Details

sample3.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 11.71875%

Guaranteed chance to sample good point: 24.612832%

Results

13.0ms	256×	body	80	valid
3.0ms	59×	body	80	nan
2.0ms	35×	body	80	invalid

simplify9.0ms

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: 24.2b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
5.9b	(* (* x y) z)
9.8b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.6b	(sqrt (- (* z z) (* t a)))

rewrite21.0ms

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))))
3.0ms	(sqrt (- (* z z) (* t a)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
6.0ms	(* (* x y) z)
29.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (44.0ms)

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

prune133.0ms

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: 2.3b

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))
2.4b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
25.6b	(sqrt (- (* z z) (* t a)))

rewrite28.0ms

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

series62.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ z (sqrt (- (* z z) (* t a))))
7.0ms	(- (* z z) (* t a))
32.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (50.0ms)

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

prune125.0ms

Filtered

81 candidates to 124 candidates (-53.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	124	9	133

Merged error: 2.3b

Counts

133 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* y (/ z (sqrt (- (* z z) (* t a)))))
0.6b	(- (* z z) (* t a))
2.1b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
25.6b	(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:

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

series68.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
7.0ms	(- (* z z) (* t a))
29.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify49.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	400	775
1	1756	676
2	5001	668

prune111.0ms

Filtered

68 candidates to 104 candidates (-52.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	105	8	113

Merged error: 2.3b

Counts

113 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
5.0b	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
25.6b	(sqrt (- (* z z) (* t a)))
25.6b	(sqrt (- (* z z) (* t a)))

rewrite44.0ms

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)))))
23.0ms	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
3.0ms	(sqrt (- (* z z) (* t a)))
3.0ms	(sqrt (- (* z z) (* t a)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (* 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))))))
14.0ms	(sqrt (- (* z z) (* t a)))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify83.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (65.0ms)

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

prune115.0ms

Filtered

100 candidates to 153 candidates (-53.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	153	8	161

Merged error: 2.3b

Counts

161 → 8

regimes863.0ms

Accuracy

79% (4.3b remaining)

Error of 7.5b against oracle of 3.2b and baseline of 23.5b

bsearch56.0ms

Steps

Iters	Range		Point
8	6.046224563230577e+64	4.280697951522181e+67	2.1280368556537537e+65
6	-3.2303978612255717e+47	-3.3889518445468483e+46	-2.8085321758333e+47

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

sample4.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 11.71875%

Guaranteed chance to sample good point: 24.612832%

Results

472.0ms	8000×	body	80	valid
76.0ms	1579×	body	80	nan
44.0ms	827×	body	80	invalid

Details

sample3.5s

simplify9.0ms

prune5.0ms

localize15.0ms

rewrite21.0ms

series54.0ms

simplify54.0ms

prune133.0ms

localize10.0ms

rewrite28.0ms

series62.0ms

simplify61.0ms

prune125.0ms

localize10.0ms

rewrite32.0ms

series68.0ms

simplify49.0ms

prune111.0ms

localize13.0ms

rewrite44.0ms

series91.0ms

simplify83.0ms

prune115.0ms

regimes863.0ms

bsearch56.0ms

simplify2.0ms

end0.0ms

sample4.6s

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