Details

sample14.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
1.0ms	77×	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))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
13×	`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×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

2 → 49

Calls

2 calls:

7.0ms	(sqrt (+ x 1.0))
30.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series169.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(sqrt (+ x 1.0))
139.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify34.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	292	385
1	1096	351
2	5002	346

prune109.0ms

Pruning

5 alts after pruning (4 fresh and 1 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))

rewrite47.0ms

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:

24.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
9.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
8.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))

series500.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
222.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
90.0ms	(cbrt (+ x 1.0))
90.0ms	(cbrt (+ x 1.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (62.0ms)

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

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
0.1b	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.2b	(cbrt (+ x 1.0))
0.2b	(cbrt (+ x 1.0))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

13.0ms	(/ 1 (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
25.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
4.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))

series420.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ 1 (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
97.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
89.0ms	(cbrt (+ x 1.0))
91.0ms	(cbrt (+ x 1.0))

simplify75.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	676	1326
1	3044	1242
2	5001	1211

prune277.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
0.2b	(pow (sqrt (+ x 1.0)) 3)
4.2b	(cbrt (pow (sqrt (+ x 1.0)) 3))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
20×	`cbrt-prod` `sqrt-prod`
14×	`unpow-prod-down` `cube-prod`
12×	`times-frac`
9×	`distribute-lft-out`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`sqrt-div`
4×	`cube-div` `flip3-+` `associate-/r*` `flip-+` `add-log-exp`
3×	`pow-unpow` `pow-pow` `associate-/l*`
2×	`cube-mult` `cbrt-div` `sqrt-pow1` `pow1/2` `unpow3` `associate-/r/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `pow1/3` `div-exp` `pow-exp` `clear-num` `sqrt-pow2` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 116

Calls

4 calls:

7.0ms	(sqrt (+ x 1.0))
66.0ms	(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
10.0ms	(pow (sqrt (+ x 1.0)) 3)
14.0ms	(cbrt (pow (sqrt (+ x 1.0)) 3))

series266.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ x 1.0))
142.0ms	(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
65.0ms	(pow (sqrt (+ x 1.0)) 3)
30.0ms	(cbrt (pow (sqrt (+ x 1.0)) 3))

simplify51.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	438	828
1	1823	728
2	5002	713

prune223.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes39.0ms

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

sample353.0ms

Algorithm

intervals

Results

155.0ms	7997×	body	80	valid
47.0ms	2671×	body	80	nan
0.0ms	3×	body	1280	valid