Details

sample24.0ms

Algorithm

intervals

Results

8.0ms	52×	body	640	valid
4.0ms	145×	body	80	valid
2.0ms	30×	body	320	valid
2.0ms	15×	body	1280	valid
1.0ms	14×	body	160	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 7.4b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.2b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite144.0ms

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:

5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (+ x 1.0))
25.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
56.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1.0 (- x 1.0))
27.0ms	(/ 1.0 (+ x 1.0))
41.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
214.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify150.0ms

Algorithm

egg-herbie

Counts

630 → 630

Iterations

Useful iterations: 2 (72.0ms)

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

prune1.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3)))
0.0b	(/ 1 (pow x 7))
0.1b	(/ 1 (pow x 5))
0.4b	(/ 2.0 (pow x 3))

rewrite22.0ms

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:

1.0ms	(fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3)))
5.0ms	(/ 1 (pow x 7))
5.0ms	(/ 1 (pow x 5))
6.0ms	(/ 2.0 (pow x 3))

series260.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3)))
57.0ms	(/ 1 (pow x 7))
42.0ms	(/ 1 (pow x 5))
41.0ms	(/ 2.0 (pow x 3))

simplify54.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	450	904
1	2278	777
2	5001	777

prune455.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (pow x 7))
0.1b	(/ (/ 2.0 (* x x)) x)
0.1b	(/ 1 (pow x 5))
0.7b	(/ 2.0 (* x x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
54×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`add-exp-log`
24×	`unpow-prod-down`
22×	`add-cbrt-cube`
19×	`div-exp`
18×	`associate-/r*`
16×	`associate-/l*`
9×	`cbrt-undiv`
8×	`div-inv` `sqr-pow`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`pow-flip` `prod-exp` `cbrt-unprod` `inv-pow`
1×	`associate-/l/`

Counts

4 → 183

Calls

4 calls:

8.0ms	(/ 1 (pow x 7))
6.0ms	(/ (/ 2.0 (* x x)) x)
5.0ms	(/ 1 (pow x 5))
5.0ms	(/ 2.0 (* x x))

series160.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ 1 (pow x 7))
34.0ms	(/ (/ 2.0 (* x x)) x)
46.0ms	(/ 1 (pow x 5))
24.0ms	(/ 2.0 (* x x))

simplify51.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	511	914
1	2528	828
2	5001	768

prune392.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (pow x 5))
0.1b	(* (/ (sqrt 2.0) x) (/ (sqrt 2.0) (* x x)))
0.5b	(/ (sqrt 2.0) x)
0.9b	(/ (sqrt 2.0) (* x x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

81×	`times-frac`
79×	`add-sqr-sqrt`
55×	`add-cube-cbrt` `*-un-lft-identity`
41×	`add-exp-log`
36×	`sqrt-prod`
34×	`add-cbrt-cube`
22×	`associate-l`
16×	`div-exp`
15×	`associate-/l*`
12×	`unpow-prod-down`
11×	`cbrt-undiv` `associate-/r*`
10×	`associate-r`
9×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `rec-exp` `frac-2neg` `1-exp` `pow-exp` `clear-num`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 192

Calls

4 calls:

5.0ms	(/ 1 (pow x 5))
14.0ms	(* (/ (sqrt 2.0) x) (/ (sqrt 2.0) (* x x)))
4.0ms	(/ (sqrt 2.0) x)
6.0ms	(/ (sqrt 2.0) (* x x))

series227.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ 1 (pow x 5))
87.0ms	(* (/ (sqrt 2.0) x) (/ (sqrt 2.0) (* x x)))
51.0ms	(/ (sqrt 2.0) x)
47.0ms	(/ (sqrt 2.0) (* x x))

simplify72.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	536	1192
1	2890	1043
2	5001	962

prune518.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes56.0ms

Accuracy

98.9% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 9.9b

bsearch89.0ms

Steps

Iters	Range		Point
10	4.9177062248324165e-05	42925490.781275615	129.8241176321693
8	-1816.595590764893	-1.0806682141483241	-108.88679580976668

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	24
1	37	24

end0.0ms

sample598.0ms

Algorithm

intervals

Results

196.0ms	1860×	body	640	valid
118.0ms	4139×	body	80	valid
80.0ms	974×	body	320	valid
76.0ms	565×	body	1280	valid
26.0ms	466×	body	160	valid