Details

sample16.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
2.0ms	78×	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:

5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
3.0ms	(sqrt (+ x 1.0))
8.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series207.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ 1.0 (sqrt (+ x 1.0)))
32.0ms	(sqrt (+ x 1.0))
134.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify36.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	317	483
1	1159	435
2	5002	427

prune116.0ms

Filtered

70 candidates to 52 candidates (74.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	4	71

Merged error: 0b

Counts

71 → 4

localize8.0ms

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))

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))))
4.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
3.0ms	(cbrt (+ x 1.0))
5.0ms	(cbrt (+ x 1.0))

series468.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
205.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
84.0ms	(cbrt (+ x 1.0))
85.0ms	(cbrt (+ x 1.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	681	1304
1	3037	1229
2	5003	1209

prune239.0ms

Filtered

98 candidates to 79 candidates (80.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	98	4	102

Merged error: 0b

Counts

102 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
0.7b	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
106×	`times-frac`
101×	`*-un-lft-identity`
71×	`sqrt-prod`
65×	`add-cube-cbrt`
32×	`add-exp-log`
27×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
15×	`distribute-lft-out` `unswap-sqr`
14×	`associate-/r*`
11×	`div-exp`
10×	`sqrt-div`
9×	`pow1`
8×	`prod-exp` `associate-/r/`
6×	`cbrt-undiv` `associate-/l*`
5×	`flip3-+` `flip-+`
4×	`cbrt-unprod` `div-inv` `add-log-exp`
3×	`rec-exp` `pow-flip` `1-exp`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`frac-times` `rem-sqrt-square` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 205

Calls

4 calls:

6.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
9.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
33.0ms	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
9.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series868.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
414.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
133.0ms	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
198.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify104.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	794	2673
1	3958	2343
2	5003	2180

prune296.0ms

Filtered

217 candidates to 117 candidates (53.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	217	4	221

Merged error: 0b

Counts

221 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
52×	`times-frac`
39×	`add-cube-cbrt` `sqrt-prod`
30×	`associate-r`
15×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-l` `associate-/l*` `add-log-exp` `unswap-sqr`
4×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 132

Calls

4 calls:

10.0ms	(+ 1.0 (sqrt (+ x 1.0)))
8.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
3.0ms	(sqrt (+ x 1.0))
16.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series510.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ 1.0 (sqrt (+ x 1.0)))
293.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
36.0ms	(sqrt (+ x 1.0))
133.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	529	1281
1	2243	1134
2	5001	1107

prune217.0ms

Filtered

144 candidates to 91 candidates (63.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	144	4	148

Merged error: 0b

Counts

148 → 4

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

sample407.0ms

Algorithm

intervals

Results

206.0ms	7998×	body	80	valid
70.0ms	2782×	body	80	nan
0.0ms	2×	body	1280	valid

Details

sample16.0ms

simplify4.0ms

prune2.0ms

localize8.0ms

rewrite18.0ms

series207.0ms

simplify36.0ms

prune116.0ms

localize8.0ms

rewrite23.0ms

series468.0ms

simplify80.0ms

prune239.0ms

localize9.0ms

rewrite65.0ms

series868.0ms

simplify104.0ms

prune296.0ms

localize7.0ms

rewrite43.0ms

series510.0ms

simplify64.0ms

prune217.0ms

regimes39.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample407.0ms

Profiling