Details

sample12.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	5
1	12	5
2	12	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
50×	`times-frac`
45×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
21×	`fma-def`
11×	`distribute-lft-out`
9×	`associate-/r*` `distribute-lft-out--`
7×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-/r/` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+`
1×	`+-commutative` `frac-add` `sum-log`

Counts

3 → 114

Calls

3 calls:

5.0ms	(/ x (+ x 1.0))
48.0ms	(+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))
5.0ms	(/ 1.0 (- x 1.0))

series191.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ x (+ x 1.0))
128.0ms	(+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))
29.0ms	(/ 1.0 (- x 1.0))

simplify43.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	400	551
1	1470	525
2	5001	521

prune235.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (pow (/ 1.0 (- x 1.0)) 3) (pow (/ x (+ x 1.0)) 3)) (fma (/ x (+ x 1.0)) (- (/ x (+ x 1.0)) (/ 1.0 (- x 1.0))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))))
0.0b	(pow (/ x (+ x 1.0)) 3)
0.1b	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
0.1b	(pow (/ 1.0 (- x 1.0)) 3)

rewrite486.0ms

Algorithm

rewrite-expression-head

Rules

536×	`*-un-lft-identity`
333×	`times-frac`
158×	`add-sqr-sqrt`
122×	`distribute-lft-out`
119×	`unpow-prod-down` `cube-prod`
110×	`add-cube-cbrt`
56×	`distribute-lft-out--`
27×	`swap-sqr`
25×	`associate-/l*`
24×	`add-exp-log` `add-cbrt-cube`
21×	`associate-r` `associate-l`
18×	`difference-of-squares`
16×	`associate-/r/`
13×	`pow1`
9×	`div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`pow-unpow` `flip3--` `flip--`
4×	`cube-div` `expm1-log1p-u` `pow-exp` `prod-exp` `sum-cubes` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `rem-cube-cbrt` `unswap-sqr`
3×	`flip3-+` `associate-/r*` `flip-+` `associate-/l/`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `sqr-pow`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 341

Calls

4 calls:

407.0ms	(/ (+ (pow (/ 1.0 (- x 1.0)) 3) (pow (/ x (+ x 1.0)) 3)) (fma (/ x (+ x 1.0)) (- (/ x (+ x 1.0)) (/ 1.0 (- x 1.0))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))))
8.0ms	(pow (/ x (+ x 1.0)) 3)
33.0ms	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
8.0ms	(pow (/ 1.0 (- x 1.0)) 3)

series644.0ms

Counts

4 → 12

Calls

4 calls:

494.0ms	(/ (+ (pow (/ 1.0 (- x 1.0)) 3) (pow (/ x (+ x 1.0)) 3)) (fma (/ x (+ x 1.0)) (- (/ x (+ x 1.0)) (/ 1.0 (- x 1.0))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))))
56.0ms	(pow (/ x (+ x 1.0)) 3)
43.0ms	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
50.0ms	(pow (/ 1.0 (- x 1.0)) 3)

simplify88.0ms

Algorithm

egg-herbie

Counts

353 → 353

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1279	5605
1	5002	5314

prune646.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (- x 1.0))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.1b	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

200×	`*-un-lft-identity`
170×	`times-frac`
164×	`add-sqr-sqrt`
100×	`add-cube-cbrt`
51×	`swap-sqr`
39×	`associate-r` `associate-l`
32×	`add-exp-log` `add-cbrt-cube`
26×	`distribute-lft-out--`
20×	`associate-/r/` `difference-of-squares`
18×	`pow1` `distribute-lft-out`
10×	`cbrt-undiv` `div-exp` `associate-/r*` `div-inv`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`flip3--` `flip--` `associate-/l*`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 267

Calls

4 calls:

5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (- x 1.0))
34.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
33.0ms	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))

series148.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1.0 (- x 1.0))
32.0ms	(/ 1.0 (- x 1.0))
43.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
45.0ms	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))

simplify125.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	971	2069
1	4922	1855
2	5001	1855

prune746.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes12.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	21
1	16	21

end0.0ms

sample284.0ms

Algorithm

intervals

Results

192.0ms

8000×

body

valid