Details

sample281.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
8.0ms	288×	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	(/ (- 1.0 x) (+ 1.0 x))
0.0b	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

rewrite23.0ms

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:

8.0ms	(/ (- 1.0 x) (+ 1.0 x))
9.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series148.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ (- 1.0 x) (+ 1.0 x))
103.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
9.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify41.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (31.0ms)

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

prune182.0ms

Filtered

100 candidates to 70 candidates (70.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	2	101

Merged error: 0b

Counts

101 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

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

series159.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (- 1.0 x))
35.0ms	(sqrt (+ 1.0 x))
89.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
2.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))

simplify45.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (32.0ms)

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

prune219.0ms

Filtered

140 candidates to 80 candidates (57.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	140	2	142

Merged error: 0b

Counts

142 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

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

series29.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
12.0ms	(sqrt (atan (sqrt (/ (- 1.0 x) (+ 1.0 x)))))
12.0ms	(sqrt (atan (sqrt (/ (- 1.0 x) (+ 1.0 x)))))
2.0ms	(* (sqrt (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))) (sqrt (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))

simplify110.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	106	756
1	373	670
2	2183	638
3	5002	615

prune126.0ms

Filtered

94 candidates to 48 candidates (51.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	94	2	96

Merged error: 0b

Counts

96 → 2

regimes53.0ms

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	12	7
1	12	7

end0.0ms

sample682.0ms

Algorithm

intervals

Results

303.0ms	8000×	body	80	valid
188.0ms	7915×	body	80	nan