Details

sample25.0ms

Algorithm

intervals

Results

7.0ms	206×	body	80	valid
3.0ms	24×	body	640	valid
2.0ms	14×	body	320	valid
2.0ms	9×	body	1280	valid
0.0ms	3×	body	160	valid

simplify11.1s

Counts

1 → 1

Iterations

Useful iterations: 4 (65.0ms)

Iter	Nodes	Cost
0	8	11
1	16	11
2	35	11
3	76	11
4	131	10
5	242	10
6	309	10
7	374	10
8	424	10
9	513	10
10	582	10
11	591	10
12	610	10
13	648	10
14	777	10
15	915	10
16	1233	10
17	1689	10
18	2270	10
19	2436	10
20	2442	10
done	2442	10

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- x 1.0) (+ y 1.0))
11.8b	(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)

series139.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ (- x 1.0) (+ y 1.0))
99.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify2.3s

Counts

64 → 64

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	114	834
1	277	799
2	718	745
3	1747	739
done	5000	737

prune174.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 1 expressions with local error:

0.1b	(* (/ 1.0 y) (- 1 x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff`
13×	`associate-l`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`times-frac`
6×	`add-exp-log` `associate-r` `add-cbrt-cube`
3×	`pow1`
2×	`frac-times` `sub-neg` `flip3--` `associate-*r/` `prod-exp` `flip--` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `log1p-expm1-u` `div-inv` `distribute-lft-out--` `add-log-exp`

Counts

1 → 63

Calls

1 calls:

45.0ms

(* (/ 1.0 y) (- 1 x))

series55.0ms

Counts

1 → 3

Calls

1 calls:

55.0ms

(* (/ 1.0 y) (- 1 x))

simplify3.9s

Counts

66 → 66

Iterations

Useful iterations: 3 (2.2s)

Iter	Nodes	Cost
0	148	1063
1	364	794
2	1029	684
3	4153	662
done	5000	662

prune166.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x 1.0) (+ y 1.0))
0.0b	(exp (fma (/ (- x 1.0) (+ y 1.0)) y 1.0))
4.0b	(log (exp (fma (/ (- x 1.0) (+ y 1.0)) y 1.0)))
11.8b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

39.0ms	(/ (- x 1.0) (+ y 1.0))
2.0ms	(exp (fma (/ (- x 1.0) (+ y 1.0)) y 1.0))
3.0ms	(log (exp (fma (/ (- x 1.0) (+ y 1.0)) y 1.0)))
0.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series346.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (- x 1.0) (+ y 1.0))
79.0ms	(exp (fma (/ (- x 1.0) (+ y 1.0)) y 1.0))
104.0ms	(log (exp (fma (/ (- x 1.0) (+ y 1.0)) y 1.0)))
114.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify2.8s

Counts

102 → 102

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	169	1465
1	387	1382
2	990	1267
3	2514	1254
done	5000	1252

prune438.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (fma (/ (- x 1.0) (+ y 1.0)) y 1.0))
0.5b	(log1p (exp (fma (/ (- x 1.0) (+ y 1.0)) y 1.0)))
11.8b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)
12.8b	(log (expm1 (log1p (exp (fma (/ (- x 1.0) (+ y 1.0)) y 1.0)))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `expm1-log1p-u` `add-log-exp`
4×	`add-cbrt-cube` `log1p-expm1-u`
3×	`log-prod` `exp-prod`
2×	`fma-udef`
1×	`log1p-udef` `log1p-expm1` `rem-log-exp` `exp-sum` `log-pow` `rem-exp-log`

Counts

4 → 49

Calls

4 calls:

4.0ms	(exp (fma (/ (- x 1.0) (+ y 1.0)) y 1.0))
1.0ms	(log1p (exp (fma (/ (- x 1.0) (+ y 1.0)) y 1.0)))
1.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)
3.0ms	(log (expm1 (log1p (exp (fma (/ (- x 1.0) (+ y 1.0)) y 1.0)))))

series569.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(exp (fma (/ (- x 1.0) (+ y 1.0)) y 1.0))
225.0ms	(log1p (exp (fma (/ (- x 1.0) (+ y 1.0)) y 1.0)))
104.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)
130.0ms	(log (expm1 (log1p (exp (fma (/ (- x 1.0) (+ y 1.0)) y 1.0)))))

simplify3.6s

Counts

61 → 61

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	142	1270
1	365	1168
2	1112	1043
3	4703	1013
done	5000	1013

prune364.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes96.0ms

Accuracy

97.3% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 14.9b

bsearch103.0ms

Steps

Iters	Range		Point
9	3495.1882749471233	4103444128.4880795	303708.4300355311
5	-1.6030899885608685e+28	-7.296408209838224e+27	-7.385014489371157e+27

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	24	62
1	32	41
done	32	41

end0.0ms

sample1.2s

Algorithm

intervals

Results

404.0ms	6039×	body	80	valid
209.0ms	383×	body	1280	valid
200.0ms	709×	body	640	valid
95.0ms	567×	body	320	valid
84.0ms	302×	body	160	valid