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))))

rewrite31.0ms

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)))
17.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series224.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(sqrt (+ x 1.0))
47.0ms	(+ 1.0 (sqrt (+ x 1.0)))
146.0ms	(/ 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

prune167.0ms

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))

rewrite28.0ms

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×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `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 → 94

Calls

4 calls:

17.0ms	(* (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))

series506.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
220.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
92.0ms	(cbrt (+ x 1.0))
93.0ms	(cbrt (+ x 1.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	707	1346
1	3177	1264
2	5001	1230

prune338.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize12.0ms

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))

rewrite18.0ms

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` `expm1-log1p-u` `flip3-+` `sqrt-div` `flip-+` `log1p-expm1-u` `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 → 85

Calls

4 calls:

4.0ms	(/ x (+ 1.0 (* (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (sqrt (+ x 1.0))))) (sqrt (cbrt (sqrt (+ x 1.0)))))))
6.0ms	(cbrt (sqrt (+ x 1.0)))
3.0ms	(cbrt (sqrt (+ x 1.0)))
2.0ms	(cbrt (+ x 1.0))

series492.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(/ x (+ 1.0 (* (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (sqrt (+ x 1.0))))) (sqrt (cbrt (sqrt (+ x 1.0)))))))
92.0ms	(cbrt (sqrt (+ x 1.0)))
94.0ms	(cbrt (sqrt (+ x 1.0)))
92.0ms	(cbrt (+ x 1.0))

simplify69.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	658	1467
1	2771	1355
2	5002	1286

prune376.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (sqrt (+ x 1.0)))
0.2b	(* (sqrt (cbrt (sqrt (+ x 1.0)))) (sqrt (cbrt (sqrt (+ x 1.0)))))
0.2b	(cbrt (+ x 1.0))
0.2b	(/ 1 (/ (fma (fabs (cbrt (+ x 1.0))) (* (sqrt (cbrt (sqrt (+ x 1.0)))) (sqrt (cbrt (sqrt (+ x 1.0))))) 1.0) x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

108×	`sqrt-prod`
105×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
75×	`times-frac`
65×	`add-cube-cbrt`
63×	`cbrt-prod`
26×	`sqrt-div`
20×	`pow1`
19×	`swap-sqr`
17×	`add-exp-log`
16×	`cbrt-div` `unswap-sqr`
14×	`sqrt-pow1`
13×	`associate-r` `associate-l` `associate-/r*`
11×	`add-cbrt-cube`
8×	`flip3-+` `pow1/2` `pow1/3` `flip-+` `distribute-lft-out`
7×	`div-exp`
6×	`pow-prod-up`
5×	`div-inv`
4×	`expm1-log1p-u` `frac-times` `pow-prod-down` `pow-sqr` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `1-exp` `associate-r/` `associate-l/`
1×	`pow2` `pow-flip` `frac-2neg` `pow-plus` `sqrt-unprod` `prod-exp` `clear-num` `rem-square-sqrt` `associate-/r/` `*-commutative` `cbrt-unprod` `inv-pow`

Counts

4 → 212

Calls

4 calls:

3.0ms	(cbrt (sqrt (+ x 1.0)))
32.0ms	(* (sqrt (cbrt (sqrt (+ x 1.0)))) (sqrt (cbrt (sqrt (+ x 1.0)))))
2.0ms	(cbrt (+ x 1.0))
5.0ms	(/ 1 (/ (fma (fabs (cbrt (+ x 1.0))) (* (sqrt (cbrt (sqrt (+ x 1.0)))) (sqrt (cbrt (sqrt (+ x 1.0))))) 1.0) x))

series491.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (sqrt (+ x 1.0)))
91.0ms	(* (sqrt (cbrt (sqrt (+ x 1.0)))) (sqrt (cbrt (sqrt (+ x 1.0)))))
90.0ms	(cbrt (+ x 1.0))
219.0ms	(/ 1 (/ (fma (fabs (cbrt (+ x 1.0))) (* (sqrt (cbrt (sqrt (+ x 1.0)))) (sqrt (cbrt (sqrt (+ x 1.0))))) 1.0) x))

simplify138.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	951	3432
1	4930	3051
2	5001	3051

prune609.0ms

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

sample494.0ms

Algorithm

intervals

Results

300.0ms	7998×	body	80	valid
70.0ms	2687×	body	80	nan
0.0ms	2×	body	1280	valid