Details

sample298.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
11.0ms	230×	body	80	nan

simplify11.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite31.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 97

Calls

3 calls:

11.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
15.0ms	(/ (- 1.0 x) (+ 1.0 x))

series145.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
49.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify41.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	370	779
1	1128	734
2	5001	719

prune234.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

675×	`sqrt-prod`
589×	`*-un-lft-identity`
528×	`times-frac`
518×	`add-sqr-sqrt`
229×	`add-cube-cbrt`
138×	`swap-sqr`
82×	`distribute-lft-out`
75×	`distribute-lft-out--`
62×	`associate-r` `associate-l`
53×	`difference-of-squares`
25×	`unswap-sqr`
20×	`add-exp-log` `add-cbrt-cube`
18×	`sqrt-div`
16×	`associate-/l*`
14×	`associate-/r*`
12×	`pow1` `associate-/r/`
6×	`cbrt-undiv` `sqrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`flip3--` `flip--`
2×	`frac-2neg` `clear-num`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `sqrt-unprod` `associate-r/` `pow-prod-down` `associate-l/` `rem-square-sqrt` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 514

Calls

4 calls:

5.0ms	(sqrt (- 1.0 x))
13.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
13.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
116.0ms	(* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))

series254.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (- 1.0 x))
90.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
91.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
41.0ms	(* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))

simplify87.0ms

Algorithm

egg-herbie

Counts

526 → 526

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	985	7873
1	5001	6759

prune837.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

170×	`add-sqr-sqrt`
169×	`times-frac`
159×	`*-un-lft-identity`
106×	`add-exp-log`
102×	`sqrt-prod`
85×	`add-cube-cbrt`
49×	`prod-exp`
41×	`swap-sqr`
36×	`add-cbrt-cube`
34×	`pow1` `div-exp`
32×	`associate-l`
28×	`associate-r`
27×	`pow-flip`
26×	`unswap-sqr`
22×	`distribute-lft-out`
17×	`rec-exp` `1-exp`
13×	`cbrt-unprod`
12×	`frac-times`
10×	`sqrt-div` `associate-/r/`
9×	`cbrt-undiv` `sqrt-pow1` `pow1/2` `pow-prod-up` `inv-pow`
8×	`associate-*r/` `pow-prod-down`
7×	`associate-/r*` `div-inv`
6×	`associate-*l/`
5×	`flip3--` `flip3-+` `pow-sqr` `flip--` `flip-+`
4×	`expm1-log1p-u` `un-div-inv` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`*-commutative`
1×	`pow2` `frac-2neg` `pow-plus` `clear-num` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 292

Calls

4 calls:

7.0ms	(/ 1 (sqrt (+ 1.0 x)))
0.0ms	(atan (sqrt (* (- 1.0 x) (* (/ 1 (sqrt (+ 1.0 x))) (/ 1 (sqrt (+ 1.0 x)))))))
49.0ms	(* (/ 1 (sqrt (+ 1.0 x))) (/ 1 (sqrt (+ 1.0 x))))
62.0ms	(* (- 1.0 x) (* (/ 1 (sqrt (+ 1.0 x))) (/ 1 (sqrt (+ 1.0 x)))))

series114.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ 1 (sqrt (+ 1.0 x)))
2.0ms	(atan (sqrt (* (- 1.0 x) (* (/ 1 (sqrt (+ 1.0 x))) (/ 1 (sqrt (+ 1.0 x)))))))
23.0ms	(* (/ 1 (sqrt (+ 1.0 x))) (/ 1 (sqrt (+ 1.0 x))))
33.0ms	(* (- 1.0 x) (* (/ 1 (sqrt (+ 1.0 x))) (/ 1 (sqrt (+ 1.0 x)))))

simplify123.0ms

Algorithm

egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	929	2996
1	4794	2381
2	5001	2381

prune441.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes14.0ms

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	18	12
1	18	12

end0.0ms

sample1.1s

Algorithm

intervals

Results

520.0ms	8000×	body	80	valid
361.0ms	7977×	body	80	nan