Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

sample32.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
3.0ms	72×	body	80	nan
1.0ms	27×	body	80	invalid

simplify32.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	805	14
1	805	14

prune23.0ms

Filtered

1 candidates to 1 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: 20.7b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
1.2b	(* y (/ z (sqrt (- (* z z) (* t a)))))
2.4b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
24.6b	(sqrt (- (* z z) (* t a)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
12×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l` `add-log-exp`
4×	`sqrt-div` `pow-prod-down`
3×	`flip3--` `associate-*r/` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `*-commutative`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-inv`

Counts

4 → 91

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
11.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
18.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
7.0ms	(sqrt (- (* z z) (* t a)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
21.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
30.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify44.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4973	1238
1	4973	1238

prune163.0ms

Filtered

70 candidates to 103 candidates (-47.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	95	10	105

Merged error: 3.2b

Counts

105 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

2.4b	(* x (* (* y (* (cbrt z) (/ (cbrt z) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
24.6b	(sqrt (- (* z z) (* t a)))
24.6b	(sqrt (- (* z z) (* t a)))
24.6b	(sqrt (- (* z z) (* t a)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log`
37×	`prod-exp` `add-cbrt-cube` `cbrt-unprod`
21×	`pow1`
11×	`add-sqr-sqrt`
10×	`pow-prod-down`
9×	`cbrt-undiv` `div-exp` `sqrt-prod`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r/`
6×	`sqrt-div`
4×	`add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-l` `flip--`
1×	`frac-times` `associate-r` `associate-l/` `-commutative`

Counts

4 → 86

Calls

4 calls:

31.0ms	(* x (* (* y (* (cbrt z) (/ (cbrt z) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* x (* (* y (* (cbrt z) (/ (cbrt z) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
21.0ms	(sqrt (- (* z z) (* t a)))
26.0ms	(sqrt (- (* z z) (* t a)))
22.0ms	(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	6093	1175

prune120.0ms

Filtered

62 candidates to 98 candidates (-58.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	98	10	108

Merged error: 3.2b

Counts

108 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.2b	(- (* z z) (* t a))
3.1b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.6b	(sqrt (- (* z z) (* t a)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-r` `sqrt-prod`
18×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
6×	`sqrt-div` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
4×	`flip3--` `associate-/r/` `flip--`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*`
2×	`div-inv`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `associate-l` `clear-num` `-commutative`

Counts

4 → 111

Calls

4 calls:

6.0ms	(/ z (sqrt (- (* z z) (* t a))))
4.0ms	(- (* z z) (* t a))
12.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ z (sqrt (- (* z z) (* t a))))
7.0ms	(- (* z z) (* t a))
31.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5256	1640

prune137.0ms

Filtered

85 candidates to 123 candidates (-44.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	121	12	133

Merged error: 3.2b

Counts

133 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))
3.1b	(* (* x y) (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))))
25.3b	(cbrt (- (* z z) (* t a)))
25.3b	(cbrt (- (* z z) (* t a)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log` `add-cbrt-cube`
18×	`add-sqr-sqrt` `associate-r`
12×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp` `cbrt-unprod`
11×	`pow1`
10×	`cbrt-prod`
8×	`cbrt-div` `sqrt-prod`
5×	`associate-*r/`
4×	`cbrt-undiv` `flip3--` `sqrt-div` `div-exp` `associate-l` `pow-prod-down` `flip--` `add-log-exp`
3×	`times-frac` `unswap-sqr`
2×	`pow1/3` `associate-/r/` `*-commutative`
1×	`div-inv`

Counts

4 → 87

Calls

4 calls:

11.0ms	(* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))
12.0ms	(* (* x y) (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))))
4.0ms	(cbrt (- (* z z) (* t a)))
4.0ms	(cbrt (- (* z z) (* t a)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))
89.0ms	(* (* x y) (/ z (* (fabs (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))))
24.0ms	(cbrt (- (* z z) (* t a)))
23.0ms	(cbrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5003	1993

prune114.0ms

Filtered

77 candidates to 99 candidates (-28.6%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	2	7	9
Picked	0	1	1
Done	0	2	2
Total	99	12	111

Merged error: 3.2b

Counts

111 → 12

regimes1.1s

Accuracy

84.8% (2.9b remaining)

Error of 6.2b against oracle of 3.2b and baseline of 22.6b

bsearch52.0ms

Steps

Iters	Range		Point
9	6.394088315654496e+133	1.7943580247488647e+141	1.2713248643122116e+134
10	-2.2207467811401345e+99	-5.309336657314481e+86	-9.892107016045583e+95

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	85	80
1	85	80

end0.0ms

sample955.0ms

Algorithm

intervals

Results

422.0ms	8000×	body	80	valid
113.0ms	2136×	body	80	nan
50.0ms	910×	body	80	invalid

Details

analyze1.1s

sample32.0ms

simplify32.0ms

prune23.0ms

localize17.0ms

rewrite43.0ms

series71.0ms

simplify44.0ms

prune163.0ms

localize22.0ms

rewrite47.0ms

series127.0ms

simplify61.0ms

prune120.0ms

localize13.0ms

rewrite30.0ms

series65.0ms

simplify56.0ms

prune137.0ms

localize14.0ms

rewrite33.0ms

series174.0ms

simplify56.0ms

prune114.0ms

regimes1.1s

bsearch52.0ms

simplify2.0ms

end0.0ms

sample955.0ms

Profiling