Details

sample40.0ms

Algorithm

intervals

Results

12.0ms	54×	body	640	valid
7.0ms	131×	body	80	valid
6.0ms	21×	body	1280	valid
5.0ms	31×	body	320	valid
2.0ms	19×	body	160	valid

simplify18.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.2b

localize9.0ms

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))
2.4b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite342.0ms

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))
50.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
226.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series20.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ 1.0 (- x 1.0))
2.0ms	(/ 1.0 (+ x 1.0))
4.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
11.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify152.0ms

Algorithm

egg-herbie

Counts

630 → 630

Iterations

Useful iterations: 2 (73.0ms)

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

prune4.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

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)) (/ 2.0 x))
2.4b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (log1p (expm1 (/ 1.0 (- x 1.0)))))

rewrite310.0ms

Algorithm

rewrite-expression-head

Rules

664×	`times-frac`
662×	`*-un-lft-identity`
497×	`add-sqr-sqrt`
473×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
85×	`distribute-lft-out`
63×	`div-inv`
54×	`associate-/r/`
28×	`flip3-+` `flip-+`
18×	`fma-neg`
14×	`add-log-exp`
10×	`fma-def`
8×	`difference-of-squares`
7×	`distribute-lft-out--`
5×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sum-log` `add-cbrt-cube`
3×	`log1p-udef` `diff-log`
2×	`sub-neg`
1×	`+-commutative` `associate-+l-` `expm1-log1p` `flip3--` `log1p-expm1` `frac-sub` `flip--` `expm1-udef`

Counts

4 → 561

Calls

4 calls:

0.0ms	(expm1 (/ 1.0 (- x 1.0)))
0.0ms	(log1p (expm1 (/ 1.0 (- x 1.0))))
50.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
210.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (log1p (expm1 (/ 1.0 (- x 1.0)))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(expm1 (/ 1.0 (- x 1.0)))
10.0ms	(log1p (expm1 (/ 1.0 (- x 1.0))))
4.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
25.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (log1p (expm1 (/ 1.0 (- x 1.0)))))

simplify144.0ms

Algorithm

egg-herbie

Counts

573 → 573

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	1075	10673
1	3105	7997
2	5001	7376

prune4.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3)))
0.2b	(/ 1 (pow x 7))
0.3b	(/ 1 (pow x 5))
0.5b	(/ 2.0 (pow x 3))

rewrite18.0ms

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 5)) (/ 2.0 (pow x 3)))
4.0ms	(/ 1 (pow x 7))
4.0ms	(/ 1 (pow x 5))
4.0ms	(/ 2.0 (pow x 3))

series16.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3)))
3.0ms	(/ 1 (pow x 7))
3.0ms	(/ 1 (pow x 5))
3.0ms	(/ 2.0 (pow x 3))

simplify50.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (12.0ms)

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

prune918.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (* x x)) (/ 2.0 x))
0.2b	(/ 1 (pow x 7))
0.3b	(/ 1 (pow x 5))
0.6b	(/ 1 (* x x))

rewrite40.0ms

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:

21.0ms	(* (/ 1 (* x x)) (/ 2.0 x))
4.0ms	(/ 1 (pow x 7))
4.0ms	(/ 1 (pow x 5))
5.0ms	(/ 1 (* x x))

series12.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* (/ 1 (* x x)) (/ 2.0 x))
3.0ms	(/ 1 (pow x 7))
3.0ms	(/ 1 (pow x 5))
2.0ms	(/ 1 (* x x))

simplify74.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	649	986
1	3582	855
2	5001	762

prune957.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes86.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 10.2b

bsearch40.0ms

Steps

Iters	Range		Point
9	0.006665254470786589	7065.8830381017015	115.29908004264922
9	-14674.600957416102	-0.00012459925560949148	-109.21801109479635

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	19
1	38	19

end0.0ms

sample1.1s

Algorithm

intervals

Results

419.0ms	1898×	body	640	valid
229.0ms	4039×	body	80	valid
163.0ms	589×	body	1280	valid
159.0ms	975×	body	320	valid
59.0ms	500×	body	160	valid