Details

sample14.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
1.0ms	80×	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 2 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 54

Calls

2 calls:

7.0ms	(sqrt (+ x 1.0))
33.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series168.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(sqrt (+ x 1.0))
134.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify38.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	304	400
1	1151	366
2	5002	357

prune115.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
0.1b	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
26×	`times-frac`
22×	`add-cube-cbrt`
18×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`distribute-lft-out`
7×	`pow1`
4×	`div-exp` `prod-exp` `associate-/r*` `sqrt-prod` `associate-/r/`
3×	`expm1-log1p-u` `flip3-+` `associate-l` `flip-+` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sqrt-div` `1-exp` `cbrt-unprod` `div-inv`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `hypot-def` `inv-pow`

Counts

3 → 101

Calls

3 calls:

7.0ms	(sqrt (+ x 1.0))
33.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
70.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

series268.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(sqrt (+ x 1.0))
98.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
136.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	442	749
1	1974	650
2	5001	606

prune162.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `frac-times` `rem-sqrt-square` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`associate-r/` `associate-l/` `associate-/r/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 169

Calls

4 calls:

10.0ms	(sqrt (sqrt (+ x 1.0)))
8.0ms	(sqrt (sqrt (+ x 1.0)))
9.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
48.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series328.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(sqrt (sqrt (+ x 1.0)))
84.0ms	(sqrt (sqrt (+ x 1.0)))
135.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
30.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify75.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	530	1344
1	2375	1172
2	5001	1120

prune308.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 127

Calls

3 calls:

9.0ms	(sqrt (+ x 1.0))
32.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
78.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series449.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(sqrt (+ x 1.0))
289.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
129.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	524	1216
1	2253	1083
2	5001	1050

prune231.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes15.0ms

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	13	5
1	13	5

end0.0ms

sample342.0ms

Algorithm

intervals

Results

155.0ms	7998×	body	80	valid
39.0ms	2712×	body	80	nan
0.0ms	2×	body	1280	valid