Details

sample40.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
8.0ms	231×	body	80	nan

simplify439.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

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

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite34.0ms

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:

1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
18.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
10.0ms	(/ (- 1.0 x) (+ 1.0 x))

series21.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
5.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
12.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify40.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (31.0ms)

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

prune163.0ms

Filtered

100 candidates to 70 candidates (30.0%)

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

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- 1.0 x) (+ x 1.0)))
0.0b	(/ (- 1.0 x) (+ x 1.0))
0.0b	(cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))
0.0b	(pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

183×	`*-un-lft-identity`
130×	`sqrt-prod`
124×	`add-sqr-sqrt`
121×	`times-frac`
71×	`add-cube-cbrt`
64×	`cbrt-prod`
58×	`unpow-prod-down` `cube-prod`
31×	`distribute-lft-out`
25×	`distribute-lft-out--` `difference-of-squares`
12×	`associate-/r/`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`flip3-+` `flip-+` `div-inv`
5×	`associate-/l*`
4×	`associate-/r*` `add-log-exp`
3×	`pow-unpow` `pow-pow` `sqrt-div`
2×	`cube-div` `cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `flip3--` `frac-2neg` `pow1/3` `div-sub` `div-exp` `pow-exp` `clear-num` `sqrt-pow2` `flip--` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 237

Calls

4 calls:

8.0ms	(sqrt (/ (- 1.0 x) (+ x 1.0)))
7.0ms	(/ (- 1.0 x) (+ x 1.0))
12.0ms	(cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))
11.0ms	(pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)

series20.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (/ (- 1.0 x) (+ x 1.0)))
3.0ms	(/ (- 1.0 x) (+ x 1.0))
5.0ms	(cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))
8.0ms	(pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)

simplify76.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	702	2237
1	2389	2095
2	5001	2063

prune312.0ms

Filtered

249 candidates to 121 candidates (51.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	249	0	249
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	249	2	251

Merged error: 0b

Counts

251 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt` `*-un-lft-identity`
56×	`sqrt-prod`
42×	`times-frac`
33×	`add-cube-cbrt`
21×	`associate-r`
12×	`pow1`
10×	`add-exp-log` `sqrt-div` `distribute-lft-out`
8×	`associate-l` `add-cbrt-cube` `unswap-sqr`
6×	`sqrt-pow1` `associate-/r/`
4×	`rem-sqrt-square` `pow1/2` `associate-/r*` `add-log-exp`
3×	`flip3--` `flip3-+` `pow-prod-down` `flip--` `flip-+` `div-inv` `associate-/l*`
2×	`frac-times` `pow-flip` `div-exp` `associate-*l/` `distribute-lft-out--` `inv-pow` `difference-of-squares`
1×	`cbrt-undiv` `rec-exp` `frac-2neg` `sqrt-unprod` `1-exp` `associate-r/` `prod-exp` `clear-num` `-commutative` `cbrt-unprod`

Counts

4 → 143

Calls

4 calls:

3.0ms	(sqrt (- 1.0 x))
5.0ms	(sqrt (/ 1 (+ 1.0 x)))
5.0ms	(/ 1 (+ 1.0 x))
15.0ms	(* (sqrt (- 1.0 x)) (sqrt (/ 1 (+ 1.0 x))))

series15.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (- 1.0 x))
5.0ms	(sqrt (/ 1 (+ 1.0 x)))
2.0ms	(/ 1 (+ 1.0 x))
5.0ms	(* (sqrt (- 1.0 x)) (sqrt (/ 1 (+ 1.0 x))))

simplify59.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	536	1073
1	2011	970
2	5001	917

prune210.0ms

Filtered

155 candidates to 93 candidates (40.0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	155	2	157

Merged error: 0b

Counts

157 → 2

regimes29.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	14	8
1	14	8

end0.0ms

sample906.0ms

Algorithm

intervals

Results

384.0ms	8000×	body	80	valid
261.0ms	7744×	body	80	nan

Details

sample40.0ms

simplify439.0ms

prune4.0ms

localize11.0ms

rewrite34.0ms

series21.0ms

simplify40.0ms

prune163.0ms

localize11.0ms

rewrite52.0ms

series20.0ms

simplify76.0ms

prune312.0ms

localize10.0ms

rewrite33.0ms

series15.0ms

simplify59.0ms

prune210.0ms

regimes29.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample906.0ms

Profiling