Details

sample22.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
3.0ms	86×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.0b	(sqrt (+ x 1.0))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `log1p-expm1-u` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `hypot-def` `div-inv`

Counts

3 → 71

Calls

3 calls:

10.0ms	(+ 1.0 (sqrt (+ x 1.0)))
4.0ms	(sqrt (+ x 1.0))
16.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series210.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ 1.0 (sqrt (+ x 1.0)))
32.0ms	(sqrt (+ x 1.0))
137.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify37.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	334	508
1	1222	457
2	5002	445

prune157.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt (+ x 1.0)) 3)
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
4.6b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
8.0b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
62×	`sqrt-div`
43×	`add-sqr-sqrt`
34×	`sqrt-prod`
32×	`flip3-+` `flip-+`
31×	`add-cube-cbrt`
28×	`associate-*r/` `distribute-lft-out`
27×	`times-frac`
23×	`unpow-prod-down` `cube-prod`
21×	`pow1`
16×	`frac-sub`
12×	`frac-times`
11×	`swap-sqr`
9×	`add-exp-log` `sqrt-pow1` `pow1/2` `associate-/r*` `add-cbrt-cube`
8×	`associate-*l/`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `sum-cubes` `log1p-expm1-u` `sub-div` `unswap-sqr`
3×	`pow-unpow` `pow-pow` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cube-div` `associate-/r/`
1×	`cbrt-undiv` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `pow-plus` `fma-neg` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `prod-diff` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 194

Calls

4 calls:

6.0ms	(pow (sqrt (+ x 1.0)) 3)
20.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
15.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
54.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(pow (sqrt (+ x 1.0)) 3)
16.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
68.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
192.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify136.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (116.0ms)

Iter	Nodes	Cost
0	825	1791
1	4123	1518
2	5001	1510

prune446.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.1b	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))
0.1b	(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

360×	`times-frac`
288×	`*-un-lft-identity`
190×	`sqrt-prod`
189×	`add-sqr-sqrt`
186×	`add-cube-cbrt`
51×	`distribute-lft-out`
34×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/l*`
9×	`div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `flip-+`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `associate-/r/` `hypot-def`

Counts

4 → 305

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
8.0ms	(+ 1.0 (sqrt (+ x 1.0)))
24.0ms	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))
28.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))

series356.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ x 1.0))
41.0ms	(+ 1.0 (sqrt (+ x 1.0)))
136.0ms	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))
143.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))

simplify116.0ms

Algorithm

egg-herbie

Counts

317 → 317

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	898	4086
1	4337	3656
2	5001	3645

prune450.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

end0.0ms

sample628.0ms

Algorithm

intervals

Results

403.0ms	7998×	body	80	valid
102.0ms	2703×	body	80	nan
0.0ms	2×	body	1280	valid