Details

sample19.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
2.0ms	89×	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	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`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×	`flip3-+` `flip-+` `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` `div-inv`

Counts

3 → 61

Calls

3 calls:

4.0ms	(sqrt (+ x 1.0))
7.0ms	(+ 1.0 (sqrt (+ x 1.0)))
16.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series210.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(sqrt (+ x 1.0))
43.0ms	(+ 1.0 (sqrt (+ x 1.0)))
138.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify36.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	317	483
1	1159	435
2	5001	427

prune132.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
13×	`cbrt-prod`
10×	`associate-r`
9×	`times-frac` `sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `cbrt-div`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`associate-l` `associate-/r` `distribute-lft-out` `associate-/l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 86

Calls

4 calls:

12.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
4.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))

series484.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
217.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
85.0ms	(cbrt (+ x 1.0))
86.0ms	(cbrt (+ x 1.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	681	1304
1	3037	1229
2	5002	1209

prune294.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
18×	`cbrt-prod`
17×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`times-frac`
8×	`sqrt-prod`
6×	`add-exp-log` `cbrt-div` `add-cbrt-cube`
4×	`pow1` `flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`pow1/3` `associate-/r` `distribute-lft-out` `associate-/l`
2×	`associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 77

Calls

4 calls:

7.0ms	(/ x (+ 1.0 (* (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (sqrt (+ x 1.0))))) (sqrt (cbrt (sqrt (+ x 1.0)))))))
2.0ms	(cbrt (sqrt (+ x 1.0)))
2.0ms	(cbrt (sqrt (+ x 1.0)))
2.0ms	(cbrt (+ x 1.0))

series481.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ x (+ 1.0 (* (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (sqrt (+ x 1.0))))) (sqrt (cbrt (sqrt (+ x 1.0)))))))
87.0ms	(cbrt (sqrt (+ x 1.0)))
89.0ms	(cbrt (sqrt (+ x 1.0)))
93.0ms	(cbrt (+ x 1.0))

simplify66.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	632	1419
1	2638	1318
2	5001	1286

prune337.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
52×	`times-frac`
39×	`add-cube-cbrt` `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×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
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`

Counts

4 → 132

Calls

4 calls:

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

series508.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ x 1.0))
48.0ms	(+ 1.0 (sqrt (+ x 1.0)))
292.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
138.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	529	1281
1	2243	1134
2	5001	1107

prune263.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes17.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	9
1	12	9

end0.0ms

sample523.0ms

Algorithm

intervals

Results

309.0ms	7998×	body	80	valid
78.0ms	2687×	body	80	nan
0.0ms	2×	body	1280	valid