Details

sample290.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
6.0ms	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))

rewrite29.0ms

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:

10.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
14.0ms	(/ (- 1.0 x) (+ 1.0 x))

series147.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
53.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify42.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (32.0ms)

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

prune236.0ms

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)))

rewrite113.0ms

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:

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))
64.0ms	(- (/ 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)))))
25.0ms	(/ 1.0 (+ x 1.0))
61.0ms	(- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))

simplify146.0ms

Algorithm

egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 2 (67.0ms)

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

prune582.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (+ x 1.0))
0.0b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
0.8b	(pow (/ (cbrt x) (cbrt (+ x 1.0))) 3)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

101×	`cbrt-prod`
90×	`*-un-lft-identity`
84×	`times-frac`
62×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`unpow-prod-down` `cube-prod`
14×	`distribute-lft-out`
8×	`cbrt-div`
7×	`add-exp-log`
5×	`pow1` `add-cbrt-cube`
4×	`expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`pow-exp` `div-inv` `rem-cube-cbrt`
1×	`cbrt-undiv` `cube-div` `cube-mult` `pow-to-exp` `pow-pow` `unpow3` `div-exp` `sqr-pow`

Counts

4 → 163

Calls

4 calls:

2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
16.0ms	(pow (/ (cbrt x) (cbrt (+ x 1.0))) 3)

series562.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(cbrt (+ x 1.0))
85.0ms	(cbrt (+ x 1.0))
171.0ms	(cbrt x)
220.0ms	(pow (/ (cbrt x) (cbrt (+ x 1.0))) 3)

simplify96.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	837	1671
1	3990	1244
2	5001	1236

prune483.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

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` `expm1-log1p-u` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

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

series338.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(cbrt (+ x 1.0))
84.0ms	(cbrt (+ x 1.0))
84.0ms	(cbrt (+ x 1.0))
85.0ms	(cbrt (+ x 1.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	182	504
1	504	472
2	1701	432
3	5001	420

prune282.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes18.0ms

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	37	31
1	37	31

end0.0ms

sample706.0ms

Algorithm

intervals

Results

309.0ms	8000×	body	80	valid
207.0ms	8112×	body	80	nan