Details

sample299.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
6.0ms	249×	body	80	nan

simplify12.0ms

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))))

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:

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))))

series158.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
53.0ms	(/ (- 1.0 x) (+ 1.0 x))
9.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify42.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (31.0ms)

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

prune231.0ms

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: 0b

Counts

101 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
41×	`times-frac`
26×	`add-cube-cbrt` `associate-l`
21×	`difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube`
10×	`distribute-lft-out--`
9×	`pow1`
7×	`flip3--` `flip--`
5×	`sqrt-div` `associate-r` `associate-/l*`
4×	`frac-times` `associate-r/` `associate-/r` `associate-/r/` `add-log-exp`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-pow1` `div-exp` `pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `pow1/2` `div-sub` `clear-num` `sqrt-prod` `*-commutative`

Counts

4 → 124

Calls

4 calls:

8.0ms	(/ (- 1.0 x) (- (* 1.0 1.0) (* x x)))
11.0ms	(sqrt (* (/ (- 1.0 x) (- (* 1.0 1.0) (* x x))) (- 1.0 x)))
1.0ms	(atan (sqrt (* (/ (- 1.0 x) (- (* 1.0 1.0) (* x x))) (- 1.0 x))))
16.0ms	(* (/ (- 1.0 x) (- (* 1.0 1.0) (* x x))) (- 1.0 x))

series162.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (- 1.0 x) (- (* 1.0 1.0) (* x x)))
71.0ms	(sqrt (* (/ (- 1.0 x) (- (* 1.0 1.0) (* x x))) (- 1.0 x)))
4.0ms	(atan (sqrt (* (/ (- 1.0 x) (- (* 1.0 1.0) (* x x))) (- 1.0 x))))
50.0ms	(* (/ (- 1.0 x) (- (* 1.0 1.0) (* x x))) (- 1.0 x))

simplify76.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	543	1279
1	2498	1150
2	5001	1027

prune354.0ms

Filtered

136 candidates to 107 candidates (78.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	137	2	139

Merged error: 0b

Counts

139 → 2

localize12.0ms

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

108×	`*-un-lft-identity`
92×	`add-sqr-sqrt`
72×	`times-frac`
65×	`sqrt-prod`
46×	`add-cube-cbrt`
22×	`distribute-lft-out--` `difference-of-squares`
16×	`associate-/l*`
9×	`pow1` `associate-/r*` `distribute-lft-out`
8×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
5×	`flip3--` `flip--`
4×	`associate-/r/` `associate-/l/` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num` `div-inv` `pow-div`
1×	`flip3-+` `flip-+`

Counts

4 → 165

Calls

4 calls:

3.0ms	(sqrt (- 1.0 x))
3.0ms	(sqrt (- 1.0 x))
9.0ms	(/ (sqrt (- 1.0 x)) (+ 1.0 x))
12.0ms	(/ (sqrt (- 1.0 x)) (- 1.0 x))

series217.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (- 1.0 x))
31.0ms	(sqrt (- 1.0 x))
102.0ms	(/ (sqrt (- 1.0 x)) (+ 1.0 x))
53.0ms	(/ (sqrt (- 1.0 x)) (- 1.0 x))

simplify56.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	435	1360
1	1422	1279
2	5002	1241

prune433.0ms

Filtered

177 candidates to 111 candidates (62.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	177	2	179

Merged error: 0b

Counts

179 → 2

regimes15.0ms

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	14	10
1	14	10

end0.0ms

sample727.0ms

Algorithm

intervals

Results

321.0ms	8000×	body	80	valid
207.0ms	8139×	body	80	nan