Details

sample37.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
10.0ms	241×	body	80	nan

simplify560.0ms

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

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	(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))

rewrite33.0ms

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))))
8.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
10.0ms	(/ (- 1.0 x) (+ 1.0 x))

series20.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
6.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
11.0ms	(/ (- 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	688

prune164.0ms

Filtered

70 candidates to 100 candidates (-42.9%)

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 (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3)))
0.0b	(/ (- 1.0 x) (+ 1.0 x))
0.0b	(cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))
0.1b	(pow (/ (- 1.0 x) (+ 1.0 x)) 3)

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

209×	`*-un-lft-identity`
145×	`add-sqr-sqrt`
142×	`times-frac`
122×	`cbrt-prod`
80×	`unpow-prod-down` `cube-prod`
79×	`add-cube-cbrt`
61×	`sqrt-prod`
36×	`distribute-lft-out`
29×	`distribute-lft-out--` `difference-of-squares`
14×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
7×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv`
6×	`pow1`
5×	`associate-/l*`
4×	`associate-/r*` `add-log-exp` `sqr-pow`
3×	`cube-div` `cube-mult` `pow-unpow` `unpow3`
2×	`cbrt-undiv` `cbrt-div` `sqrt-pow1` `pow1/3` `div-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt`
1×	`pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `pow1/2` `sqrt-div` `div-sub` `clear-num` `flip--` `rem-cbrt-cube`

Counts

4 → 265

Calls

4 calls:

15.0ms	(sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3)))
8.0ms	(/ (- 1.0 x) (+ 1.0 x))
11.0ms	(cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))
10.0ms	(pow (/ (- 1.0 x) (+ 1.0 x)) 3)

series14.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify87.0ms

Algorithm

egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	684	2359
1	2899	2188
2	5003	2131

prune304.0ms

Filtered

121 candidates to 277 candidates (-128.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	277	0	277
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	277	2	279

Merged error: 0b

Counts

279 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

254×	`sqrt-prod`
209×	`add-sqr-sqrt`
190×	`*-un-lft-identity`
177×	`times-frac`
92×	`add-cube-cbrt`
44×	`associate-r`
30×	`associate-l`
24×	`unswap-sqr`
23×	`distribute-lft-out`
22×	`distribute-lft-out--` `difference-of-squares`
15×	`sqrt-div`
14×	`associate-/r*`
12×	`add-exp-log`
11×	`pow1`
10×	`associate-/r/` `add-cbrt-cube`
8×	`associate-/l*`
5×	`flip3-+` `flip-+` `div-inv`
4×	`sqrt-pow1` `pow1/2` `add-log-exp`
3×	`rem-sqrt-square` `pow-flip` `div-exp` `pow-prod-down`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `rec-exp` `flip3--` `sqrt-unprod` `1-exp` `div-sub` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `inv-pow`

Counts

4 → 284

Calls

4 calls:

9.0ms	(sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))
6.0ms	(/ 1 (sqrt (+ 1.0 x)))
42.0ms	(* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x)))))
9.0ms	(/ (- 1.0 x) (sqrt (+ 1.0 x)))

series35.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))
4.0ms	(/ 1 (sqrt (+ 1.0 x)))
5.0ms	(* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x)))))
8.0ms	(/ (- 1.0 x) (sqrt (+ 1.0 x)))

simplify99.0ms

Algorithm

egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	981	3415
1	3740	3179
2	5001	3123

prune592.0ms

Filtered

157 candidates to 296 candidates (-88.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	296	0	296
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	296	2	298

Merged error: 0b

Counts

298 → 2

regimes51.0ms

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	8
1	14	8

end0.0ms

sample891.0ms

Algorithm

intervals

Results

372.0ms	8000×	body	80	valid
268.0ms	7787×	body	80	nan

Details

sample37.0ms

simplify560.0ms

prune4.0ms

localize10.0ms

rewrite33.0ms

series20.0ms

simplify40.0ms

prune164.0ms

localize11.0ms

rewrite62.0ms

series14.0ms

simplify87.0ms

prune304.0ms

localize12.0ms

rewrite87.0ms

series35.0ms

simplify99.0ms

prune592.0ms

regimes51.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample891.0ms

Profiling