Details

sample273.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
8.0ms	280×	body	80	nan

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

rewrite25.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 97

Calls

3 calls:

8.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
11.0ms	(/ (- 1.0 x) (+ 1.0 x))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series150.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
48.0ms	(/ (- 1.0 x) (+ 1.0 x))
9.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify43.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	370	779
1	1128	734
2	5001	719

prune202.0ms

Filtered

106 candidates to 76 candidates (71.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	3	107

Merged error: 0.0b

Counts

107 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
18×	`flip3-+` `flip-+`
16×	`add-sqr-sqrt` `sqrt-prod` `associate-/r/`
12×	`pow1` `frac-times` `add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac`
6×	`associate-r/` `swap-sqr` `associate-l/` `distribute-lft-out`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`difference-of-squares`
2×	`cbrt-undiv` `rem-sqrt-square` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`pow2` `distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow-plus` `pow1/2` `sqrt-div` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `pow-sqr` `-commutative` `pow-prod-up` `flip--` `unswap-sqr`

Counts

4 → 117

Calls

4 calls:

13.0ms	(sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x))))
1.0ms	(atan (sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))))
12.0ms	(/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))
8.0ms	(* (+ 1.0 x) (+ 1.0 x))

series155.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x))))
4.0ms	(atan (sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))))
46.0ms	(/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))
17.0ms	(* (+ 1.0 x) (+ 1.0 x))

simplify80.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	527	1107
1	2355	948
2	5001	914

prune231.0ms

Filtered

129 candidates to 90 candidates (69.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	129	3	132

Merged error: 0.0b

Counts

132 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

85×	`sqrt-prod`
78×	`*-un-lft-identity`
62×	`add-sqr-sqrt`
56×	`times-frac`
40×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`sqrt-div` `associate-/l*`
7×	`associate-/r*`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `frac-2neg` `div-exp` `clear-num` `hypot-def` `div-inv`

Counts

4 → 137

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 x))
4.0ms	(sqrt (- 1.0 x))
3.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
10.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

series151.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ 1.0 x))
31.0ms	(sqrt (- 1.0 x))
2.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
88.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	372	1291
1	1144	1218
2	5001	1156

prune238.0ms

Filtered

149 candidates to 89 candidates (59.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	149	3	152

Merged error: 0.0b

Counts

152 → 3

regimes77.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	6
1	11	6

end0.0ms

sample667.0ms

Algorithm

intervals

Results

293.0ms	8000×	body	80	valid
188.0ms	7959×	body	80	nan