Details

sample342.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
8.0ms	263×	body	80	nan

simplify11.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

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))

rewrite49.0ms

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:

17.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
26.0ms	(/ (- 1.0 x) (+ 1.0 x))

series136.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
46.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify42.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (31.0ms)

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

prune232.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

582×	`*-un-lft-identity`
484×	`times-frac`
332×	`add-sqr-sqrt`
324×	`prod-diff`
320×	`add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/r/`
41×	`flip3-+` `flip-+` `div-inv`
18×	`fma-neg`
8×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
7×	`distribute-lft-out--`
6×	`associate-/l*` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`distribute-rgt-out--`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

4 → 451

Calls

4 calls:

1.0ms	(atan (sqrt (- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))))
10.0ms	(/ 1.0 (+ x 1.0))
12.0ms	(/ x (+ x 1.0))
91.0ms	(- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))

series120.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan (sqrt (- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))))
26.0ms	(/ 1.0 (+ x 1.0))
32.0ms	(/ x (+ x 1.0))
59.0ms	(- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))

simplify145.0ms

Algorithm

egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	1032	11091
1	3079	8021
2	5001	7159

prune576.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))
0.0b	(pow (/ 1.0 (+ x 1.0)) 3)
0.0b	(pow (/ x (+ x 1.0)) 3)

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

157×	`*-un-lft-identity`
124×	`times-frac`
95×	`add-sqr-sqrt`
83×	`add-cube-cbrt`
36×	`unpow-prod-down` `cube-prod`
34×	`distribute-lft-out`
24×	`add-exp-log` `swap-sqr` `add-cbrt-cube`
18×	`associate-r` `associate-l` `associate-/r/`
13×	`pow1`
9×	`flip3-+` `flip-+` `div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`pow-unpow`
4×	`expm1-log1p-u` `pow-exp` `prod-exp` `associate-/r*` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `rem-cube-cbrt` `unswap-sqr`
3×	`associate-/l*`
2×	`cube-div` `cube-mult` `pow-to-exp` `pow-pow` `unpow3` `sqr-pow`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 241

Calls

4 calls:

10.0ms	(/ x (+ x 1.0))
50.0ms	(* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))
13.0ms	(pow (/ 1.0 (+ x 1.0)) 3)
16.0ms	(pow (/ x (+ x 1.0)) 3)

series169.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ x (+ x 1.0))
37.0ms	(* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))
45.0ms	(pow (/ 1.0 (+ x 1.0)) 3)
56.0ms	(pow (/ x (+ x 1.0)) 3)

simplify46.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	969	1643
1	5002	1398

prune654.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	24
1	20	24

end0.0ms

sample797.0ms

Algorithm

intervals

Results

308.0ms	8000×	body	80	valid
212.0ms	8416×	body	80	nan