Details

analyze12.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

sample212.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify463.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	786	11
1	786	11

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))

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:

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

series37.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
24.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
10.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify35.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5097	1256

prune162.0ms

Filtered

68 candidates to 100 candidates (-47.1%)

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

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

56×	`sqrt-prod`
51×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
30×	`times-frac`
24×	`add-cube-cbrt`
21×	`associate-r`
11×	`pow1`
10×	`sqrt-div`
8×	`associate-l` `unswap-sqr`
6×	`add-exp-log` `sqrt-pow1` `add-cbrt-cube` `distribute-lft-out`
4×	`rem-sqrt-square` `pow1/2` `associate-/r/` `add-log-exp`
3×	`flip3--` `pow-prod-down` `flip--`
2×	`frac-times` `flip3-+` `associate-*l/` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`pow-flip` `sqrt-unprod` `associate-r/` `prod-exp` `-commutative` `cbrt-unprod` `inv-pow`

Counts

4 → 113

Calls

4 calls:

1.0ms	(atan (* (sqrt (- 1.0 x)) (sqrt (/ 1 (+ 1.0 x)))))
3.0ms	(sqrt (- 1.0 x))
5.0ms	(sqrt (/ 1 (+ 1.0 x)))
16.0ms	(* (sqrt (- 1.0 x)) (sqrt (/ 1 (+ 1.0 x))))

series15.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan (* (sqrt (- 1.0 x)) (sqrt (/ 1 (+ 1.0 x)))))
4.0ms	(sqrt (- 1.0 x))
5.0ms	(sqrt (/ 1 (+ 1.0 x)))
5.0ms	(* (sqrt (- 1.0 x)) (sqrt (/ 1 (+ 1.0 x))))

simplify45.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4961	1541
1	4961	1541

prune204.0ms

Filtered

84 candidates to 125 candidates (-48.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	125	3	128

Merged error: 0b

Counts

128 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

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) (+ 1.0 x)))
12.0ms	(cbrt (pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3))
10.0ms	(/ (- 1.0 x) (+ 1.0 x))
11.0ms	(pow (sqrt (/ (- 1.0 x) (+ 1.0 x))) 3)

series20.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify74.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5148	3732

prune313.0ms

Filtered

119 candidates to 249 candidates (-109.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	249	0	249
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	249	3	252

Merged error: 0b

Counts

252 → 3

regimes141.0ms

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	21	11
1	21	11

end0.0ms

sample491.0ms

Algorithm

intervals

Results

389.0ms

8000×

body

valid

Details

analyze12.0ms

sample212.0ms

simplify463.0ms

prune4.0ms

localize10.0ms

rewrite22.0ms

series37.0ms

simplify35.0ms

prune162.0ms

localize10.0ms

rewrite29.0ms

series15.0ms

simplify45.0ms

prune204.0ms

localize11.0ms

rewrite54.0ms

series20.0ms

simplify74.0ms

prune313.0ms

regimes141.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample491.0ms

Profiling