270275452558	293663098603.6372	457167308.28551394
8	-517858925.4294923	-28361.394281441724	-127831090.9671721

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	19	40
1	26	31
done	26	31

end0.0ms

sample1.6s

Algorithm

intervals

Results

863.0ms	6110×	body	80	valid
130.0ms	730×	body	640	valid
110.0ms	339×	body	1280	valid
73.0ms	504×	body	320	valid
70.0ms	317×	body	160	valid