Details

sample43.0ms

Algorithm

intervals

Results

14.0ms	276×	body	80	valid
5.0ms	97×	body	80	nan

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	45	7
2	67	7
3	94	7
4	115	7
5	115	7

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: 21.7b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
3.5b	(* (* x y) z)
8.6b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.6b	(sqrt (- (* z z) (* t a)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
5.0ms	(* (* x y) z)
9.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms	(sqrt (- (* z z) (* t a)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
6.0ms	(* (* x y) z)
31.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
16.0ms	(sqrt (- (* z z) (* t a)))

simplify57.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	343	583
1	1850	515
2	5003	510

prune141.0ms

Filtered

88 candidates to 60 candidates (31.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Merged error: 3.2b

Counts

89 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ z (sqrt (- (* z z) (* t a))))
0.4b	(- (* z z) (* t a))
2.9b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
22.6b	(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 → 112

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:

11.0ms	(/ z (sqrt (- (* z z) (* t a))))
10.0ms	(- (* z z) (* t a))
31.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
14.0ms	(sqrt (- (* z z) (* t a)))

simplify66.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	428	1014
1	2153	912
2	5002	894

prune134.0ms

Filtered

124 candidates to 83 candidates (33.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	123	10	133

Merged error: 3.2b

Counts

133 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

4.0b	(/ (* (* x y) z) (sqrt (sqrt (- (* z z) (* t a)))))
4.7b	(/ (/ (* (* x y) z) (sqrt (sqrt (- (* z z) (* t a))))) (sqrt (sqrt (- (* z z) (* t a)))))
22.6b	(sqrt (- (* z z) (* t a)))
22.6b	(sqrt (- (* z z) (* t a)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

258×	`sqrt-prod`
234×	`times-frac`
102×	`add-sqr-sqrt`
100×	`add-cube-cbrt` `*-un-lft-identity`
52×	`sqrt-div`
27×	`add-exp-log` `add-cbrt-cube`
24×	`associate-/r/`
18×	`associate-/r*`
16×	`associate-/l*`
14×	`flip3--` `flip--`
12×	`div-inv`
10×	`cbrt-undiv` `div-exp`
6×	`pow1` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 247

Calls

4 calls:

13.0ms	(/ (* (* x y) z) (sqrt (sqrt (- (* z z) (* t a)))))
20.0ms	(/ (/ (* (* x y) z) (sqrt (sqrt (- (* z z) (* t a))))) (sqrt (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series113.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (* (* x y) z) (sqrt (sqrt (- (* z z) (* t a)))))
33.0ms	(/ (/ (* (* x y) z) (sqrt (sqrt (- (* z z) (* t a))))) (sqrt (sqrt (- (* z z) (* t a)))))
13.0ms	(sqrt (- (* z z) (* t a)))
14.0ms	(sqrt (- (* z z) (* t a)))

simplify127.0ms

Algorithm

egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	831	5182
1	4148	4613
2	5002	4613

prune186.0ms

Filtered

259 candidates to 128 candidates (50.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	259	0	259
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	259	10	269

Merged error: 3.2b

Counts

269 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

3.5b	(* (* x y) z)
8.6b	(/ (* (* x y) z) (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))
22.6b	(sqrt (- (* z z) (* t a)))
22.6b	(sqrt (- (* z z) (* t a)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log` `add-cbrt-cube`
28×	`sqrt-div`
12×	`prod-exp` `cbrt-unprod`
11×	`pow1`
9×	`add-sqr-sqrt`
8×	`flip3--` `associate-/r/` `flip--`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-undiv` `div-exp` `sqrt-prod`
4×	`frac-times` `add-log-exp`
3×	`associate-r` `pow-prod-down`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/`
1×	`frac-2neg` `times-frac` `associate-l` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 81

Calls

4 calls:

5.0ms	(* (* x y) z)
18.0ms	(/ (* (* x y) z) (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (* x y) z)
36.0ms	(/ (* (* x y) z) (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))
13.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify64.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	406	879
1	2251	691
2	5003	668

prune83.0ms

Filtered

93 candidates to 63 candidates (32.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	93	10	103

Merged error: 3.2b

Counts

103 → 10

regimes717.0ms

Accuracy

78% (4.4b remaining)

Error of 7.8b against oracle of 3.4b and baseline of 23.3b

bsearch62.0ms

Steps

Iters	Range		Point
7	6.860257456123676e+152	7.801608759782197e+154	6.971836867194791e+152
10	-1.6058317493978785e+96	-1.3384162769677997e+85	-1.6523033549097704e+92

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	17
1	33	17
2	33	17

end0.0ms

sample1.2s

Algorithm

intervals

Results

460.0ms	8867×	body	80	valid
151.0ms	2987×	body	80	nan

Details

sample43.0ms

simplify11.0ms

prune5.0ms

localize11.0ms

rewrite23.0ms

series60.0ms

simplify57.0ms

prune141.0ms

localize11.0ms

rewrite30.0ms

series65.0ms

simplify66.0ms

prune134.0ms

localize13.0ms

rewrite55.0ms

series113.0ms

simplify127.0ms

prune186.0ms

localize16.0ms

rewrite34.0ms

series68.0ms

simplify64.0ms

prune83.0ms

regimes717.0ms

bsearch62.0ms

simplify3.0ms

end0.0ms

sample1.2s

Profiling