Details

sample14.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
2.0ms	103×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.2b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite18.0ms

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:

6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series211.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ 1.0 (sqrt (+ x 1.0)))
32.0ms	(sqrt (+ x 1.0))
137.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify37.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (30.0ms)

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

prune115.0ms

Filtered

70 candidates to 52 candidates (74.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	68	3	71

Merged error: 0b

Counts

71 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

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

8.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
3.0ms	(cbrt (+ x 1.0))
6.0ms	(cbrt (+ x 1.0))
4.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))

series490.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
91.0ms	(cbrt (+ x 1.0))
91.0ms	(cbrt (+ x 1.0))
211.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))

simplify82.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (64.0ms)

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

prune241.0ms

Filtered

98 candidates to 79 candidates (80.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	98	3	101

Merged error: 0b

Counts

101 → 3

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

360×	`times-frac`
287×	`*-un-lft-identity`
190×	`sqrt-prod`
186×	`add-sqr-sqrt`
185×	`add-cube-cbrt`
51×	`distribute-lft-out`
34×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/l*`
9×	`div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`flip3-+` `flip-+`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `associate-/r/`

Counts

4 → 293

Calls

4 calls:

5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
12.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))
15.0ms	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ 1.0 (sqrt (+ x 1.0)))
35.0ms	(sqrt (+ x 1.0))
156.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))
142.0ms	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))

simplify123.0ms

Algorithm

egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	870	4044
1	4205	3616
2	5003	3601

prune343.0ms

Filtered

305 candidates to 139 candidates (45.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	305	0	305
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	305	3	308

Merged error: 0b

Counts

308 → 3

regimes33.0ms

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

sample319.0ms

Algorithm

intervals

Results

156.0ms	7996×	body	80	valid
45.0ms	2702×	body	80	nan
0.0ms	4×	body	1280	valid