Details

sample17.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
3.0ms	104×	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

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`distribute-lft-out`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 45

Calls

2 calls:

8.0ms	(+ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series186.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(+ 1.0 (sqrt (+ x 1.0)))
141.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify33.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	278	393
1	1058	351
2	5002	347

prune86.0ms

Filtered

51 candidates to 38 candidates (74.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	48	4	52

Merged error: 0b

Counts

52 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.0b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

378×	`times-frac`
306×	`*-un-lft-identity`
232×	`sqrt-prod`
192×	`add-sqr-sqrt`
190×	`add-cube-cbrt`
58×	`distribute-lft-out`
30×	`associate-/l*`
24×	`sqrt-div`
20×	`associate-/r/`
14×	`associate-/r*`
12×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 317

Calls

4 calls:

5.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
5.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
8.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
22.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series834.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
133.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
424.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
147.0ms	(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify117.0ms

Algorithm

egg-herbie

Counts

329 → 329

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	887	5646
1	3501	5039
2	5002	4953

prune384.0ms

Filtered

329 candidates to 143 candidates (43.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	329	0	329
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	329	4	333

Merged error: 0b

Counts

333 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sqrt (+ x 1.0)) 3)
0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
3.9b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
9.2b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
62×	`sqrt-div`
43×	`add-sqr-sqrt`
34×	`sqrt-prod`
32×	`flip3-+` `flip-+`
31×	`add-cube-cbrt`
28×	`associate-*r/` `distribute-lft-out`
27×	`times-frac`
23×	`unpow-prod-down` `cube-prod`
21×	`pow1`
16×	`frac-sub`
12×	`frac-times`
11×	`swap-sqr`
9×	`add-exp-log` `sqrt-pow1` `pow1/2` `associate-/r*` `add-cbrt-cube`
8×	`associate-*l/`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`pow-prod-up`
4×	`sum-cubes` `sub-div` `unswap-sqr`
3×	`pow-unpow` `pow-pow` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cube-div` `associate-/r/`
1×	`cbrt-undiv` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `pow-plus` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 184

Calls

4 calls:

5.0ms	(pow (sqrt (+ x 1.0)) 3)
10.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
12.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
17.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(pow (sqrt (+ x 1.0)) 3)
17.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
68.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
196.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify136.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (116.0ms)

Iter	Nodes	Cost
0	771	1703
1	3870	1474
2	5002	1458

prune533.0ms

Filtered

196 candidates to 98 candidates (50.0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	196	4	200

Merged error: 0b

Counts

200 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
53×	`add-sqr-sqrt`
52×	`times-frac`
37×	`add-cube-cbrt`
35×	`sqrt-prod`
30×	`associate-r`
14×	`distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-l` `associate-/l*` `unswap-sqr`
5×	`pow1` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

3 → 116

Calls

3 calls:

5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
8.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
16.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series465.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ 1.0 (sqrt (+ x 1.0)))
290.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
133.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	491	1191
1	2142	1050
2	5001	1025

prune176.0ms

Filtered

125 candidates to 76 candidates (60.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	125	4	129

Merged error: 0b

Counts

129 → 4

regimes36.0ms

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

sample398.0ms

Algorithm

intervals

Results

206.0ms	7996×	body	80	valid
71.0ms	2696×	body	80	nan
1.0ms	4×	body	1280	valid

Details

sample17.0ms

simplify4.0ms

prune2.0ms

localize5.0ms

rewrite16.0ms

series186.0ms

simplify33.0ms

prune86.0ms

localize7.0ms

rewrite59.0ms

series834.0ms

simplify117.0ms

prune384.0ms

localize15.0ms

rewrite56.0ms

series352.0ms

simplify136.0ms

prune533.0ms

localize7.0ms

rewrite37.0ms

series465.0ms

simplify67.0ms

prune176.0ms

regimes36.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample398.0ms

Profiling