Details

sample275.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
8.0ms	288×	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

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite23.0ms

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	(/ (- 1.0 x) (+ 1.0 x))
9.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series157.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ (- 1.0 x) (+ 1.0 x))
110.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
9.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify43.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (31.0ms)

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

prune206.0ms

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

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

85×	`sqrt-prod`
78×	`*-un-lft-identity`
62×	`add-sqr-sqrt`
56×	`times-frac`
40×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`sqrt-div` `associate-/l*`
7×	`associate-/r*`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `frac-2neg` `div-exp` `clear-num` `hypot-def` `div-inv`

Counts

4 → 137

Calls

4 calls:

4.0ms	(sqrt (- 1.0 x))
3.0ms	(sqrt (+ 1.0 x))
10.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
3.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))

series167.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (- 1.0 x))
32.0ms	(sqrt (+ 1.0 x))
100.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
2.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))

simplify46.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	372	1291
1	1144	1218
2	5002	1156

prune257.0ms

Filtered

149 candidates to 89 candidates (59.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	149	3	152

Merged error: 0b

Counts

152 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
20×	`times-frac`
12×	`cbrt-prod`
7×	`add-exp-log` `add-cbrt-cube`
6×	`unpow-prod-down` `cube-prod` `distribute-lft-out`
5×	`pow1` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `associate-/r/` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `flip3-+` `pow1/3` `div-sub` `div-exp` `pow-exp` `clear-num` `flip--` `rem-cbrt-cube` `flip-+` `div-inv` `rem-cube-cbrt`

Counts

4 → 105

Calls

4 calls:

9.0ms	(/ (- 1.0 x) (+ x 1.0))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ x 1.0))))
2.0ms	(cbrt (pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) 3))
2.0ms	(pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) 3)

series78.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- 1.0 x) (+ x 1.0))
2.0ms	(atan (sqrt (/ (- 1.0 x) (+ x 1.0))))
2.0ms	(cbrt (pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) 3))
40.0ms	(pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) 3)

simplify44.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	319	855
1	1176	809
2	5001	800

prune214.0ms

Filtered

117 candidates to 71 candidates (60.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	117	3	120

Merged error: 0b

Counts

120 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 x) (+ 1.0 x))
0.0b	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
1.0b	(log1p (atan (sqrt (/ (- 1.0 x) (+ 1.0 x)))))
1.0b	(expm1 (log1p (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
20×	`times-frac`
15×	`add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
5×	`expm1-log1p-u` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`pow1` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `flip3--` `frac-2neg` `flip3-+` `div-sub` `log1p-expm1` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `expm1-udef`

Counts

4 → 79

Calls

4 calls:

12.0ms	(/ (- 1.0 x) (+ 1.0 x))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
1.0ms	(log1p (atan (sqrt (/ (- 1.0 x) (+ 1.0 x)))))
1.0ms	(expm1 (log1p (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))

series230.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- 1.0 x) (+ 1.0 x))
2.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
76.0ms	(log1p (atan (sqrt (/ (- 1.0 x) (+ 1.0 x)))))
118.0ms	(expm1 (log1p (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))

simplify96.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	267	606
1	753	553
2	3245	549
3	5002	546

prune185.0ms

Filtered

91 candidates to 63 candidates (69.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	91	3	94

Merged error: 0b

Counts

94 → 3

regimes65.0ms

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	12	7
1	12	7

end0.0ms

sample699.0ms

Algorithm

intervals

Results

317.0ms	8000×	body	80	valid
195.0ms	7915×	body	80	nan