Details

sample329.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
9.0ms	242×	body	80	nan

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	6
1	19	6
2	21	6
3	21	6

prune4.0ms

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: 0.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b	(/ (- 1.0 x) (+ 1.0 x))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
41×	`times-frac`
26×	`sqrt-prod`
24×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
5×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
4×	`pow1` `associate-/r*` `associate-/r/`
3×	`add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num` `flip--`

Counts

3 → 91

Calls

3 calls:

29.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
11.0ms	(/ (- 1.0 x) (+ 1.0 x))

series137.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
42.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify42.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	354	753
1	1071	709
2	5001	688

prune195.0ms

Filtered

100 candidates to 70 candidates (70.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	4	101

Merged error: 0b

Counts

101 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan (sqrt (* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))))
0.0b	(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))
0.0b	(/ 1 (sqrt (+ 1.0 x)))
0.0b	(/ (- 1.0 x) (sqrt (+ 1.0 x)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

148×	`add-sqr-sqrt`
144×	`*-un-lft-identity`
134×	`times-frac`
83×	`sqrt-prod`
72×	`add-cube-cbrt`
41×	`associate-r`
32×	`add-exp-log`
27×	`associate-l`
20×	`add-cbrt-cube`
18×	`distribute-lft-out`
15×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
14×	`associate-/r*`
11×	`div-exp`
8×	`pow1` `sqrt-div` `prod-exp` `associate-/r/` `associate-/l*`
6×	`cbrt-undiv`
4×	`flip3-+` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`
3×	`rec-exp` `pow-flip` `1-exp`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `flip3--` `sqrt-pow1` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `inv-pow`

Counts

4 → 229

Calls

4 calls:

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

series184.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan (sqrt (* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))))
35.0ms	(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))
51.0ms	(/ 1 (sqrt (+ 1.0 x)))
95.0ms	(/ (- 1.0 x) (sqrt (+ 1.0 x)))

simplify92.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	750	2276
1	3533	1966
2	5001	1845

prune357.0ms

Filtered

241 candidates to 124 candidates (51.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	241	0	241
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	241	4	245

Merged error: 0b

Counts

245 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x)))))
0.0b	(atan (* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))))
0.0b	(/ 1 (sqrt (+ 1.0 x)))
0.0b	(/ (- 1.0 x) (sqrt (+ 1.0 x)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

192×	`sqrt-prod`
172×	`add-sqr-sqrt`
148×	`*-un-lft-identity`
140×	`times-frac`
74×	`add-cube-cbrt`
44×	`associate-r`
30×	`associate-l`
24×	`unswap-sqr`
18×	`distribute-lft-out`
15×	`distribute-lft-out--` `difference-of-squares`
14×	`associate-/r*`
12×	`add-exp-log` `sqrt-div`
10×	`pow1` `add-cbrt-cube`
8×	`associate-/r/` `associate-/l*`
4×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
3×	`pow-flip` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `rec-exp` `flip3--` `sqrt-unprod` `1-exp` `div-sub` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `inv-pow`

Counts

4 → 237

Calls

4 calls:

39.0ms	(* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x)))))
1.0ms	(atan (* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))))
6.0ms	(/ 1 (sqrt (+ 1.0 x)))
11.0ms	(/ (- 1.0 x) (sqrt (+ 1.0 x)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x)))))
2.0ms	(atan (* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))))
51.0ms	(/ 1 (sqrt (+ 1.0 x)))
93.0ms	(/ (- 1.0 x) (sqrt (+ 1.0 x)))

simplify83.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	672	2764
1	2457	2529
2	5001	2489

prune426.0ms

Filtered

249 candidates to 129 candidates (51.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	249	0	249
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	249	4	253

Merged error: 0b

Counts

253 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (- 1.0 x) (/ 1 (+ 1.0 x))))
0.0b	(atan (sqrt (* (- 1.0 x) (/ 1 (+ 1.0 x)))))
0.0b	(/ 1 (+ 1.0 x))
0.0b	(* (- 1.0 x) (/ 1 (+ 1.0 x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
26×	`times-frac`
22×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`pow1`
7×	`distribute-lft-out`
6×	`sqrt-div`
5×	`associate-l`
4×	`frac-times` `flip3--` `div-exp` `associate-l/` `prod-exp` `associate-/r` `associate-/r/` `flip--` `add-log-exp`
3×	`associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sqrt-pow1` `flip3-+` `1-exp` `associate-*r/` `pow-prod-down` `un-div-inv` `cbrt-unprod` `flip-+` `div-inv`
1×	`pow-flip` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `*-commutative` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 108

Calls

4 calls:

11.0ms	(sqrt (* (- 1.0 x) (/ 1 (+ 1.0 x))))
1.0ms	(atan (sqrt (* (- 1.0 x) (/ 1 (+ 1.0 x)))))
5.0ms	(/ 1 (+ 1.0 x))
13.0ms	(* (- 1.0 x) (/ 1 (+ 1.0 x)))

series146.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (* (- 1.0 x) (/ 1 (+ 1.0 x))))
2.0ms	(atan (sqrt (* (- 1.0 x) (/ 1 (+ 1.0 x)))))
23.0ms	(/ 1 (+ 1.0 x))
32.0ms	(* (- 1.0 x) (/ 1 (+ 1.0 x)))

simplify57.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	430	716
1	1909	632
2	5001	580

prune170.0ms

Filtered

120 candidates to 73 candidates (60.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	120	4	124

Merged error: 0b

Counts

124 → 4

regimes73.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	11
1	18	11

end0.0ms

sample803.0ms

Algorithm

intervals

Results

358.0ms	8000×	body	80	valid
247.0ms	7952×	body	80	nan

Details

sample329.0ms

simplify12.0ms

prune4.0ms

localize10.0ms

rewrite46.0ms

series137.0ms

simplify42.0ms

prune195.0ms

localize14.0ms

rewrite60.0ms

series184.0ms

simplify92.0ms

prune357.0ms

localize12.0ms

rewrite70.0ms

series234.0ms

simplify83.0ms

prune426.0ms

localize9.0ms

rewrite34.0ms

series146.0ms

simplify57.0ms

prune170.0ms

regimes73.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample803.0ms

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