Details

sample292.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
7.0ms	254×	body	80	nan

simplify10.0ms

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

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))

rewrite28.0ms

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:

10.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
13.0ms	(/ (- 1.0 x) (+ 1.0 x))

series153.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
55.0ms	(/ (- 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	690

prune217.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
40×	`times-frac`
36×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
12×	`distribute-lft-out`
8×	`add-exp-log` `associate-/r*` `associate-/r/` `add-cbrt-cube`
7×	`distribute-lft-out--`
6×	`associate-/l*` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `div-inv` `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 → 101

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
0.0ms	(atan (sqrt (- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))))
5.0ms	(/ 1.0 (+ x 1.0))
48.0ms	(- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))

series122.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ x (+ x 1.0))
3.0ms	(atan (sqrt (- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))))
28.0ms	(/ 1.0 (+ x 1.0))
57.0ms	(- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))

simplify183.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	357	705
1	1162	658
2	4906	650
3	5002	650

prune256.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (/ x (+ x 1.0)) (+ (/ x (+ x 1.0)) (/ 1.0 (+ x 1.0)))) (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0))))
0.0b	(* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))
0.1b	(pow (/ 1.0 (+ x 1.0)) 3)
0.1b	(pow (/ x (+ x 1.0)) 3)

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

140×	`*-un-lft-identity`
112×	`times-frac`
86×	`add-sqr-sqrt`
74×	`add-cube-cbrt`
36×	`unpow-prod-down` `cube-prod`
30×	`distribute-lft-out`
27×	`frac-add`
24×	`swap-sqr`
22×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r` `associate-l`
17×	`frac-times` `associate-*r/`
16×	`associate-/r/`
15×	`flip3-+` `flip-+`
13×	`pow1`
11×	`associate-*l/`
8×	`div-inv`
6×	`cbrt-undiv` `pow-unpow` `div-exp` `add-log-exp`
4×	`pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`
2×	`cube-div` `cube-mult` `pow-to-exp` `associate-+l+` `pow-pow` `unpow3` `sqr-pow`
1×	`+-commutative` `pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `pow-prod-down` `sum-log` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 234

Calls

4 calls:

44.0ms	(+ (* (/ x (+ x 1.0)) (+ (/ x (+ x 1.0)) (/ 1.0 (+ x 1.0)))) (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0))))
33.0ms	(* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))
8.0ms	(pow (/ 1.0 (+ x 1.0)) 3)
8.0ms	(pow (/ x (+ x 1.0)) 3)

series245.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(+ (* (/ x (+ x 1.0)) (+ (/ x (+ x 1.0)) (/ 1.0 (+ x 1.0)))) (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0))))
34.0ms	(* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))
53.0ms	(pow (/ 1.0 (+ x 1.0)) 3)
60.0ms	(pow (/ x (+ x 1.0)) 3)

simplify62.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1377	2432
1	5002	2113

prune632.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (+ x 1.0))
0.0b	(cbrt (+ x 1.0))
0.0b	(cbrt (+ x 1.0))
0.0b	(cbrt (+ x 1.0))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod` `*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

4 → 56

Calls

4 calls:

2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))

series359.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (+ x 1.0))
89.0ms	(cbrt (+ x 1.0))
89.0ms	(cbrt (+ x 1.0))
92.0ms	(cbrt (+ x 1.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	173	484
1	465	456
2	1523	412
3	5002	412

prune256.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes16.0ms

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	23	25
1	23	25

end0.0ms

sample706.0ms

Algorithm

intervals

Results

310.0ms	8000×	body	80	valid
210.0ms	8112×	body	80	nan