Details

sample279.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
8.0ms	280×	body	80	nan

simplify13.0ms

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

rewrite22.0ms

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:

7.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
9.0ms	(/ (- 1.0 x) (+ 1.0 x))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series149.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
49.0ms	(/ (- 1.0 x) (+ 1.0 x))
9.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify40.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	354	753
1	1071	709
2	5001	690

prune184.0ms

Filtered

100 candidates to 70 candidates (70.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	98	3	101

Merged error: 0.0b

Counts

101 → 3

localize9.0ms

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)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

85×	`sqrt-prod`
78×	`*-un-lft-identity`
60×	`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×	`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` `div-inv`

Counts

4 → 128

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 x))
3.0ms	(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)))

series154.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ 1.0 x))
33.0ms	(sqrt (- 1.0 x))
2.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
89.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	353	1256
1	1084	1184
2	5001	1121

prune213.0ms

Filtered

140 candidates to 80 candidates (57.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	140	3	143

Merged error: 0.0b

Counts

143 → 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))

rewrite35.0ms

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×	`associate-r` `associate-l` `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 → 109

Calls

4 calls:

10.0ms	(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))

series154.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(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)))))
48.0ms	(/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))
17.0ms	(* (+ 1.0 x) (+ 1.0 x))

simplify75.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	506	1051
1	2239	894
2	5001	856

prune201.0ms

Filtered

121 candidates to 82 candidates (67.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	121	3	124

Merged error: 0.0b

Counts

124 → 3

regimes76.0ms

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

sample680.0ms

Algorithm

intervals

Results

306.0ms	8000×	body	80	valid
193.0ms	7959×	body	80	nan