Details

sample283.0ms

Algorithm

intervals

Results

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

simplify14.0ms

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

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))

rewrite25.0ms

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:

8.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
11.0ms	(/ (- 1.0 x) (+ 1.0 x))

series157.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
56.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify43.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (32.0ms)

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

prune202.0ms

Filtered

106 candidates to 76 candidates (71.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	3	107

Merged error: 0b

Counts

107 → 3

localize13.0ms

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))

rewrite25.0ms

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` `expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `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 → 114

Calls

4 calls:

12.0ms	(/ (- 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))

series405.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- 1.0 x) (cbrt (+ 1.0 x)))
87.0ms	(cbrt (+ 1.0 x))
88.0ms	(cbrt (+ 1.0 x))
92.0ms	(cbrt (+ 1.0 x))

simplify53.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	447	991
1	1318	952
2	5002	938

prune344.0ms

Filtered

126 candidates to 102 candidates (81.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	126	3	129

Merged error: 0b

Counts

129 → 3

localize10.0ms

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)

rewrite40.0ms

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×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `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 → 201

Calls

4 calls:

1.0ms	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))))
9.0ms	(/ (- 1.0 x) (+ 1.0 x))
11.0ms	(cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))
10.0ms	(pow (/ (- 1.0 x) (+ 1.0 x)) 3)

series134.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))))
37.0ms	(/ (- 1.0 x) (+ 1.0 x))
33.0ms	(cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))
63.0ms	(pow (/ (- 1.0 x) (+ 1.0 x)) 3)

simplify77.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	589	1594
1	2524	1477
2	5001	1459

prune288.0ms

Filtered

213 candidates to 101 candidates (47.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	213	3	216

Merged error: 0b

Counts

216 → 3

localize13.0ms

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))))

rewrite69.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 183

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))))))
41.0ms	(* (/ (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (sqrt (+ 1.0 x))) (/ (cbrt (- 1.0 x)) (sqrt (+ 1.0 x))))

series395.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (- 1.0 x))
260.0ms	(/ (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (sqrt (+ 1.0 x)))
3.0ms	(atan (sqrt (* (/ (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (sqrt (+ 1.0 x))) (/ (cbrt (- 1.0 x)) (sqrt (+ 1.0 x))))))
39.0ms	(* (/ (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (sqrt (+ 1.0 x))) (/ (cbrt (- 1.0 x)) (sqrt (+ 1.0 x))))

simplify115.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	962	2914
1	4566	2668
2	5001	2665

prune490.0ms

Filtered

195 candidates to 138 candidates (70.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	195	3	198

Merged error: 0b

Counts

198 → 3

regimes29.0ms

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

sample850.0ms

Algorithm

intervals

Results

378.0ms	8000×	body	80	valid
271.0ms	7999×	body	80	nan