Details

sample15.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
2.0ms	74×	body	80	nan

simplify3.0ms

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 (100.0%)

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

localize5.0ms

Local error

Found 3 expressions with local error:

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

rewrite20.0ms

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

series23.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
15.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify46.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	460	585
1	1938	554
2	5002	551

prune121.0ms

Filtered

70 candidates to 55 candidates (21.4%)

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

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

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:

6.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
14.0ms	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))
8.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))

series38.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
19.0ms	(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))
11.0ms	(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))

simplify64.0ms

Algorithm

egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1143	4181
1	5001	3783

prune296.0ms

Filtered

305 candidates to 146 candidates (52.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Merged error: 0b

Counts

308 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.3b	(* (/ (sqrt x) (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ (sqrt x) (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
0.3b	(/ (sqrt x) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.3b	(/ (sqrt x) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

438×	`sqrt-prod`
384×	`times-frac`
364×	`add-sqr-sqrt`
331×	`*-un-lft-identity`
197×	`add-cube-cbrt`
94×	`swap-sqr`
59×	`distribute-lft-out`
48×	`associate-r` `associate-l`
25×	`unswap-sqr`
20×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-div` `associate-/r*`
12×	`pow1` `associate-/r/` `associate-/l*`
7×	`flip3-+` `flip-+`
6×	`cbrt-undiv` `sqrt-undiv` `div-exp` `div-inv`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `sqrt-unprod` `associate-r/` `pow-prod-down` `associate-l/` `rem-square-sqrt` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 397

Calls

4 calls:

6.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
52.0ms	(* (/ (sqrt x) (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ (sqrt x) (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
9.0ms	(/ (sqrt x) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
9.0ms	(/ (sqrt x) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series113.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
16.0ms	(* (/ (sqrt x) (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ (sqrt x) (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
40.0ms	(/ (sqrt x) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
46.0ms	(/ (sqrt x) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify93.0ms

Algorithm

egg-herbie

Counts

409 → 409

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1370	7649
1	5002	6889

prune669.0ms

Filtered

409 candidates to 175 candidates (57.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	409	0	409
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	409	3	412

Merged error: 0b

Counts

412 → 3

regimes63.0ms

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

sample424.0ms

Algorithm

intervals

Results

207.0ms	7997×	body	80	valid
66.0ms	2709×	body	80	nan
0.0ms	3×	body	1280	valid

Details

sample15.0ms

simplify3.0ms

prune2.0ms

localize5.0ms

rewrite20.0ms

series23.0ms

simplify46.0ms

prune121.0ms

localize9.0ms

rewrite47.0ms

series38.0ms

simplify64.0ms

prune296.0ms

localize11.0ms

rewrite102.0ms

series113.0ms

simplify93.0ms

prune669.0ms

regimes63.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample424.0ms

Profiling