Details

sample307.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
9.0ms	265×	body	80	nan

simplify13.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

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

localize11.0ms

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))

rewrite24.0ms

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:

8.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
10.0ms	(/ (- 1.0 x) (+ 1.0 x))

series150.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
57.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify44.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	354	753
1	1071	709
2	5001	690

prune188.0ms

Filtered

100 candidates to 70 candidates (70.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	3	101

Merged error: 0b

Counts

101 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

61×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
36×	`cbrt-prod`
35×	`times-frac`
27×	`add-cube-cbrt`
9×	`distribute-lft-out`
8×	`cbrt-div` `distribute-lft-out--` `difference-of-squares`
7×	`associate-/r*`
6×	`add-exp-log`
5×	`add-cbrt-cube` `associate-/l*`
4×	`pow1` `flip3-+` `flip-+` `add-log-exp`
3×	`pow1/3`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 106

Calls

4 calls:

9.0ms	(/ (- 1.0 x) (cbrt (+ 1.0 x)))
3.0ms	(cbrt (+ 1.0 x))
3.0ms	(cbrt (+ 1.0 x))
3.0ms	(cbrt (+ 1.0 x))

series386.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (- 1.0 x) (cbrt (+ 1.0 x)))
84.0ms	(cbrt (+ 1.0 x))
84.0ms	(cbrt (+ 1.0 x))
87.0ms	(cbrt (+ 1.0 x))

simplify48.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	428	970
1	1235	932
2	5001	923

prune305.0ms

Filtered

118 candidates to 94 candidates (79.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	118	3	121

Merged error: 0b

Counts

121 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

151×	`*-un-lft-identity`
100×	`times-frac`
99×	`add-sqr-sqrt`
58×	`cbrt-prod`
57×	`add-cube-cbrt`
52×	`unpow-prod-down` `cube-prod`
26×	`distribute-lft-out`
21×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3-+` `flip-+` `div-inv` `associate-/l*`
4×	`associate-/r*` `add-log-exp`
3×	`pow-unpow`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `div-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `div-sub` `clear-num` `flip--` `rem-cbrt-cube`

Counts

4 → 193

Calls

4 calls:

1.0ms	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))))
8.0ms	(/ (- 1.0 x) (+ 1.0 x))
14.0ms	(cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))
10.0ms	(pow (/ (- 1.0 x) (+ 1.0 x)) 3)

series129.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))))
32.0ms	(/ (- 1.0 x) (+ 1.0 x))
32.0ms	(cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))
62.0ms	(pow (/ (- 1.0 x) (+ 1.0 x)) 3)

simplify83.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	572	1553
1	2472	1443
2	5003	1425

prune255.0ms

Filtered

205 candidates to 93 candidates (45.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	205	3	208

Merged error: 0b

Counts

208 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
92×	`times-frac`
81×	`*-un-lft-identity`
62×	`associate-r`
55×	`sqrt-prod`
46×	`cbrt-prod`
43×	`add-cube-cbrt`
30×	`add-exp-log`
21×	`add-cbrt-cube`
15×	`unswap-sqr`
14×	`cbrt-div`
13×	`associate-l`
11×	`distribute-lft-out`
9×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
8×	`associate-/l/` `distribute-lft-out--` `difference-of-squares`
7×	`flip3--` `associate-/r*` `flip--`
6×	`pow1` `sqrt-div` `associate-/r/`
5×	`frac-times`
4×	`add-log-exp`
3×	`flip3-+` `associate-r/` `associate-l/` `flip-+` `div-inv`
1×	`frac-2neg` `pow1/3` `pow-prod-down` `clear-num` `-commutative` `associate-/l`

Counts

4 → 175

Calls

4 calls:

3.0ms	(cbrt (- 1.0 x))
14.0ms	(/ (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (sqrt (+ 1.0 x)))
1.0ms	(atan (sqrt (* (/ (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (sqrt (+ 1.0 x))) (/ (cbrt (- 1.0 x)) (sqrt (+ 1.0 x))))))
37.0ms	(* (/ (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (sqrt (+ 1.0 x))) (/ (cbrt (- 1.0 x)) (sqrt (+ 1.0 x))))

series388.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (- 1.0 x))
260.0ms	(/ (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (sqrt (+ 1.0 x)))
2.0ms	(atan (sqrt (* (/ (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (sqrt (+ 1.0 x))) (/ (cbrt (- 1.0 x)) (sqrt (+ 1.0 x))))))
33.0ms	(* (/ (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (sqrt (+ 1.0 x))) (/ (cbrt (- 1.0 x)) (sqrt (+ 1.0 x))))

simplify118.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	936	2831
1	4460	2588
2	5003	2370

prune400.0ms

Filtered

187 candidates to 116 candidates (62.0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	187	3	190

Merged error: 0b

Counts

190 → 3

regimes31.0ms

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	19	14
1	19	14

end0.0ms

sample846.0ms

Algorithm

intervals

Results

380.0ms	8000×	body	80	valid
267.0ms	7999×	body	80	nan