Details

sample40.0ms

Algorithm

intervals

Results

15.0ms	284×	body	80	valid
4.0ms	75×	body	80	nan

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

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: 23.3b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* z z) (* t a))
5.6b	(* (* x y) z)
7.9b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.7b	(sqrt (- (* z z) (* t a)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

940×	`add-sqr-sqrt`
440×	`times-frac`
430×	`associate-l`
408×	`sqrt-prod`
360×	`*-un-lft-identity`
263×	`unswap-sqr`
250×	`difference-of-squares`
160×	`add-cube-cbrt`
132×	`associate-r`
100×	`distribute-lft-out--`
94×	`*-commutative`
50×	`swap-sqr`
22×	`associate-/l*`
20×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`sqrt-div`
3×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `flip--`
2×	`associate-/r/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `clear-num` `div-inv`

Counts

4 → 586

Calls

4 calls:

15.0ms	(- (* z z) (* t a))
7.0ms	(* (* x y) z)
35.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
30.0ms	(sqrt (- (* z z) (* t a)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* z z) (* t a))
25.0ms	(* (* x y) z)
89.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
69.0ms	(sqrt (- (* z z) (* t a)))

simplify109.0ms

Algorithm

egg-herbie

Counts

598 → 598

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1295	7635
1	5001	7555

prune931.0ms

Filtered

598 candidates to 262 candidates (56.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	590	8	598
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	590	9	599

Merged error: 3.5b

Counts

599 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
1.4b	(- (* z z) (* t a))
2.7b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.7b	(sqrt (- (* z z) (* t a)))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

1864×	`add-sqr-sqrt`
1608×	`times-frac`
951×	`*-un-lft-identity`
765×	`sqrt-prod`
583×	`add-cube-cbrt`
460×	`difference-of-squares`
387×	`unswap-sqr`
379×	`associate-l`
195×	`associate-r`
184×	`distribute-lft-out--`
157×	`*-commutative`
92×	`swap-sqr`
70×	`associate-/r*`
52×	`associate-/l*`
28×	`associate-/r/`
18×	`add-exp-log` `add-cbrt-cube`
15×	`div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`sqrt-div` `add-log-exp`
5×	`pow1`
4×	`flip3--` `flip--` `associate-/l/`
3×	`frac-2neg` `clear-num`
2×	`prod-exp` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 1042

Calls

4 calls:

19.0ms	(/ (sqrt (- (* z z) (* t a))) z)
15.0ms	(- (* z z) (* t a))
49.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
15.0ms	(sqrt (- (* z z) (* t a)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ (sqrt (- (* z z) (* t a))) z)
33.0ms	(- (* z z) (* t a))
82.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
66.0ms	(sqrt (- (* z z) (* t a)))

simplify191.0ms

Algorithm

egg-herbie

Counts

1054 → 1054

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2916	15462
1	5001	14940

prune1.3s

Filtered

1054 candidates to 422 candidates (60.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	1051	3	1054
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	1055	8	1063

Merged error: 3.5b

Counts

1063 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.9b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
1.4b	(- (* z z) (* t a))
1.5b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
23.7b	(sqrt (- (* z z) (* t a)))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

1073×	`add-sqr-sqrt`
869×	`times-frac`
584×	`*-un-lft-identity`
460×	`sqrt-prod`
359×	`add-cube-cbrt`
280×	`difference-of-squares`
224×	`associate-r`
200×	`unswap-sqr`
134×	`associate-/r*`
115×	`associate-l`
112×	`distribute-lft-out--`
70×	`associate-*r/`
57×	`*-commutative`
56×	`swap-sqr` `associate-/r/`
47×	`associate-/l*`
18×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
7×	`pow1`
6×	`cbrt-undiv` `sqrt-div` `div-exp` `add-log-exp`
5×	`clear-num`
4×	`flip3--` `frac-2neg` `flip--` `associate-/l/`
3×	`prod-exp` `cbrt-unprod`
2×	`un-div-inv`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down`

Counts

4 → 674

Calls

4 calls:

82.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
15.0ms	(- (* z z) (* t a))
31.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
15.0ms	(sqrt (- (* z z) (* t a)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
38.0ms	(- (* z z) (* t a))
55.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
78.0ms	(sqrt (- (* z z) (* t a)))

simplify102.0ms

Algorithm

egg-herbie

Counts

686 → 686

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1569	6984
1	5002	6557

prune1.1s

Filtered

686 candidates to 343 candidates (50.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	686	0	686
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	686	8	694

Merged error: 3.5b

Counts

694 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
1.4b	(- (* z z) (* t a))
2.7b	(/ (* x y) (* 1 (/ (sqrt (- (* z z) (* t a))) z)))
23.7b	(sqrt (- (* z z) (* t a)))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

2129×	`add-sqr-sqrt`
1828×	`times-frac`
1069×	`associate-r`
1059×	`*-un-lft-identity`
791×	`sqrt-prod`
651×	`add-cube-cbrt`
479×	`unswap-sqr`
460×	`associate-l` `difference-of-squares`
184×	`*-commutative` `distribute-lft-out--`
92×	`swap-sqr`
84×	`associate-/r*`
53×	`associate-/l*`
39×	`add-exp-log`
30×	`associate-/r/`
28×	`associate-*r/`
27×	`add-cbrt-cube`
15×	`div-exp` `div-inv`
13×	`prod-exp`
9×	`cbrt-undiv`
7×	`cbrt-unprod`
6×	`sqrt-div` `add-log-exp`
5×	`pow1`
4×	`flip3--` `1-exp` `clear-num` `flip--` `associate-/l/`
3×	`frac-2neg`
2×	`un-div-inv`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 1234

Calls

4 calls:

21.0ms	(/ (sqrt (- (* z z) (* t a))) z)
15.0ms	(- (* z z) (* t a))
70.0ms	(/ (* x y) (* 1 (/ (sqrt (- (* z z) (* t a))) z)))
15.0ms	(sqrt (- (* z z) (* t a)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ (sqrt (- (* z z) (* t a))) z)
38.0ms	(- (* z z) (* t a))
88.0ms	(/ (* x y) (* 1 (/ (sqrt (- (* z z) (* t a))) z)))
62.0ms	(sqrt (- (* z z) (* t a)))

simplify231.0ms

Algorithm

egg-herbie

Counts

1246 → 1246

Iterations

Useful iterations: 1 (58.0ms)

Iter	Nodes	Cost
0	4007	18529
1	5001	17936

prune1.6s

Filtered

1246 candidates to 455 candidates (63.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	1246	0	1246
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	1246	8	1254

Merged error: 3.5b

Counts

1254 → 8

regimes351.0ms

Accuracy

85.6% (2.7b remaining)

Error of 6.0b against oracle of 3.2b and baseline of 22.3b

bsearch73.0ms

Steps

Iters	Range		Point
7	5.980436183971059e+94	9.936034952497785e+95	9.681419240575677e+95
8	-7.68418680011678e+155	-7.681330329978954e+152	-1.774092619626311e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	10
1	32	10
2	32	10

end0.0ms

sample781.0ms

Algorithm

intervals

Results

330.0ms	8818×	body	80	valid
102.0ms	2894×	body	80	nan