Details

sample22.0ms

Algorithm

intervals

Results

13.0ms	249×	body	80	valid
0.0ms	2×	body	1280	valid
0.0ms	2×	body	640	valid
0.0ms	1×	body	2560	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	4
1	11	4
2	11	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ x (/ (fabs (- y x)) 2.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity`
3×	`fma-def` `add-log-exp`
2×	`add-sqr-sqrt` `add-cube-cbrt`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`

Counts

1 → 17

Calls

1 calls:

6.0ms

(+ x (/ (fabs (- y x)) 2.0))

series20.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

(+ x (/ (fabs (- y x)) 2.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	88	110
1	226	97
2	540	97
3	1522	97
4	5001	97

prune51.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma (sqrt x) (sqrt x) (/ (fabs (- y x)) 2.0))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma (sqrt x) (sqrt x) (/ (fabs (- y x)) 2.0))

series106.0ms

Counts

1 → 3

Calls

1 calls:

106.0ms

(fma (sqrt x) (sqrt x) (/ (fabs (- y x)) 2.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	88	117
1	275	101
2	1326	95
3	5001	92

prune40.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (/ (fabs (- y x)) 2.0) x)
0.1b	(pow (+ (/ (fabs (- y x)) 2.0) x) 3)
39.1b	(cbrt (pow (+ (/ (fabs (- y x)) 2.0) x) 3))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`cbrt-prod`
13×	`fma-def`
9×	`times-frac`
8×	`unpow-prod-down` `cube-prod`
5×	`distribute-lft-out` `add-log-exp`
4×	`pow1` `add-exp-log` `cube-div` `add-cbrt-cube`
3×	`expm1-log1p-u` `pow-unpow` `flip3-+` `flip-+` `log1p-expm1-u`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `sum-log` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

3 → 83

Calls

3 calls:

10.0ms	(+ (/ (fabs (- y x)) 2.0) x)
16.0ms	(pow (+ (/ (fabs (- y x)) 2.0) x) 3)
15.0ms	(cbrt (pow (+ (/ (fabs (- y x)) 2.0) x) 3))

series84.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (/ (fabs (- y x)) 2.0) x)
30.0ms	(pow (+ (/ (fabs (- y x)) 2.0) x) 3)
29.0ms	(cbrt (pow (+ (/ (fabs (- y x)) 2.0) x) 3))

simplify38.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	242	601
1	991	564
2	5001	554

prune184.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (fabs (- y x)) 2.0) (- (/ (fabs (- y x)) 2.0) x))
5.3b	(+ (* (/ (fabs (- y x)) 2.0) (- (/ (fabs (- y x)) 2.0) x)) (pow x 2))
9.7b	(+ (pow (/ (fabs (- y x)) 2.0) 3) (pow x 3))
39.7b	(/ (+ (pow (/ (fabs (- y x)) 2.0) 3) (pow x 3)) (+ (* (/ (fabs (- y x)) 2.0) (- (/ (fabs (- y x)) 2.0) x)) (pow x 2)))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

229×	`*-un-lft-identity`
187×	`add-sqr-sqrt`
177×	`add-cube-cbrt`
164×	`times-frac`
156×	`prod-diff`
82×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
33×	`unpow-prod-down` `fma-def` `cube-prod`
25×	`distribute-lft-out`
16×	`div-inv`
13×	`associate-l`
11×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
8×	`add-log-exp`
6×	`pow1` `associate-r`
5×	`sum-cubes`
4×	`expm1-log1p-u` `sub-neg` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`associate-/r*`
2×	`cbrt-undiv` `+-commutative` `frac-times` `flip3--` `associate-*r/` `div-exp` `prod-exp` `sum-log` `associate-/r/` `flip--` `cbrt-unprod` `associate-/l/` `difference-of-squares` `unswap-sqr`
1×	`cube-mult` `frac-2neg` `unpow3` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `distribute-lft-out--` `sqr-pow`

Counts

4 → 327

Calls

4 calls:

47.0ms	(* (/ (fabs (- y x)) 2.0) (- (/ (fabs (- y x)) 2.0) x))
29.0ms	(+ (* (/ (fabs (- y x)) 2.0) (- (/ (fabs (- y x)) 2.0) x)) (pow x 2))
47.0ms	(+ (pow (/ (fabs (- y x)) 2.0) 3) (pow x 3))
137.0ms	(/ (+ (pow (/ (fabs (- y x)) 2.0) 3) (pow x 3)) (+ (* (/ (fabs (- y x)) 2.0) (- (/ (fabs (- y x)) 2.0) x)) (pow x 2)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (/ (fabs (- y x)) 2.0) (- (/ (fabs (- y x)) 2.0) x))
44.0ms	(+ (* (/ (fabs (- y x)) 2.0) (- (/ (fabs (- y x)) 2.0) x)) (pow x 2))
100.0ms	(+ (pow (/ (fabs (- y x)) 2.0) 3) (pow x 3))
175.0ms	(/ (+ (pow (/ (fabs (- y x)) 2.0) 3) (pow x 3)) (+ (* (/ (fabs (- y x)) 2.0) (- (/ (fabs (- y x)) 2.0) x)) (pow x 2)))

simplify133.0ms

Algorithm

egg-herbie

Counts

339 → 339

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	954	5425
1	3897	4515
2	5001	4508

prune992.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes64.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

end0.0ms

sample625.0ms

Algorithm

intervals

Results

416.0ms	7680×	body	80	valid
27.0ms	113×	body	1280	valid
16.0ms	73×	body	640	valid
11.0ms	44×	body	2560	valid
10.0ms	51×	body	320	valid
4.0ms	40×	body	160	valid