Details

sample37.0ms

Algorithm

intervals

Results

16.0ms	283×	body	80	valid
5.0ms	94×	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

prune3.0ms

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: 24.4b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
3.8b	(* (* x y) z)
8.4b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.4b	(sqrt (- (* z z) (* t a)))

rewrite24.0ms

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)
10.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms	(sqrt (- (* z z) (* t a)))

series201.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* z z) (* t a))
26.0ms	(* (* x y) z)
84.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
58.0ms	(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	346	584
1	1863	515
2	5001	510

prune223.0ms

Filtered

88 candidates to 60 candidates (68.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	11	89

Merged error: 3.6b

Counts

89 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
1.0b	(- (* z z) (* t a))
2.6b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.4b	(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)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ z (sqrt (- (* z z) (* t a))))
32.0ms	(- (* z z) (* t a))
84.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
61.0ms	(sqrt (- (* z z) (* t a)))

simplify62.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	431	1015
1	2166	912
2	5002	893

prune258.0ms

Filtered

124 candidates to 81 candidates (65.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	124	11	135

Merged error: 3.3b

Counts

135 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

2.7b	(/ (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (- (* z z) (* t a)))))
3.7b	(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z))
24.2b	(cbrt (- (* z z) (* t a)))
24.2b	(cbrt (- (* z z) (* t a)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

413×	`times-frac`
157×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
114×	`sqrt-prod`
63×	`cbrt-prod`
34×	`add-exp-log` `add-cbrt-cube`
24×	`div-inv`
22×	`associate-/r*`
19×	`associate-/l*`
17×	`cbrt-undiv` `div-exp`
13×	`associate-/r/`
6×	`cbrt-div`
4×	`pow1` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`flip3--` `flip--`
2×	`frac-2neg` `pow1/3` `sqrt-div` `clear-num`
1×	`associate-/l/`

Counts

4 → 284

Calls

4 calls:

19.0ms	(/ (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (- (* z z) (* t a)))))
7.0ms	(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z))
4.0ms	(cbrt (- (* z z) (* t a)))
4.0ms	(cbrt (- (* z z) (* t a)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(/ (/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (- (* z z) (* t a)))))
64.0ms	(/ (* x y) (/ (fabs (cbrt (- (* z z) (* t a)))) z))
83.0ms	(cbrt (- (* z z) (* t a)))
87.0ms	(cbrt (- (* z z) (* t a)))

simplify75.0ms

Algorithm

egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1261	6499
1	5001	6166

prune919.0ms

Filtered

296 candidates to 223 candidates (75.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	292	4	296
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	296	11	307

Merged error: 3.3b

Counts

307 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

3.6b	(* (/ x (/ (fabs (cbrt (cbrt (- (* z z) (* t a))))) y)) (/ (/ 1 (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (cbrt (- (* z z) (* t a)))))))
24.2b	(cbrt (- (* z z) (* t a)))
24.2b	(cbrt (- (* z z) (* t a)))
24.2b	(cbrt (- (* z z) (* t a)))

rewrite459.0ms

Algorithm

rewrite-expression-head

Rules

1581×	`times-frac`
936×	`add-sqr-sqrt`
663×	`*-un-lft-identity`
639×	`add-cube-cbrt`
534×	`associate-r`
450×	`cbrt-prod`
441×	`sqrt-prod`
112×	`add-exp-log`
66×	`div-exp`
63×	`unswap-sqr`
58×	`add-cbrt-cube`
53×	`div-inv`
44×	`associate-l`
30×	`cbrt-undiv`
24×	`prod-exp`
15×	`associate-/r/`
12×	`cbrt-unprod`
10×	`cbrt-div`
6×	`pow1` `rec-exp` `1-exp`
4×	`flip3--` `flip--` `add-log-exp`
3×	`pow1/3`
2×	`sqrt-div`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 728

Calls

4 calls:

366.0ms	(* (/ x (/ (fabs (cbrt (cbrt (- (* z z) (* t a))))) y)) (/ (/ 1 (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (cbrt (- (* z z) (* t a)))))))
4.0ms	(cbrt (- (* z z) (* t a)))
4.0ms	(cbrt (- (* z z) (* t a)))
4.0ms	(cbrt (- (* z z) (* t a)))

series699.0ms

Counts

4 → 12

Calls

4 calls:

443.0ms	(* (/ x (/ (fabs (cbrt (cbrt (- (* z z) (* t a))))) y)) (/ (/ 1 (/ (fabs (cbrt (- (* z z) (* t a)))) z)) (sqrt (cbrt (cbrt (- (* z z) (* t a)))))))
84.0ms	(cbrt (- (* z z) (* t a)))
84.0ms	(cbrt (- (* z z) (* t a)))
88.0ms	(cbrt (- (* z z) (* t a)))

simplify222.0ms

Algorithm

egg-herbie

Counts

740 → 740

Iterations

Useful iterations: 1 (72.0ms)

Iter	Nodes	Cost
0	4810	20569
1	5001	19948

prune3.1s

Filtered

740 candidates to 541 candidates (73.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	739	1	740
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	740	11	751

Merged error: 3.3b

Counts

751 → 11

regimes491.0ms

Accuracy

84.1% (3.2b remaining)

Error of 6.4b against oracle of 3.2b and baseline of 23.1b

bsearch61.0ms

Steps

Iters	Range		Point
6	4.9741377948850473e+95	5.057378677691522e+96	4.946545439463063e+96
5	-2.759058300683335e+143	-1.2415478284024965e+143	-1.4677331513848081e+143

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	10
1	31	10
2	31	10

end0.0ms

sample1.2s

Algorithm

intervals

Results

559.0ms	8887×	body	80	valid
185.0ms	3002×	body	80	nan

Details

sample37.0ms

simplify11.0ms

prune3.0ms

localize15.0ms

rewrite24.0ms

series201.0ms

simplify54.0ms

prune223.0ms

localize12.0ms

rewrite30.0ms

series226.0ms

simplify62.0ms

prune258.0ms

localize15.0ms

rewrite49.0ms

series437.0ms

simplify75.0ms

prune919.0ms

localize21.0ms

rewrite459.0ms

series699.0ms

simplify222.0ms

prune3.1s

regimes491.0ms

bsearch61.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling