Details

sample44.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
10.0ms	261×	body	80	nan

simplify431.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	16	6
1	19	6
2	21	6
3	21	6

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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

rewrite35.0ms

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:

18.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
9.0ms	(/ (- 1.0 x) (+ 1.0 x))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series19.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
4.0ms	(/ (- 1.0 x) (+ 1.0 x))
9.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify39.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	354	753
1	1071	709
2	5001	688

prune173.0ms

Filtered

100 candidates to 70 candidates (30.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	98	3	101

Merged error: 0.0b

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))

rewrite22.0ms

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:

8.0ms	(/ (- 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))

series32.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ (- 1.0 x) (cbrt (+ 1.0 x)))
6.0ms	(cbrt (+ 1.0 x))
6.0ms	(cbrt (+ 1.0 x))
8.0ms	(cbrt (+ 1.0 x))

simplify43.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	428	1022
1	1185	984
2	5001	897

prune316.0ms

Filtered

118 candidates to 91 candidates (22.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Merged error: 0.0b

Counts

121 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

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×	`associate-/r*` `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 → 97

Calls

4 calls:

1.0ms	(atan (sqrt (/ (- 1.0 x) (+ x 1.0))))
7.0ms	(/ (- 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)

series17.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(atan (sqrt (/ (- 1.0 x) (+ x 1.0))))
3.0ms	(/ (- 1.0 x) (+ x 1.0))
2.0ms	(cbrt (pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) 3))
11.0ms	(pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) 3)

simplify43.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	306	810
1	1133	765
2	5002	753

prune164.0ms

Filtered

109 candidates to 63 candidates (42.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	109	3	112

Merged error: 0b

Counts

112 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

23×	`unpow-prod-down`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`pow-unpow`
11×	`cbrt-prod`
7×	`add-exp-log`
6×	`sqrt-prod`
5×	`pow1` `pow-exp` `sqr-pow`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp`
2×	`pow-pow`
1×	`pow1/3`

Counts

4 → 72

Calls

4 calls:

1.0ms	(atan (sqrt (/ (- 1.0 x) (+ x 1.0))))
2.0ms	(pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) (sqrt 3))
3.0ms	(cbrt (pow (pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) (sqrt 3)) (sqrt 3)))
4.0ms	(pow (pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) (sqrt 3)) (sqrt 3))

series193.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan (sqrt (/ (- 1.0 x) (+ x 1.0))))
29.0ms	(pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) (sqrt 3))
100.0ms	(cbrt (pow (pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) (sqrt 3)) (sqrt 3)))
62.0ms	(pow (pow (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))) (sqrt 3)) (sqrt 3))

simplify55.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	172	1031
1	496	963
2	1623	959
3	5002	956

prune215.0ms

Filtered

84 candidates to 53 candidates (36.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	84	3	87

Merged error: 0b

Counts

87 → 3

regimes147.0ms

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	11	6
1	11	6

end0.0ms

sample952.0ms

Algorithm

intervals

Results

401.0ms	8000×	body	80	valid
277.0ms	7994×	body	80	nan

Details

sample44.0ms

simplify431.0ms

prune5.0ms

localize10.0ms

rewrite35.0ms

series19.0ms

simplify39.0ms

prune173.0ms

localize12.0ms

rewrite22.0ms

series32.0ms

simplify43.0ms

prune316.0ms

localize10.0ms

rewrite15.0ms

series17.0ms

simplify43.0ms

prune164.0ms

localize19.0ms

rewrite12.0ms

series193.0ms

simplify55.0ms

prune215.0ms

regimes147.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample952.0ms

Profiling