Details

analyze1.1s

Algorithm: search

sample35.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
3.0ms	72×	body	80	nan
2.0ms	33×	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

prune4.0ms

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: 24.4b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
6.4b	(* (* x y) z)
7.3b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.3b	(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))
5.0ms	(* (* 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))
5.0ms	(* (* x y) z)
29.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
16.0ms	(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (44.0ms)

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

prune131.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	78	10	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	10	89

Merged error: 2.9b

Counts

89 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt (- (* z z) (* t a))) z)
0.6b	(- (* z z) (* t a))
3.7b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.3b	(sqrt (- (* z z) (* t a)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
47×	`add-sqr-sqrt`
46×	`add-cube-cbrt` `*-un-lft-identity`
33×	`sqrt-prod`
25×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
3×	`flip3--` `flip--`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/`

Counts

4 → 132

Calls

4 calls:

6.0ms	(/ (sqrt (- (* z z) (* t a))) z)
3.0ms	(- (* z z) (* t a))
9.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
5.0ms	(sqrt (- (* z z) (* t a)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ (sqrt (- (* z z) (* t a))) z)
7.0ms	(- (* z z) (* t a))
29.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	512	1325
1	2358	1230
2	5002	1214

prune152.0ms

Filtered

99 candidates to 144 candidates (-45.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	141	3	144
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	144	10	154

Merged error: 2.9b

Counts

154 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
5.7b	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
24.3b	(sqrt (- (* z z) (* t a)))
24.3b	(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)))))
27.0ms	(* (/ (* 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:

35.0ms	(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
33.0ms	(* (/ (* 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)))

simplify88.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (71.0ms)

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

prune153.0ms

Filtered

101 candidates to 153 candidates (-51.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	153	10	163

Merged error: 2.9b

Counts

163 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
4.2b	(* x (* y z))
7.3b	(/ (* x (* y z)) (sqrt (- (* z z) (* t a))))
24.3b	(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-l` `pow-prod-down` `flip--`
2×	`associate-/r/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r` `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)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
5.0ms	(* x (* y z))
31.0ms	(/ (* x (* y z)) (sqrt (- (* z z) (* t a))))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify41.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	337	588
1	1532	515
2	5001	509

prune67.0ms

Filtered

58 candidates to 88 candidates (-51.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	88	10	98

Merged error: 2.9b

Counts

98 → 10

regimes880.0ms

Accuracy

81.2% (3.7b remaining)

Error of 6.9b against oracle of 3.2b and baseline of 22.8b

bsearch3.5s

Steps

Iters	Range	Point
9	2.7597403929966105e+133	5.500726182052972e+138	1.004006194098766e+137
8	4.8830895846909604e-265	3.5193801515589914e-261	3.839974583069632e-264
7	-2.3029499104498693e+64	-2.0031060213774672e+62	-1.0926732846231359e+64

Iters

Range

Point

2.7597403929966105e+133

5.500726182052972e+138

1.004006194098766e+137

4.8830895846909604e-265

3.5193801515589914e-261

3.839974583069632e-264

-2.3029499104498693e+64

-2.0031060213774672e+62

-1.0926732846231359e+64

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	17
1	38	17
2	38	17

end0.0ms

analyze1.1s

Algorithm: search

sample944.0ms

Algorithm

intervals

Results

437.0ms	8000×	body	80	valid
102.0ms	2193×	body	80	nan
51.0ms	921×	body	80	invalid

Details

analyze1.1s

sample35.0ms

simplify9.0ms

prune4.0ms

localize12.0ms

rewrite22.0ms

series57.0ms

simplify52.0ms

prune131.0ms

localize10.0ms

rewrite28.0ms

series64.0ms

simplify65.0ms

prune152.0ms

localize13.0ms

rewrite48.0ms

series93.0ms

simplify88.0ms

prune153.0ms

localize10.0ms

rewrite22.0ms

series55.0ms

simplify41.0ms

prune67.0ms

regimes880.0ms

bsearch3.5s

simplify2.0ms

end0.0ms

analyze1.1s

sample944.0ms

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