Details

sample24.0ms

Algorithm

intervals

Results

7.0ms	66×	body	640	valid
4.0ms	130×	body	80	valid
3.0ms	32×	body	320	valid
2.0ms	16×	body	1280	valid
1.0ms	12×	body	160	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	7
1	31	7
2	43	7
3	57	7
4	73	7
5	92	7
6	126	7
7	158	7
8	207	7
9	209	7
10	209	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.2b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b	(/ 1.0 (- x 1.0))
1.5b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite471.0ms

Algorithm

rewrite-expression-head

Rules

725×	`*-un-lft-identity`
703×	`times-frac`
524×	`add-sqr-sqrt`
492×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
95×	`distribute-lft-out`
65×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
18×	`fma-neg`
17×	`distribute-lft-out--`
12×	`difference-of-squares`
11×	`add-log-exp`
10×	`fma-def`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub`
1×	`+-commutative` `associate-+l-`

Counts

4 → 618

Calls

4 calls:

12.0ms	(/ 1.0 (+ x 1.0))
76.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
11.0ms	(/ 1.0 (- x 1.0))
324.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ 1.0 (+ x 1.0))
38.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
24.0ms	(/ 1.0 (- x 1.0))
195.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify156.0ms

Algorithm

egg-herbie

Counts

630 → 630

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	1156	10955
1	3607	8288
2	5001	7670

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (/ 1.0 (- x 1.0)))
0.0b	(log1p (expm1 (/ 1.0 (- x 1.0))))
0.0b	(/ 1.0 (- x 1.0))
1.5b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (log1p (expm1 (/ 1.0 (- x 1.0)))))

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

347×	`*-un-lft-identity`
341×	`times-frac`
265×	`add-sqr-sqrt`
245×	`add-cube-cbrt`
236×	`associate-+l+`
234×	`prod-diff`
42×	`distribute-lft-out`
32×	`div-inv`
28×	`associate-/r/`
14×	`flip3-+` `flip-+`
12×	`add-log-exp`
10×	`fma-def`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-/r*` `log1p-expm1-u`
4×	`pow1` `expm1-log1p-u` `sum-log`
3×	`log1p-udef` `associate-/l*`
2×	`diff-log`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `sub-neg` `expm1-log1p` `flip3--` `frac-2neg` `log1p-expm1` `div-exp` `clear-num` `flip--` `expm1-udef`

Counts

4 → 326

Calls

4 calls:

0.0ms	(expm1 (/ 1.0 (- x 1.0)))
0.0ms	(log1p (expm1 (/ 1.0 (- x 1.0))))
11.0ms	(/ 1.0 (- x 1.0))
309.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (log1p (expm1 (/ 1.0 (- x 1.0)))))

series745.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(expm1 (/ 1.0 (- x 1.0)))
149.0ms	(log1p (expm1 (/ 1.0 (- x 1.0))))
46.0ms	(/ 1.0 (- x 1.0))
486.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (log1p (expm1 (/ 1.0 (- x 1.0)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

338 → 338

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	593	4402
1	2051	3413
2	5003	2518

prune967.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3))))
0.0b	(/ 1 (pow x 7))
0.0b	(/ 1 (pow x 5))
0.6b	(/ 2.0 (pow x 3))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
61×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`unpow-prod-down`
27×	`add-exp-log`
26×	`associate-/r*`
15×	`div-exp`
12×	`cube-prod` `sqr-pow`
10×	`add-cbrt-cube`
9×	`associate-/l*`
7×	`pow-to-exp` `pow-exp`
6×	`rec-exp` `1-exp`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv`
2×	`pow-flip` `inv-pow`
1×	`fma-udef`

Counts

4 → 187

Calls

4 calls:

0.0ms	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3))))
8.0ms	(/ 1 (pow x 7))
8.0ms	(/ 1 (pow x 5))
11.0ms	(/ 2.0 (pow x 3))

series191.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3))))
55.0ms	(/ 1 (pow x 7))
45.0ms	(/ 1 (pow x 5))
33.0ms	(/ 2.0 (pow x 3))

simplify53.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	460	949
1	2326	816
2	5001	816

prune395.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (pow x 7))
0.0b	(/ 1 (pow x 5))
0.1b	(* (/ 1 (* x x)) (/ 2.0 x))
0.4b	(/ 1 (* x x))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-exp-log`
64×	`times-frac`
60×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
47×	`add-cube-cbrt`
34×	`add-cbrt-cube`
31×	`div-exp`
24×	`unpow-prod-down`
23×	`prod-exp`
15×	`associate-/r*`
14×	`pow1`
13×	`associate-r`
12×	`rec-exp` `1-exp`
11×	`cbrt-undiv`
9×	`cbrt-unprod` `associate-/l*`
8×	`pow-flip` `sqr-pow`
7×	`associate-l`
6×	`pow-to-exp` `pow-exp` `unswap-sqr`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `inv-pow`
2×	`pow-prod-down`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 204

Calls

4 calls:

8.0ms	(/ 1 (pow x 7))
8.0ms	(/ 1 (pow x 5))
43.0ms	(* (/ 1 (* x x)) (/ 2.0 x))
11.0ms	(/ 1 (* x x))

series144.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ 1 (pow x 7))
44.0ms	(/ 1 (pow x 5))
32.0ms	(* (/ 1 (* x x)) (/ 2.0 x))
18.0ms	(/ 1 (* x x))

simplify79.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	649	986
1	3593	855
2	5001	762

prune383.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes47.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 9.5b

bsearch103.0ms

Steps

Iters	Range		Point
10	8.950540206577903e-05	66689094922.78456	107.91934125672991
10	-1500.694570789724	-6.177030851099824e-09	-112.31575512255452

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	19
1	39	19

end0.0ms

sample630.0ms

Algorithm

intervals

Results

209.0ms	1914×	body	640	valid
123.0ms	4184×	body	80	valid
80.0ms	949×	body	320	valid
72.0ms	529×	body	1280	valid
23.0ms	428×	body	160	valid