Details

sample16.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
2.0ms	75×	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

localize9.0ms

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))))

rewrite17.0ms

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))))

series212.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ 1.0 (sqrt (+ x 1.0)))
33.0ms	(sqrt (+ x 1.0))
138.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify39.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (32.0ms)

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

prune124.0ms

Filtered

70 candidates to 52 candidates (74.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	4	71

Merged error: 0b

Counts

71 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.1b	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
0.1b	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
26×	`times-frac`
23×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`distribute-lft-out`
8×	`pow1`
6×	`add-log-exp`
4×	`flip3-+` `div-exp` `prod-exp` `associate-/r*` `sqrt-prod` `associate-/r/` `flip-+`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sqrt-div` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 106

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
12.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
10.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

series315.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ x 1.0))
41.0ms	(+ 1.0 (sqrt (+ x 1.0)))
138.0ms	(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
103.0ms	(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

simplify55.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	452	822
1	1960	707
2	5001	668

prune150.0ms

Filtered

118 candidates to 73 candidates (61.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	118	4	122

Merged error: 0b

Counts

122 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x 1.0)))
0.1b	(sqrt (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
0.2b	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`associate-r/` `associate-l/` `associate-/r/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 161

Calls

4 calls:

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

series354.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (sqrt (+ x 1.0)))
90.0ms	(sqrt (sqrt (+ x 1.0)))
145.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
30.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify71.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	512	1295
1	2301	1129
2	5001	1105

prune235.0ms

Filtered

173 candidates to 93 candidates (53.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	173	4	177

Merged error: 0b

Counts

177 → 4

localize13.0ms

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))

rewrite20.0ms

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))
3.0ms	(cbrt (+ x 1.0))

series494.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
215.0ms	(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
87.0ms	(cbrt (+ x 1.0))
88.0ms	(cbrt (+ x 1.0))

simplify77.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (64.0ms)

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

prune242.0ms

Filtered

98 candidates to 79 candidates (80.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Merged error: 0b

Counts

102 → 4

regimes19.0ms

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	13	5
1	13	5

end0.0ms

sample407.0ms

Algorithm

intervals

Results

213.0ms	7997×	body	80	valid
71.0ms	2821×	body	80	nan
0.0ms	3×	body	1280	valid