Details

sample19.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
2.0ms	93×	body	80	nan

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite30.0ms

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:

4.0ms	(sqrt (+ x 1.0))
8.0ms	(+ 1.0 (sqrt (+ x 1.0)))
16.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series220.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(sqrt (+ x 1.0))
42.0ms	(+ 1.0 (sqrt (+ x 1.0)))
144.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify36.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (30.0ms)

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

prune160.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
59×	`add-sqr-sqrt`
52×	`times-frac`
40×	`add-cube-cbrt`
39×	`sqrt-prod`
30×	`associate-r`
15×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-l` `associate-/l*` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `flip3-+` `associate-/r*` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`fma-def`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `hypot-def`

Counts

4 → 144

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
17.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
8.0ms	(+ 1.0 (sqrt (+ x 1.0)))
46.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series506.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ x 1.0))
295.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
43.0ms	(+ 1.0 (sqrt (+ x 1.0)))
137.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	554	1324
1	2324	1174
2	5001	1140

prune300.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))
0.2b	(pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3)
33.2b	(cbrt (pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

82×	`*-un-lft-identity`
60×	`times-frac`
48×	`add-sqr-sqrt` `add-cube-cbrt`
42×	`cbrt-prod`
36×	`unpow-prod-down` `cube-prod`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
6×	`flip3-+` `flip-+` `add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `associate-/l*`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `sum-log` `rem-cbrt-cube`

Counts

4 → 164

Calls

4 calls:

10.0ms	(+ 1.0 (sqrt (+ x 1.0)))
16.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
19.0ms	(pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3)
20.0ms	(cbrt (pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3))

series631.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ 1.0 (sqrt (+ x 1.0)))
149.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))
284.0ms	(pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3)
155.0ms	(cbrt (pow (/ x (+ 1.0 (sqrt (+ x 1.0)))) 3))

simplify84.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	666	1535
1	3055	1397
2	5001	1367

prune288.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes33.0ms

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

sample482.0ms

Algorithm

intervals

Results

276.0ms	7997×	body	80	valid
76.0ms	2758×	body	80	nan
0.0ms	3×	body	1280	valid