Details

sample14.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
1.0ms	101×	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))
0.1b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite57.0ms

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:

15.0ms	(+ 1.0 (sqrt (+ x 1.0)))
10.0ms	(sqrt (+ x 1.0))
29.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series203.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(+ 1.0 (sqrt (+ x 1.0)))
34.0ms	(sqrt (+ x 1.0))
132.0ms	(/ 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

prune154.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

8.0ms	(sqrt (sqrt (+ x 1.0)))
9.0ms	(sqrt (sqrt (+ x 1.0)))
9.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
50.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series328.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(sqrt (sqrt (+ x 1.0)))
82.0ms	(sqrt (sqrt (+ x 1.0)))
134.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
28.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify72.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (57.0ms)

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

prune315.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) 1.0)
0.1b	(/ (+ (sqrt (+ x 1.0)) 1.0) x)
0.2b	(/ 1 (/ (+ (sqrt (+ x 1.0)) 1.0) x))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
103×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
19×	`associate-/r*` `distribute-lft-out`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp` `sqrt-prod`
7×	`fma-def` `associate-/l*`
6×	`pow1` `div-inv` `add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`rec-exp` `frac-2neg` `sqrt-div` `1-exp` `clear-num` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `sum-log` `associate-/r/` `hypot-def` `inv-pow`

Counts

4 → 165

Calls

4 calls:

7.0ms	(sqrt (+ x 1.0))
31.0ms	(+ (sqrt (+ x 1.0)) 1.0)
69.0ms	(/ (+ (sqrt (+ x 1.0)) 1.0) x)
45.0ms	(/ 1 (/ (+ (sqrt (+ x 1.0)) 1.0) x))

series280.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ x 1.0))
37.0ms	(+ (sqrt (+ x 1.0)) 1.0)
80.0ms	(/ (+ (sqrt (+ x 1.0)) 1.0) x)
130.0ms	(/ 1 (/ (+ (sqrt (+ x 1.0)) 1.0) x))

simplify66.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	614	1444
1	2709	1287
2	5002	1194

prune256.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (* (fabs (cbrt (sqrt (+ x 1.0)))) (sqrt (cbrt (sqrt (+ x 1.0))))))))
0.2b	(cbrt (sqrt (+ x 1.0)))
0.2b	(cbrt (sqrt (+ x 1.0)))
0.2b	(* (sqrt (sqrt (+ x 1.0))) (* (fabs (cbrt (sqrt (+ x 1.0)))) (sqrt (cbrt (sqrt (+ x 1.0))))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

28×	`sqrt-div`
25×	`*-un-lft-identity`
19×	`add-sqr-sqrt` `add-cube-cbrt` `sqrt-prod`
14×	`cbrt-prod`
11×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-div` `associate-l`
9×	`pow1` `flip3-+` `times-frac` `flip-+`
8×	`associate-*r/`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `associate-/r` `cbrt-unprod` `distribute-lft-out` `associate-/l`
2×	`pow1/3` `associate-*l/` `associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv`

Counts

4 → 104

Calls

4 calls:

9.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (* (fabs (cbrt (sqrt (+ x 1.0)))) (sqrt (cbrt (sqrt (+ x 1.0))))))))
5.0ms	(cbrt (sqrt (+ x 1.0)))
5.0ms	(cbrt (sqrt (+ x 1.0)))
62.0ms	(* (sqrt (sqrt (+ x 1.0))) (* (fabs (cbrt (sqrt (+ x 1.0)))) (sqrt (cbrt (sqrt (+ x 1.0))))))

series465.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (* (fabs (cbrt (sqrt (+ x 1.0)))) (sqrt (cbrt (sqrt (+ x 1.0))))))))
82.0ms	(cbrt (sqrt (+ x 1.0)))
84.0ms	(cbrt (sqrt (+ x 1.0)))
93.0ms	(* (sqrt (sqrt (+ x 1.0))) (* (fabs (cbrt (sqrt (+ x 1.0)))) (sqrt (cbrt (sqrt (+ x 1.0))))))

simplify86.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	791	2007
1	3237	1861
2	5002	1824

prune412.0ms

Pruning

4 alts after pruning (1 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	10	9
1	10	9

end0.0ms

sample349.0ms

Algorithm

intervals

Results

159.0ms	7998×	body	80	valid
38.0ms	2609×	body	80	nan
0.0ms	2×	body	1280	valid