Details

sample32.0ms

Algorithm

intervals

Results

13.0ms	280×	body	80	valid
3.0ms	102×	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

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
5.6b	(* (* x y) z)
9.6b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.4b	(sqrt (- (* z z) (* t a)))

rewrite23.0ms

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)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* z z) (* t a))
23.0ms	(* (* x y) z)
82.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
62.0ms	(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	346	584
1	1863	515
2	5002	510

prune297.0ms

Filtered

88 candidates to 60 candidates (68.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	12	89

Merged error: 4.7b

Counts

89 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.6b	(- (* z z) (* t a))
2.3b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.4b	(sqrt (- (* z z) (* t a)))

rewrite35.0ms

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

series245.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ (sqrt (- (* z z) (* t a))) z)
36.0ms	(- (* z z) (* t a))
82.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
58.0ms	(sqrt (- (* z z) (* t a)))

simplify68.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	519	1327
1	2380	1230
2	5001	1214

prune305.0ms

Filtered

144 candidates to 98 candidates (68.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	140	4	144
Fresh	5	5	10
Picked	0	1	1
Done	0	1	1
Total	145	11	156

Merged error: 4.5b

Counts

156 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (- (* z z) (* t a))) (/ 1 z))
0.6b	(- (* z z) (* t a))
2.3b	(/ (* x y) (* (sqrt (- (* z z) (* t a))) (/ 1 z)))
23.4b	(sqrt (- (* z z) (* t a)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
30×	`add-cbrt-cube`
29×	`add-sqr-sqrt`
17×	`prod-exp`
16×	`*-un-lft-identity` `div-exp`
14×	`add-cube-cbrt` `times-frac`
13×	`associate-r`
10×	`sqrt-div`
9×	`cbrt-undiv` `sqrt-prod` `cbrt-unprod`
7×	`pow1`
6×	`flip3--` `associate-l` `associate-/r/` `flip--` `add-log-exp` `unswap-sqr`
4×	`frac-times` `associate-*l/`
3×	`rec-exp` `1-exp`
2×	`associate-*r/` `un-div-inv` `div-inv`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `associate-/l*`

Counts

4 → 108

Calls

4 calls:

11.0ms	(* (sqrt (- (* z z) (* t a))) (/ 1 z))
3.0ms	(- (* z z) (* t a))
11.0ms	(/ (* x y) (* (sqrt (- (* z z) (* t a))) (/ 1 z)))
4.0ms	(sqrt (- (* z z) (* t a)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (sqrt (- (* z z) (* t a))) (/ 1 z))
32.0ms	(- (* z z) (* t a))
84.0ms	(/ (* x y) (* (sqrt (- (* z z) (* t a))) (/ 1 z)))
61.0ms	(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	546	1010
1	2693	885
2	5002	865

prune255.0ms

Filtered

120 candidates to 77 candidates (64.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	120	11	131

Merged error: 4.5b

Counts

131 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.0b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
3.0b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
23.4b	(sqrt (- (* z z) (* t a)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

263×	`times-frac`
157×	`add-sqr-sqrt`
143×	`add-cube-cbrt` `*-un-lft-identity`
71×	`associate-r`
67×	`sqrt-prod`
22×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`unswap-sqr`
3×	`associate-l` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`flip3--` `sqrt-div` `associate-/r/` `flip--`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 227

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
9.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
26.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
4.0ms	(sqrt (- (* z z) (* t a)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* z z) (* t a))
53.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
84.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
64.0ms	(sqrt (- (* z z) (* t a)))

simplify100.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	817	2502
1	4005	2347
2	5002	2347

prune476.0ms

Filtered

239 candidates to 160 candidates (66.9%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	239	11	250

Merged error: 4.5b

Counts

250 → 11

regimes442.0ms

Accuracy

85.3% (3.0b remaining)

Error of 6.4b against oracle of 3.4b and baseline of 23.5b

bsearch129.0ms

Steps

Iters	Range	Point
7	4.904842434366931e+136	2.583983515518581e+138	1.998388355114222e+137
8	-5.198330287526027e-251	-6.309453960374173e-254	-8.504918652399411e-253
9	-3.291745184388977e+160	-2.9340887831229106e+153	-6.761458302909995e+153

Iters

Range

Point

4.904842434366931e+136

2.583983515518581e+138

1.998388355114222e+137

-5.198330287526027e-251

-6.309453960374173e-254

-8.504918652399411e-253

-3.291745184388977e+160

-2.9340887831229106e+153

-6.761458302909995e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	17
1	36	17
2	36	17

end0.0ms

sample805.0ms

Algorithm

intervals

Results

329.0ms	8850×	body	80	valid
113.0ms	2933×	body	80	nan