Details

sample16.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 11.71875%

Guaranteed chance to sample good point: 34.706858%

Results

13.0ms	256×	body	80	valid
3.0ms	59×	body	80	nan
2.0ms	34×	body	80	invalid

simplify10.0ms

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

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: 24.6b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
6.0b	(* (* x y) z)
9.4b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
27.3b	(sqrt (- (* z z) (* t a)))

rewrite22.0ms

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

series57.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
6.0ms	(* (* x y) z)
32.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (45.0ms)

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

prune134.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	9	89

Merged error: 3.3b

Counts

89 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.6b	(- (* z z) (* t a))
2.5b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
27.3b	(sqrt (- (* z z) (* t a)))

rewrite31.0ms

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))))
3.0ms	(- (* z z) (* t a))
12.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
5.0ms	(sqrt (- (* z z) (* t a)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ z (sqrt (- (* z z) (* t a))))
7.0ms	(- (* z z) (* t a))
29.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify64.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (50.0ms)

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

prune122.0ms

Filtered

81 candidates to 124 candidates (-53.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	125	8	133

Merged error: 3.2b

Counts

133 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
0.8b	(* y (/ z (sqrt (- (* z z) (* t a)))))
1.7b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
27.3b	(sqrt (- (* z z) (* t a)))

rewrite32.0ms

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 → 92

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
11.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
10.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
18.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
32.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	400	774
1	1768	676
2	5001	668

prune109.0ms

Filtered

68 candidates to 104 candidates (-52.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	104	8	112

Merged error: 3.2b

Counts

112 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
5.2b	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
27.3b	(sqrt (- (* z z) (* t a)))
27.3b	(sqrt (- (* z z) (* t a)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

63×	`sqrt-prod`
48×	`add-sqr-sqrt` `times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
33×	`associate-r`
30×	`add-exp-log` `add-cbrt-cube`
16×	`sqrt-div`
15×	`associate-l`
9×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r*` `cbrt-unprod`
8×	`pow1`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l`

Counts

4 → 141

Calls

4 calls:

8.0ms	(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
25.0ms	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
3.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series93.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
29.0ms	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
12.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify86.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	661	1959
1	3424	1748
2	5002	1624

prune119.0ms

Filtered

100 candidates to 153 candidates (-53.0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	153	8	161

Merged error: 3.2b

Counts

161 → 8

regimes857.0ms

Accuracy

85.5% (2.8b remaining)

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

bsearch107.0ms

Steps

Iters	Range		Point
8	5.062167009111041e+111	3.321408613895475e+115	3.214897243408058e+114
7	-3.215135282449047e+155	-1.300856616977498e+154	-1.3127934339355977e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	10
1	33	10
2	33	10

end0.0ms

sample17.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 11.71875%

Guaranteed chance to sample good point: 34.706858%

Results

430.0ms	8000×	body	80	valid
75.0ms	1583×	body	80	nan
47.0ms	835×	body	80	invalid

Details

sample16.4s

simplify10.0ms

prune5.0ms

localize10.0ms

rewrite22.0ms

series57.0ms

simplify53.0ms

prune134.0ms

localize10.0ms

rewrite31.0ms

series59.0ms

simplify64.0ms

prune122.0ms

localize10.0ms

rewrite32.0ms

series70.0ms

simplify53.0ms

prune109.0ms

localize13.0ms

rewrite48.0ms

series93.0ms

simplify86.0ms

prune119.0ms

regimes857.0ms

bsearch107.0ms

simplify2.0ms

end0.0ms

sample17.9s

Profiling